ift6266: writeup/techreport.tex annotate

annotate writeup/techreport.tex @ 479:6593e67381a3

Added transformation figure

author	Xavier Glorot <glorotxa@iro.umontreal.ca>
date	Sun, 30 May 2010 18:54:36 -0400
parents	534d4ecf1bd1
children	8aad1c6ec39a

rev	line source
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	1 \documentclass[12pt,letterpaper]{article}
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	2 \usepackage[utf8]{inputenc}
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	3 \usepackage{graphicx}
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	4 \usepackage{times}
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	5 \usepackage{mlapa}
452 b0622f78cfec Add a small paragraph mentionning the distribution differences and a figure illustrating the difference. Arnaud Bergeron <abergeron@gmail.com> parents: 444 diff changeset	6 \usepackage{subfigure}
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	7
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	8 \begin{document}
462 f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	9 \title{Generating and Exploiting Perturbed and Multi-Task Handwritten Training Data for Deep Architectures}
381 0a91fc69ff90 authors Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 379 diff changeset	10 \author{The IFT6266 Gang}
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	11 \date{April 2010, Technical Report, Dept. IRO, U. Montreal}
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	12
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	13 \maketitle
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	14
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	15 \begin{abstract}
392 5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	16 Recent theoretical and empirical work in statistical machine learning has
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	17 demonstrated the importance of learning algorithms for deep
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	18 architectures, i.e., function classes obtained by composing multiple
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	19 non-linear transformations. In the area of handwriting recognition,
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	20 deep learning algorithms
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	21 had been evaluated on rather small datasets with a few tens of thousands
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	22 of examples. Here we propose a powerful generator of variations
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	23 of examples for character images based on a pipeline of stochastic
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	24 transformations that include not only the usual affine transformations
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	25 but also the addition of slant, local elastic deformations, changes
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	26 in thickness, background images, color, contrast, occlusion, and
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	27 various types of pixel and spatially correlated noise.
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	28 We evaluate a deep learning algorithm (Stacked Denoising Autoencoders)
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	29 on the task of learning to classify digits and letters transformed
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	30 with this pipeline, using the hundreds of millions of generated examples
462 f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	31 and testing on the full 62-class NIST test set.
392 5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	32 We find that the SDA outperforms its
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	33 shallow counterpart, an ordinary Multi-Layer Perceptron,
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	34 and that it is better able to take advantage of the additional
438 a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	35 generated data, as well as better able to take advantage of
462 f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	36 the multi-task setting, i.e.,
438 a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	37 training from more classes than those of interest in the end.
a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	38 In fact, we find that the SDA reaches human performance as
462 f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	39 estimated by the Amazon Mechanical Turk on the 62-class NIST test characters.
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	40 \end{abstract}
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	41
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	42 \section{Introduction}
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	43
392 5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	44 Deep Learning has emerged as a promising new area of research in
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	45 statistical machine learning (see~\emcite{Bengio-2009} for a review).
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	46 Learning algorithms for deep architectures are centered on the learning
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	47 of useful representations of data, which are better suited to the task at hand.
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	48 This is in great part inspired by observations of the mammalian visual cortex,
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	49 which consists of a chain of processing elements, each of which is associated with a
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	50 different representation. In fact,
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	51 it was found recently that the features learnt in deep architectures resemble
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	52 those observed in the first two of these stages (in areas V1 and V2
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	53 of visual cortex)~\cite{HonglakL2008}.
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	54 Processing images typically involves transforming the raw pixel data into
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	55 new {\bf representations} that can be used for analysis or classification.
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	56 For example, a principal component analysis representation linearly projects
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	57 the input image into a lower-dimensional feature space.
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	58 Why learn a representation? Current practice in the computer vision
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	59 literature converts the raw pixels into a hand-crafted representation
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	60 (e.g.\ SIFT features~\cite{Lowe04}), but deep learning algorithms
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	61 tend to discover similar features in their first few
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	62 levels~\cite{HonglakL2008,ranzato-08,Koray-08,VincentPLarochelleH2008-very-small}.
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	63 Learning increases the
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	64 ease and practicality of developing representations that are at once
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	65 tailored to specific tasks, yet are able to borrow statistical strength
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	66 from other related tasks (e.g., modeling different kinds of objects). Finally, learning the
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	67 feature representation can lead to higher-level (more abstract, more
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	68 general) features that are more robust to unanticipated sources of
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	69 variance extant in real data.
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	70
462 f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	71 Whereas a deep architecture can in principle be more powerful than a
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	72 shallow one in terms of representation, depth appears to render the
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	73 training problem more difficult in terms of optimization and local minima.
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	74 It is also only recently that successful algorithms were proposed to
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	75 overcome some of these difficulties. All are based on unsupervised
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	76 learning, often in an greedy layer-wise ``unsupervised pre-training''
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	77 stage~\cite{Bengio-2009}. One of these layer initialization techniques,
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	78 applied here, is the Denoising
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	79 Auto-Encoder~(DEA)~\cite{VincentPLarochelleH2008-very-small}, which
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	80 performed similarly or better than previously proposed Restricted Boltzmann
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	81 Machines in terms of unsupervised extraction of a hierarchy of features
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	82 useful for classification. The principle is that each layer starting from
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	83 the bottom is trained to encode their input (the output of the previous
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	84 layer) and try to reconstruct it from a corrupted version of it. After this
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	85 unsupervised initialization, the stack of denoising auto-encoders can be
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	86 converted into a deep supervised feedforward neural network and trained by
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	87 stochastic gradient descent.
420 a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	88
407 fe2e2964e7a3 description des transformations en cours ajout d un fichier special.bib pour des references specifiques Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 393 diff changeset	89
462 f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	90 \section{Perturbation and Transformation of Character Images}
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	91
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	92 This section describes the different transformations we used to generate data, in their order.
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	93 The code for these transformations (mostly python) is available at
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	94 {\tt http://anonymous.url.net}. All the modules in the pipeline share
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	95 a global control parameter ($0 \le complexity \le 1$) that allows one to modulate the
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	96 amount of deformation or noise introduced.
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	97
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	98 We can differentiate two important parts in the pipeline. The first one,
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	99 from slant to pinch, performs transformations of the character. The second
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	100 part, from blur to contrast, adds noise to the image.
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	101
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	102 \subsection{Slant}
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	103
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	104 In order to mimic a slant effect, we simply shift each row of the image
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	105 proportionnaly to its height: $shift = round(slant \times height)$. We
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	106 round the shift in order to have a discret displacement. We do not use a
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	107 filter to smooth the result in order to save computing time and also
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	108 because latter transformations have similar effects.
420 a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	109
462 f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	110 The $slant$ coefficient can be negative or positive with equal probability
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	111 and its value is randomly sampled according to the complexity level. In
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	112 our case we take uniformly a number in the range $[0,complexity]$, so the
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	113 maximum displacement for the lowest or highest pixel line is of
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	114 $round(complexity \times 32)$.
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	115
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	116
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	117 \subsection{Thickness}
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	118
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	119 To change the thickness of the characters we used morpholigical operators:
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	120 dilation and erosion~\cite{Haralick87,Serra82}.
420 a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	121
462 f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	122 The basic idea of such transform is, for each pixel, to multiply in the
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	123 element-wise manner its neighbourhood with a matrix called the structuring
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	124 element. Then for dilation we remplace the pixel value by the maximum of
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	125 the result, or the minimum for erosion. This will dilate or erode objects
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	126 in the image and the strength of the transform only depends on the
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	127 structuring element.
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	128
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	129 We used ten different structural elements with increasing dimensions (the
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	130 biggest is $5\times5$). for each image, we radomly sample the operator
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	131 type (dilation or erosion) with equal probability and one structural
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	132 element from a subset of the $n$ smallest structuring elements where $n$ is
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	133 $round(10 \times complexity)$ for dilation and $round(6 \times complexity)$
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	134 for erosion. A neutral element is always present in the set, if it is
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	135 chosen the transformation is not applied. Erosion allows only the six
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	136 smallest structural elements because when the character is too thin it may
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	137 erase it completly.
407 fe2e2964e7a3 description des transformations en cours ajout d un fichier special.bib pour des references specifiques Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 393 diff changeset	138
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	139 \subsection{Affine Transformations}
462 f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	140
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	141 We generate an affine transform matrix according to the complexity level,
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	142 then we apply it directly to the image. The matrix is of size $2 \times
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	143 3$, so we can represent it by six parameters $(a,b,c,d,e,f)$. Formally,
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	144 for each pixel $(x,y)$ of the output image, we give the value of the pixel
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	145 nearest to : $(ax+by+c,dx+ey+f)$, in the input image. This allows to
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	146 produce scaling, translation, rotation and shearing variances.
431 bfa349f567e8 correction in the transformation descripition Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 428 diff changeset	147
462 f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	148 The sampling of the parameters $(a,b,c,d,e,f)$ have been tuned by hand to
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	149 forbid important rotations (not to confuse classes) but to give good
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	150 variability of the transformation. For each image we sample uniformly the
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	151 parameters in the following ranges: $a$ and $d$ in $[1-3 \times
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	152 complexity,1+3 \times complexity]$, $b$ and $e$ in $[-3 \times complexity,3
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	153 \times complexity]$ and $c$ and $f$ in $[-4 \times complexity, 4 \times
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	154 complexity]$.
431 bfa349f567e8 correction in the transformation descripition Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 428 diff changeset	155
407 fe2e2964e7a3 description des transformations en cours ajout d un fichier special.bib pour des references specifiques Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 393 diff changeset	156
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	157 \subsection{Local Elastic Deformations}
462 f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	158
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	159 This filter induces a "wiggly" effect in the image. The description here
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	160 will be brief, as the algorithm follows precisely what is described in
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	161 \cite{SimardSP03}.
415 1e9788ce1680 Added the parts concerning the transformations I'd announced I'd do: Local elastic deformations; occlusions; gimp transformations; salt and pepper noise; background images fsavard parents: 411 diff changeset	162
462 f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	163 The general idea is to generate two "displacements" fields, for horizontal
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	164 and vertical displacements of pixels. Each of these fields has the same
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	165 size as the original image.
415 1e9788ce1680 Added the parts concerning the transformations I'd announced I'd do: Local elastic deformations; occlusions; gimp transformations; salt and pepper noise; background images fsavard parents: 411 diff changeset	166
462 f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	167 When generating the transformed image, we'll loop over the x and y
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	168 positions in the fields and select, as a value, the value of the pixel in
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	169 the original image at the (relative) position given by the displacement
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	170 fields for this x and y. If the position we'd retrieve is outside the
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	171 borders of the image, we use a 0 value instead.
415 1e9788ce1680 Added the parts concerning the transformations I'd announced I'd do: Local elastic deformations; occlusions; gimp transformations; salt and pepper noise; background images fsavard parents: 411 diff changeset	172
462 f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	173 To generate a pixel in either field, first a value between -1 and 1 is
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	174 chosen from a uniform distribution. Then all the pixels, in both fields, is
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	175 multiplied by a constant $\alpha$ which controls the intensity of the
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	176 displacements (bigger $\alpha$ translates into larger wiggles).
415 1e9788ce1680 Added the parts concerning the transformations I'd announced I'd do: Local elastic deformations; occlusions; gimp transformations; salt and pepper noise; background images fsavard parents: 411 diff changeset	177
462 f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	178 As a final step, each field is convoluted with a Gaussian 2D kernel of
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	179 standard deviation $\sigma$. Visually, this results in a "blur"
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	180 filter. This has the effect of making values next to each other in the
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	181 displacement fields similar. In effect, this makes the wiggles more
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	182 coherent, less noisy.
415 1e9788ce1680 Added the parts concerning the transformations I'd announced I'd do: Local elastic deformations; occlusions; gimp transformations; salt and pepper noise; background images fsavard parents: 411 diff changeset	183
462 f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	184 As displacement fields were long to compute, 50 pairs of fields were
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	185 generated per complexity in increments of 0.1 (50 pairs for 0.1, 50 pairs
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	186 for 0.2, etc.), and afterwards, given a complexity, we selected randomly
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	187 among the 50 corresponding pairs.
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	188
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	189 $\sigma$ and $\alpha$ were linked to complexity through the formulas
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	190 $\alpha = \sqrt[3]{complexity} \times 10.0$ and $\sigma = 10 - 7 \times
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	191 \sqrt[3]{complexity}$.
415 1e9788ce1680 Added the parts concerning the transformations I'd announced I'd do: Local elastic deformations; occlusions; gimp transformations; salt and pepper noise; background images fsavard parents: 411 diff changeset	192
1e9788ce1680 Added the parts concerning the transformations I'd announced I'd do: Local elastic deformations; occlusions; gimp transformations; salt and pepper noise; background images fsavard parents: 411 diff changeset	193
1e9788ce1680 Added the parts concerning the transformations I'd announced I'd do: Local elastic deformations; occlusions; gimp transformations; salt and pepper noise; background images fsavard parents: 411 diff changeset	194 \subsection{Pinch}
1e9788ce1680 Added the parts concerning the transformations I'd announced I'd do: Local elastic deformations; occlusions; gimp transformations; salt and pepper noise; background images fsavard parents: 411 diff changeset	195
462 f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	196 This is another GIMP filter we used. The filter is in fact named "Whirl and
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	197 pinch", but we don't use the "whirl" part (whirl is set to 0). As described
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	198 in GIMP, a pinch is "similar to projecting the image onto an elastic
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	199 surface and pressing or pulling on the center of the surface".
416 5f9d04dda707 Correction d'une erreur pour pinch et ajout d'une ref bibliographique fsavard parents: 415 diff changeset	200
462 f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	201 Mathematically, for a square input image, think of drawing a circle of
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	202 radius $r$ around a center point $C$. Any point (pixel) $P$ belonging to
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	203 that disk (region inside circle) will have its value recalculated by taking
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	204 the value of another "source" pixel in the original image. The position of
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	205 that source pixel is found on the line thats goes through $C$ and $P$, but
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	206 at some other distance $d_2$. Define $d_1$ to be the distance between $P$
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	207 and $C$. $d_2$ is given by $d_2 = sin(\frac{\pi{}d_1}{2r})^{-pinch} \times
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	208 d_1$, where $pinch$ is a parameter to the filter.
415 1e9788ce1680 Added the parts concerning the transformations I'd announced I'd do: Local elastic deformations; occlusions; gimp transformations; salt and pepper noise; background images fsavard parents: 411 diff changeset	209
462 f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	210 If the region considered is not square then, before computing $d_2$, the
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	211 smallest dimension (x or y) is stretched such that we may consider the
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	212 region as if it was square. Then, after $d_2$ has been computed and
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	213 corresponding components $d_2\_x$ and $d_2\_y$ have been found, the
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	214 component corresponding to the stretched dimension is compressed back by an
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	215 inverse ratio.
415 1e9788ce1680 Added the parts concerning the transformations I'd announced I'd do: Local elastic deformations; occlusions; gimp transformations; salt and pepper noise; background images fsavard parents: 411 diff changeset	216
462 f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	217 The actual value is given by bilinear interpolation considering the pixels
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	218 around the (non-integer) source position thus found.
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	219
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	220 The value for $pinch$ in our case was given by sampling from an uniform
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	221 distribution over the range $[-complexity, 0.7 \times complexity]$.
415 1e9788ce1680 Added the parts concerning the transformations I'd announced I'd do: Local elastic deformations; occlusions; gimp transformations; salt and pepper noise; background images fsavard parents: 411 diff changeset	222
426 a7fab59de174 change order of transformations Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 425 diff changeset	223 \subsection{Motion Blur}
415 1e9788ce1680 Added the parts concerning the transformations I'd announced I'd do: Local elastic deformations; occlusions; gimp transformations; salt and pepper noise; background images fsavard parents: 411 diff changeset	224
462 f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	225 This is a GIMP filter we applied, a "linear motion blur" in GIMP
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	226 terminology. The description will be brief as it is a well-known filter.
420 a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	227
462 f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	228 This algorithm has two input parameters, $length$ and $angle$. The value of
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	229 a pixel in the final image is the mean value of the $length$ first pixels
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	230 found by moving in the $angle$ direction. An approximation of this idea is
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	231 used, as we won't fall onto precise pixels by following that
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	232 direction. This is done using the Bresenham line algorithm.
420 a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	233
462 f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	234 The angle, in our case, is chosen from a uniform distribution over
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	235 $[0,360]$ degrees. The length, though, depends on the complexity; it's
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	236 sampled from a Gaussian distribution of mean 0 and standard deviation
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	237 $\sigma = 3 \times complexity$.
420 a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	238
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	239 \subsection{Occlusion}
415 1e9788ce1680 Added the parts concerning the transformations I'd announced I'd do: Local elastic deformations; occlusions; gimp transformations; salt and pepper noise; background images fsavard parents: 411 diff changeset	240
462 f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	241 This filter selects random parts of other (hereafter "occlusive") letter
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	242 images and places them over the original letter (hereafter "occluded")
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	243 image. To be more precise, having selected a subregion of the occlusive
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	244 image and a desination position in the occluded image, to determine the
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	245 final value for a given overlapping pixel, it selects whichever pixel is
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	246 the lightest. As a reminder, the background value is 0, black, so the value
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	247 nearest to 1 is selected.
415 1e9788ce1680 Added the parts concerning the transformations I'd announced I'd do: Local elastic deformations; occlusions; gimp transformations; salt and pepper noise; background images fsavard parents: 411 diff changeset	248
462 f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	249 To select a subpart of the occlusive image, four numbers are generated. For
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	250 compability with the code, we'll call them "haut", "bas", "gauche" and
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	251 "droite" (respectively meaning top, bottom, left and right). Each of these
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	252 numbers is selected according to a Gaussian distribution of mean $8 \times
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	253 complexity$ and standard deviation $2$. This means the largest the
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	254 complexity is, the biggest the occlusion will be. The absolute value is
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	255 taken, as the numbers must be positive, and the maximum value is capped at
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	256 15.
415 1e9788ce1680 Added the parts concerning the transformations I'd announced I'd do: Local elastic deformations; occlusions; gimp transformations; salt and pepper noise; background images fsavard parents: 411 diff changeset	257
462 f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	258 These four sizes collectively define a window centered on the middle pixel
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	259 of the occlusive image. This is the part that will be extracted as the
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	260 occlusion.
415 1e9788ce1680 Added the parts concerning the transformations I'd announced I'd do: Local elastic deformations; occlusions; gimp transformations; salt and pepper noise; background images fsavard parents: 411 diff changeset	261
462 f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	262 The next step is to select a destination position in the occluded
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	263 image. Vertical and horizontal displacements $y\_arrivee$ and $x\_arrivee$
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	264 are selected according to Gaussian distributions of mean 0 and of standard
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	265 deviations of, respectively, 3 and 2. Then an horizontal placement mode,
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	266 $place$, is selected to be of three values meaning
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	267 left, middle or right.
415 1e9788ce1680 Added the parts concerning the transformations I'd announced I'd do: Local elastic deformations; occlusions; gimp transformations; salt and pepper noise; background images fsavard parents: 411 diff changeset	268
462 f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	269 If $place$ is "middle", the occlusion will be horizontally centered
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	270 around the horizontal middle of the occluded image, then shifted according
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	271 to $x\_arrivee$. If $place$ is "left", it will be placed on the left of
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	272 the occluded image, then displaced right according to $x\_arrivee$. The
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	273 contrary happens if $place$ is $right$.
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	274
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	275 In both the horizontal and vertical positionning, the maximum position in
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	276 either direction is such that the selected occlusion won't go beyond the
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	277 borders of the occluded image.
415 1e9788ce1680 Added the parts concerning the transformations I'd announced I'd do: Local elastic deformations; occlusions; gimp transformations; salt and pepper noise; background images fsavard parents: 411 diff changeset	278
416 5f9d04dda707 Correction d'une erreur pour pinch et ajout d'une ref bibliographique fsavard parents: 415 diff changeset	279 This filter has a probability of not being applied, at all, of 60\%.
415 1e9788ce1680 Added the parts concerning the transformations I'd announced I'd do: Local elastic deformations; occlusions; gimp transformations; salt and pepper noise; background images fsavard parents: 411 diff changeset	280
426 a7fab59de174 change order of transformations Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 425 diff changeset	281
462 f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	282 \subsection{Pixel Permutation}
442 d5b2b6397a5a added permut pixel Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 431 diff changeset	283
462 f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	284 This filter permuts neighbouring pixels. It selects first
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	285 $\frac{complexity}{3}$ pixels randomly in the image. Each of them are then
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	286 sequentially exchanged to one other pixel in its $V4$ neighbourhood. Number
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	287 of exchanges to the left, right, top, bottom are equal or does not differ
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	288 from more than 1 if the number of selected pixels is not a multiple of 4.
442 d5b2b6397a5a added permut pixel Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 431 diff changeset	289
d5b2b6397a5a added permut pixel Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 431 diff changeset	290 It has has a probability of not being applied, at all, of 80\%.
d5b2b6397a5a added permut pixel Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 431 diff changeset	291
d5b2b6397a5a added permut pixel Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 431 diff changeset	292
462 f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	293 \subsection{Gaussian Noise}
426 a7fab59de174 change order of transformations Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 425 diff changeset	294
462 f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	295 This filter simply adds, to each pixel of the image independently, a
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	296 Gaussian noise of mean $0$ and standard deviation $\frac{complexity}{10}$.
426 a7fab59de174 change order of transformations Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 425 diff changeset	297
a7fab59de174 change order of transformations Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 425 diff changeset	298 It has has a probability of not being applied, at all, of 70\%.
a7fab59de174 change order of transformations Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 425 diff changeset	299
a7fab59de174 change order of transformations Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 425 diff changeset	300
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	301 \subsection{Background Images}
415 1e9788ce1680 Added the parts concerning the transformations I'd announced I'd do: Local elastic deformations; occlusions; gimp transformations; salt and pepper noise; background images fsavard parents: 411 diff changeset	302
462 f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	303 Following~\cite{Larochelle-jmlr-2009}, this transformation adds a random
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	304 background behind the letter. The background is chosen by first selecting,
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	305 at random, an image from a set of images. Then we choose a 32x32 subregion
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	306 of that image as the background image (by sampling x and y positions
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	307 uniformly while making sure not to cross image borders).
415 1e9788ce1680 Added the parts concerning the transformations I'd announced I'd do: Local elastic deformations; occlusions; gimp transformations; salt and pepper noise; background images fsavard parents: 411 diff changeset	308
462 f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	309 To combine the original letter image and the background image, contrast
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	310 adjustments are made. We first get the maximal values (i.e. maximal
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	311 intensity) for both the original image and the background image, $maximage$
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	312 and $maxbg$. We also have a parameter, $contrast$, given by sampling from a
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	313 uniform distribution over $[complexity, 1]$.
415 1e9788ce1680 Added the parts concerning the transformations I'd announced I'd do: Local elastic deformations; occlusions; gimp transformations; salt and pepper noise; background images fsavard parents: 411 diff changeset	314
462 f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	315 Once we have all these numbers, we first adjust the values for the
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	316 background image. Each pixel value is multiplied by $\frac{max(maximage -
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	317 contrast, 0)}{maxbg}$. Therefore the higher the contrast, the darkest the
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	318 background will be.
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	319
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	320 The final image is found by taking the brightest (i.e. value nearest to 1)
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	321 pixel from either the background image or the corresponding pixel in the
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	322 original image.
415 1e9788ce1680 Added the parts concerning the transformations I'd announced I'd do: Local elastic deformations; occlusions; gimp transformations; salt and pepper noise; background images fsavard parents: 411 diff changeset	323
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	324 \subsection{Salt and Pepper Noise}
415 1e9788ce1680 Added the parts concerning the transformations I'd announced I'd do: Local elastic deformations; occlusions; gimp transformations; salt and pepper noise; background images fsavard parents: 411 diff changeset	325
462 f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	326 This filter adds noise to the image by randomly selecting a certain number
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	327 of them and, for those selected pixels, assign a random value according to
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	328 a uniform distribution over the $[0,1]$ ranges. This last distribution does
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	329 not change according to complexity. Instead, the number of selected pixels
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	330 does: the proportion of changed pixels corresponds to $complexity / 5$,
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	331 which means, as a maximum, 20\% of the pixels will be randomized. On the
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	332 lowest extreme, no pixel is changed.
415 1e9788ce1680 Added the parts concerning the transformations I'd announced I'd do: Local elastic deformations; occlusions; gimp transformations; salt and pepper noise; background images fsavard parents: 411 diff changeset	333
420 a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	334 This filter also has a probability of not being applied, at all, of 75\%.
415 1e9788ce1680 Added the parts concerning the transformations I'd announced I'd do: Local elastic deformations; occlusions; gimp transformations; salt and pepper noise; background images fsavard parents: 411 diff changeset	335
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	336 \subsection{Spatially Gaussian Noise}
426 a7fab59de174 change order of transformations Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 425 diff changeset	337
462 f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	338 The aim of this transformation is to filter, with a gaussian kernel,
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	339 different regions of the image. In order to save computing time we decided
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	340 to convolve the whole image only once with a symmetric gaussian kernel of
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	341 size and variance choosen uniformly in the ranges: $[12,12 + 20 \times
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	342 complexity]$ and $[2,2 + 6 \times complexity]$. The result is normalized
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	343 between $0$ and $1$. We also create a symmetric averaging window, of the
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	344 kernel size, with maximum value at the center. For each image we sample
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	345 uniformly from $3$ to $3 + 10 \times complexity$ pixels that will be
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	346 averaging centers between the original image and the filtered one. We
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	347 initialize to zero a mask matrix of the image size. For each selected pixel
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	348 we add to the mask the averaging window centered to it. The final image is
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	349 computed from the following element-wise operation: $\frac{image + filtered
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	350 image \times mask}{mask+1}$.
420 a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	351
a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	352 This filter has a probability of not being applied, at all, of 75\%.
a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	353
462 f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	354 \subsection{Scratches}
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	355
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	356 The scratches module places line-like white patches on the image. The
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	357 lines are in fact heavily transformed images of the digit "1" (one), chosen
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	358 at random among five thousands such start images of this digit.
428 9fcd0215b8d5 Added text for ratures filter fsavard parents: 427 diff changeset	359
462 f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	360 Once the image is selected, the transformation begins by finding the first
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	361 $top$, $bottom$, $right$ and $left$ non-zero pixels in the image. It is
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	362 then cropped to the region thus delimited, then this cropped version is
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	363 expanded to $32\times32$ again. It is then rotated by a random angle having a
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	364 Gaussian distribution of mean 90 and standard deviation $100 \times
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	365 complexity$ (in degrees). The rotation is done with bicubic interpolation.
428 9fcd0215b8d5 Added text for ratures filter fsavard parents: 427 diff changeset	366
462 f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	367 The rotated image is then resized to $50\times50$, with anti-aliasing. In
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	368 that image, we crop the image again by selecting a region delimited
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	369 horizontally to $left$ to $left+32$ and vertically by $top$ to $top+32$.
428 9fcd0215b8d5 Added text for ratures filter fsavard parents: 427 diff changeset	370
462 f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	371 Once this is done, two passes of a greyscale morphological erosion filter
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	372 are applied. Put briefly, this erosion filter reduces the width of the line
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	373 by a certain $smoothing$ amount. For small complexities (< 0.5),
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	374 $smoothing$ is 6, so the line is very small. For complexities ranging from
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	375 0.25 to 0.5, $smoothing$ is 5. It is 4 for complexities 0.5 to 0.75, and 3
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	376 for higher complexities.
428 9fcd0215b8d5 Added text for ratures filter fsavard parents: 427 diff changeset	377
462 f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	378 To compensate for border effects, the image is then cropped to 28x28 by
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	379 removing two pixels everywhere on the borders, then expanded to 32x32
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	380 again. The pixel values are then linearly expanded such that the minimum
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	381 value is 0 and the maximal one is 1. Then, 50\% of the time, the image is
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	382 vertically flipped.
428 9fcd0215b8d5 Added text for ratures filter fsavard parents: 427 diff changeset	383
462 f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	384 This filter is only applied only 15\% of the time. When it is applied, 50\%
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	385 of the time, only one patch image is generated and applied. In 30\% of
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	386 cases, two patches are generated, and otherwise three patches are
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	387 generated. The patch is applied by taking the maximal value on any given
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	388 patch or the original image, for each of the 32x32 pixel locations.
420 a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	389
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	390 \subsection{Color and Contrast Changes}
426 a7fab59de174 change order of transformations Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 425 diff changeset	391
462 f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	392 This filter changes the constrast and may invert the image polarity (white
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	393 on black to black on white). The contrast $C$ is defined here as the
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	394 difference between the maximum and the minimum pixel value of the image. A
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	395 contrast value is sampled uniformly between $1$ and $1-0.85 \times
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	396 complexity$ (this insure a minimum constrast of $0.15$). We then simply
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	397 normalize the image to the range $[\frac{1-C}{2},1-\frac{1-C}{2}]$. The
f59af1648d83 cleaner le techreport Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 461 diff changeset	398 polarity is inverted with $0.5$ probability.
420 a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	399
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	400
393 4c840798d290 added examples of figure and table of results Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 392 diff changeset	401 \begin{figure}[h]
4c840798d290 added examples of figure and table of results Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 392 diff changeset	402 \resizebox{.99\textwidth}{!}{\includegraphics{images/example_t.png}}\\
4c840798d290 added examples of figure and table of results Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 392 diff changeset	403 \caption{Illustration of the pipeline of stochastic
4c840798d290 added examples of figure and table of results Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 392 diff changeset	404 transformations applied to the image of a lower-case t
4c840798d290 added examples of figure and table of results Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 392 diff changeset	405 (the upper left image). Each image in the pipeline (going from
4c840798d290 added examples of figure and table of results Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 392 diff changeset	406 left to right, first top line, then bottom line) shows the result
4c840798d290 added examples of figure and table of results Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 392 diff changeset	407 of applying one of the modules in the pipeline. The last image
4c840798d290 added examples of figure and table of results Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 392 diff changeset	408 (bottom right) is used as training example.}
4c840798d290 added examples of figure and table of results Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 392 diff changeset	409 \label{fig:pipeline}
4c840798d290 added examples of figure and table of results Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 392 diff changeset	410 \end{figure}
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	411
422 e7790db265b1 Basic text for section 3, add a bit more detail to section 4.2.2 Arnaud Bergeron <abergeron@gmail.com> parents: 417 diff changeset	412
479 6593e67381a3 Added transformation figure Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 477 diff changeset	413 \begin{figure}[h]
6593e67381a3 Added transformation figure Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 477 diff changeset	414 \resizebox{.99\textwidth}{!}{\includegraphics{images/transfo.png}}\\
6593e67381a3 Added transformation figure Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 477 diff changeset	415 \caption{Illustration of each transformation applied to the same image
6593e67381a3 Added transformation figure Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 477 diff changeset	416 of the upper-case h (upper-left image). first row (from left to rigth) : original image, slant,
6593e67381a3 Added transformation figure Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 477 diff changeset	417 thickness, affine transformation, local elastic deformation; second row (from left to rigth) :
6593e67381a3 Added transformation figure Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 477 diff changeset	418 pinch, motion blur, occlusion, pixel permutation, gaussian noise; third row (from left to rigth) :
6593e67381a3 Added transformation figure Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 477 diff changeset	419 background image, salt and pepper noise, spatially gaussian noise, scratches,
6593e67381a3 Added transformation figure Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 477 diff changeset	420 color and contrast changes.}
6593e67381a3 Added transformation figure Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 477 diff changeset	421 \label{fig:transfo}
6593e67381a3 Added transformation figure Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 477 diff changeset	422 \end{figure}
6593e67381a3 Added transformation figure Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 477 diff changeset	423
6593e67381a3 Added transformation figure Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 477 diff changeset	424
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	425 \section{Experimental Setup}
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	426
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	427 \subsection{Training Datasets}
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	428
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	429 \subsubsection{Data Sources}
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	430
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	431 \begin{itemize}
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	432 \item {\bf NIST}
434 310c730516af added description of nist19 and captcha data sources goldfinger parents: 432 diff changeset	433 The NIST Special Database 19 (NIST19) is a very widely used dataset for training and testing OCR systems.
310c730516af added description of nist19 and captcha data sources goldfinger parents: 432 diff changeset	434 The dataset is composed with over 800 000 digits and characters (upper and lower cases), with hand checked classifications,
310c730516af added description of nist19 and captcha data sources goldfinger parents: 432 diff changeset	435 extracted from handwritten sample forms of 3600 writers. The characters are labelled by one of the 62 classes
310c730516af added description of nist19 and captcha data sources goldfinger parents: 432 diff changeset	436 corresponding to "0"-"9","A"-"Z" and "a"-"z". The dataset contains 8 series of different complexity.
310c730516af added description of nist19 and captcha data sources goldfinger parents: 432 diff changeset	437 The fourth series, $hsf_4$, experimentally recognized to be the most difficult one for classification task is recommended
310c730516af added description of nist19 and captcha data sources goldfinger parents: 432 diff changeset	438 by NIST as testing set and is used in our work for that purpose.
310c730516af added description of nist19 and captcha data sources goldfinger parents: 432 diff changeset	439 The performances reported by previous work on that dataset mostly use only the digits.
432 e2fd928a7de0 added description of nist19 and captcha data sources goldfinger parents: 428 diff changeset	440 Here we use the whole classes both in the training and testing phase.
e2fd928a7de0 added description of nist19 and captcha data sources goldfinger parents: 428 diff changeset	441
e2fd928a7de0 added description of nist19 and captcha data sources goldfinger parents: 428 diff changeset	442
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	443 \item {\bf Fonts}
477 534d4ecf1bd1 small desription of the font added Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 463 diff changeset	444 In order to have a good variety of sources we downloaded an important number of free fonts from: {\tt http://anonymous.url.net}
534d4ecf1bd1 small desription of the font added Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 463 diff changeset	445 %real adress {\tt http://cg.scs.carleton.ca/~luc/freefonts.html}
534d4ecf1bd1 small desription of the font added Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 463 diff changeset	446 in addition to Windows 7's, this adds up to a total of $9817$ different fonts that we can choose uniformly.
534d4ecf1bd1 small desription of the font added Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 463 diff changeset	447 The ttf file is either used as input of the Captcha generator (see next item) or, by producing a corresponding image,
534d4ecf1bd1 small desription of the font added Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 463 diff changeset	448 directly as input to our models.
534d4ecf1bd1 small desription of the font added Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 463 diff changeset	449 %Guillaume are there other details I forgot on the font selection?
534d4ecf1bd1 small desription of the font added Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 463 diff changeset	450
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	451 \item {\bf Captchas}
432 e2fd928a7de0 added description of nist19 and captcha data sources goldfinger parents: 428 diff changeset	452 The Captcha data source is an adaptation of the \emph{pycaptcha} library (a python based captcha generator library) for
e2fd928a7de0 added description of nist19 and captcha data sources goldfinger parents: 428 diff changeset	453 generating characters of the same format as the NIST dataset. The core of this data source is composed with a random character
e2fd928a7de0 added description of nist19 and captcha data sources goldfinger parents: 428 diff changeset	454 generator and various kinds of tranformations similar to those described in the previous sections.
e2fd928a7de0 added description of nist19 and captcha data sources goldfinger parents: 428 diff changeset	455 In order to increase the variability of the data generated, different fonts are used for generating the characters.
e2fd928a7de0 added description of nist19 and captcha data sources goldfinger parents: 428 diff changeset	456 Transformations (slant, distorsions, rotation, translation) are applied to each randomly generated character with a complexity
e2fd928a7de0 added description of nist19 and captcha data sources goldfinger parents: 428 diff changeset	457 depending on the value of the complexity parameter provided by the user of the data source. Two levels of complexity are
e2fd928a7de0 added description of nist19 and captcha data sources goldfinger parents: 428 diff changeset	458 allowed and can be controlled via an easy to use facade class.
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	459 \item {\bf OCR data}
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	460 \end{itemize}
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	461
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	462 \subsubsection{Data Sets}
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	463 \begin{itemize}
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	464 \item {\bf P07}
420 a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	465 The dataset P07 is sampled with our transformation pipeline with a complexity parameter of $0.7$.
a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	466 For each new exemple to generate, we choose one source with the following probability: $0.1$ for the fonts,
a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	467 $0.25$ for the captchas, $0.25$ for OCR data and $0.4$ for NIST. We apply all the transformations in their order
a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	468 and for each of them we sample uniformly a complexity in the range $[0,0.7]$.
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	469 \item {\bf NISTP} {\em ne pas utiliser PNIST mais NISTP, pour rester politically correct...}
463 5fa1c653620c added small information on NISTP Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 462 diff changeset	470 NISTP is equivalent to P07 (complexity parameter of $0.7$ with the same sources proportion) except that we only apply transformations from slant to pinch. Therefore, the character is transformed
420 a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	471 but no additionnal noise is added to the image, this gives images closer to the NIST dataset.
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	472 \end{itemize}
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	473
452 b0622f78cfec Add a small paragraph mentionning the distribution differences and a figure illustrating the difference. Arnaud Bergeron <abergeron@gmail.com> parents: 444 diff changeset	474 We noticed that the distribution of the training sets and the test sets differ.
b0622f78cfec Add a small paragraph mentionning the distribution differences and a figure illustrating the difference. Arnaud Bergeron <abergeron@gmail.com> parents: 444 diff changeset	475 Since our validation sets are sampled from the training set, they have approximately the same distribution, but the test set has a completely different distribution as illustrated in figure \ref {setsdata}.
b0622f78cfec Add a small paragraph mentionning the distribution differences and a figure illustrating the difference. Arnaud Bergeron <abergeron@gmail.com> parents: 444 diff changeset	476
b0622f78cfec Add a small paragraph mentionning the distribution differences and a figure illustrating the difference. Arnaud Bergeron <abergeron@gmail.com> parents: 444 diff changeset	477 \begin{figure}
b0622f78cfec Add a small paragraph mentionning the distribution differences and a figure illustrating the difference. Arnaud Bergeron <abergeron@gmail.com> parents: 444 diff changeset	478 \subfigure[NIST training]{\includegraphics[width=0.5\textwidth]{images/nisttrainstats}}
b0622f78cfec Add a small paragraph mentionning the distribution differences and a figure illustrating the difference. Arnaud Bergeron <abergeron@gmail.com> parents: 444 diff changeset	479 \subfigure[NIST validation]{\includegraphics[width=0.5\textwidth]{images/nistvalidstats}}
b0622f78cfec Add a small paragraph mentionning the distribution differences and a figure illustrating the difference. Arnaud Bergeron <abergeron@gmail.com> parents: 444 diff changeset	480 \subfigure[NIST test]{\includegraphics[width=0.5\textwidth]{images/nistteststats}}
b0622f78cfec Add a small paragraph mentionning the distribution differences and a figure illustrating the difference. Arnaud Bergeron <abergeron@gmail.com> parents: 444 diff changeset	481 \subfigure[NISTP validation]{\includegraphics[width=0.5\textwidth]{images/nistpvalidstats}}
b0622f78cfec Add a small paragraph mentionning the distribution differences and a figure illustrating the difference. Arnaud Bergeron <abergeron@gmail.com> parents: 444 diff changeset	482 \caption{Proportion of each class in some of the data sets}
b0622f78cfec Add a small paragraph mentionning the distribution differences and a figure illustrating the difference. Arnaud Bergeron <abergeron@gmail.com> parents: 444 diff changeset	483 \label{setsdata}
b0622f78cfec Add a small paragraph mentionning the distribution differences and a figure illustrating the difference. Arnaud Bergeron <abergeron@gmail.com> parents: 444 diff changeset	484 \end{figure}
b0622f78cfec Add a small paragraph mentionning the distribution differences and a figure illustrating the difference. Arnaud Bergeron <abergeron@gmail.com> parents: 444 diff changeset	485
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	486 \subsection{Models and their Hyperparameters}
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	487
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	488 \subsubsection{Multi-Layer Perceptrons (MLP)}
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	489
410 6330298791fb Description brève de MLP et SdA Arnaud Bergeron <abergeron@gmail.com> parents: 407 diff changeset	490 An MLP is a family of functions that are described by stacking layers of of a function similar to
6330298791fb Description brève de MLP et SdA Arnaud Bergeron <abergeron@gmail.com> parents: 407 diff changeset	491 $$g(x) = \tanh(b+Wx)$$
6330298791fb Description brève de MLP et SdA Arnaud Bergeron <abergeron@gmail.com> parents: 407 diff changeset	492 The input, $x$, is a $d$-dimension vector.
6330298791fb Description brève de MLP et SdA Arnaud Bergeron <abergeron@gmail.com> parents: 407 diff changeset	493 The output, $g(x)$, is a $m$-dimension vector.
411 4f69d915d142 Better description of the model parameters. Arnaud Bergeron <abergeron@gmail.com> parents: 410 diff changeset	494 The parameter $W$ is a $m\times d$ matrix and is called the weight matrix.
4f69d915d142 Better description of the model parameters. Arnaud Bergeron <abergeron@gmail.com> parents: 410 diff changeset	495 The parameter $b$ is a $m$-vector and is called the bias vector.
410 6330298791fb Description brève de MLP et SdA Arnaud Bergeron <abergeron@gmail.com> parents: 407 diff changeset	496 The non-linearity (here $\tanh$) is applied element-wise to the output vector.
6330298791fb Description brève de MLP et SdA Arnaud Bergeron <abergeron@gmail.com> parents: 407 diff changeset	497 Usually the input is referred to a input layer and similarly for the output.
6330298791fb Description brève de MLP et SdA Arnaud Bergeron <abergeron@gmail.com> parents: 407 diff changeset	498 You can of course chain several such functions to obtain a more complex one.
6330298791fb Description brève de MLP et SdA Arnaud Bergeron <abergeron@gmail.com> parents: 407 diff changeset	499 Here is a common example
6330298791fb Description brève de MLP et SdA Arnaud Bergeron <abergeron@gmail.com> parents: 407 diff changeset	500 $$f(x) = c + V\tanh(b+Wx)$$
6330298791fb Description brève de MLP et SdA Arnaud Bergeron <abergeron@gmail.com> parents: 407 diff changeset	501 In this case the intermediate layer corresponding to $\tanh(b+Wx)$ is called a hidden layer.
6330298791fb Description brève de MLP et SdA Arnaud Bergeron <abergeron@gmail.com> parents: 407 diff changeset	502 Here the output layer does not have the same non-linearity as the hidden layer.
6330298791fb Description brève de MLP et SdA Arnaud Bergeron <abergeron@gmail.com> parents: 407 diff changeset	503 This is a common case where some specialized non-linearity is applied to the output layer only depending on the task at hand.
6330298791fb Description brève de MLP et SdA Arnaud Bergeron <abergeron@gmail.com> parents: 407 diff changeset	504
6330298791fb Description brève de MLP et SdA Arnaud Bergeron <abergeron@gmail.com> parents: 407 diff changeset	505 If you put 3 or more hidden layers in such a network you obtain what is called a deep MLP.
411 4f69d915d142 Better description of the model parameters. Arnaud Bergeron <abergeron@gmail.com> parents: 410 diff changeset	506 The parameters to adapt are the weight matrix and the bias vector for each layer.
410 6330298791fb Description brève de MLP et SdA Arnaud Bergeron <abergeron@gmail.com> parents: 407 diff changeset	507
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	508 \subsubsection{Stacked Denoising Auto-Encoders (SDAE)}
422 e7790db265b1 Basic text for section 3, add a bit more detail to section 4.2.2 Arnaud Bergeron <abergeron@gmail.com> parents: 417 diff changeset	509 \label{SdA}
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	510
410 6330298791fb Description brève de MLP et SdA Arnaud Bergeron <abergeron@gmail.com> parents: 407 diff changeset	511 Auto-encoders are essentially a way to initialize the weights of the network to enable better generalization.
422 e7790db265b1 Basic text for section 3, add a bit more detail to section 4.2.2 Arnaud Bergeron <abergeron@gmail.com> parents: 417 diff changeset	512 This is essentially unsupervised training where the layer is made to reconstruct its input through and encoding and decoding phase.
e7790db265b1 Basic text for section 3, add a bit more detail to section 4.2.2 Arnaud Bergeron <abergeron@gmail.com> parents: 417 diff changeset	513 Denoising auto-encoders are a variant where the input is corrupted with random noise but the target is the uncorrupted input.
410 6330298791fb Description brève de MLP et SdA Arnaud Bergeron <abergeron@gmail.com> parents: 407 diff changeset	514 The principle behind these initialization methods is that the network will learn the inherent relation between portions of the data and be able to represent them thus helping with whatever task we want to perform.
6330298791fb Description brève de MLP et SdA Arnaud Bergeron <abergeron@gmail.com> parents: 407 diff changeset	515
411 4f69d915d142 Better description of the model parameters. Arnaud Bergeron <abergeron@gmail.com> parents: 410 diff changeset	516 An auto-encoder unit is formed of two MLP layers with the bottom one called the encoding layer and the top one the decoding layer.
4f69d915d142 Better description of the model parameters. Arnaud Bergeron <abergeron@gmail.com> parents: 410 diff changeset	517 Usually the top and bottom weight matrices are the transpose of each other and are fixed this way.
4f69d915d142 Better description of the model parameters. Arnaud Bergeron <abergeron@gmail.com> parents: 410 diff changeset	518 The network is trained as such and, when sufficiently trained, the MLP layer is initialized with the parameters of the encoding layer.
4f69d915d142 Better description of the model parameters. Arnaud Bergeron <abergeron@gmail.com> parents: 410 diff changeset	519 The other parameters are discarded.
4f69d915d142 Better description of the model parameters. Arnaud Bergeron <abergeron@gmail.com> parents: 410 diff changeset	520
410 6330298791fb Description brève de MLP et SdA Arnaud Bergeron <abergeron@gmail.com> parents: 407 diff changeset	521 The stacked version is an adaptation to deep MLPs where you initialize each layer with a denoising auto-encoder starting from the bottom.
411 4f69d915d142 Better description of the model parameters. Arnaud Bergeron <abergeron@gmail.com> parents: 410 diff changeset	522 During the initialization, which is usually called pre-training, the bottom layer is treated as if it were an isolated auto-encoder.
4f69d915d142 Better description of the model parameters. Arnaud Bergeron <abergeron@gmail.com> parents: 410 diff changeset	523 The second and following layers receive the same treatment except that they take as input the encoded version of the data that has gone through the layers before it.
410 6330298791fb Description brève de MLP et SdA Arnaud Bergeron <abergeron@gmail.com> parents: 407 diff changeset	524 For additional details see \cite{vincent:icml08}.
6330298791fb Description brève de MLP et SdA Arnaud Bergeron <abergeron@gmail.com> parents: 407 diff changeset	525
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	526 \section{Experimental Results}
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	527
438 a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	528 \subsection{SDA vs MLP vs Humans}
392 5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	529
438 a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	530 We compare here the best MLP (according to validation set error) that we found against
a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	531 the best SDA (again according to validation set error), along with a precise estimate
a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	532 of human performance obtained via Amazon's Mechanical Turk (AMT)
a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	533 service\footnote{http://mturk.com}. AMT users are paid small amounts
a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	534 of money to perform tasks for which human intelligence is required.
a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	535 Mechanical Turk has been used extensively in natural language
a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	536 processing \cite{SnowEtAl2008} and vision
a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	537 \cite{SorokinAndForsyth2008,whitehill09}. AMT users where presented
a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	538 with 10 character images and asked to type 10 corresponding ascii
a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	539 characters. Hence they were forced to make a hard choice among the
a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	540 62 character classes. Three users classified each image, allowing
a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	541 to estimate inter-human variability (shown as +/- in parenthesis below).
a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	542
a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	543 \begin{table}
458 c0f738f0cef0 added many results Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 452 diff changeset	544 \caption{Overall comparison of error rates ($\pm$ std.err.) on 62 character classes (10 digits +
438 a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	545 26 lower + 26 upper), except for last columns -- digits only, between deep architecture with pre-training
a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	546 (SDA=Stacked Denoising Autoencoder) and ordinary shallow architecture
458 c0f738f0cef0 added many results Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 452 diff changeset	547 (MLP=Multi-Layer Perceptron). The models shown are all trained using perturbed data (NISTP or P07)
c0f738f0cef0 added many results Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 452 diff changeset	548 and using a validation set to select hyper-parameters and other training choices.
c0f738f0cef0 added many results Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 452 diff changeset	549 \{SDA,MLP\}0 are trained on NIST,
c0f738f0cef0 added many results Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 452 diff changeset	550 \{SDA,MLP\}1 are trained on NISTP, and \{SDA,MLP\}2 are trained on P07.
c0f738f0cef0 added many results Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 452 diff changeset	551 The human error rate on digits is a lower bound because it does not count digits that were
461 9609c5cf9b6b lit. results Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 460 diff changeset	552 recognized as letters. For comparison, the results found in the literature
9609c5cf9b6b lit. results Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 460 diff changeset	553 on NIST digits classification using the same test set are included.}
438 a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	554 \label{tab:sda-vs-mlp-vs-humans}
392 5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	555 \begin{center}
438 a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	556 \begin{tabular}{\|l\|r\|r\|r\|r\|} \hline
458 c0f738f0cef0 added many results Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 452 diff changeset	557 & NIST test & NISTP test & P07 test & NIST test digits \\ \hline
c0f738f0cef0 added many results Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 452 diff changeset	558 Humans& 18.2\% $\pm$.1\% & 39.4\%$\pm$.1\% & 46.9\%$\pm$.1\% & $>1.1\%$ \\ \hline
c0f738f0cef0 added many results Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 452 diff changeset	559 SDA0 & 23.7\% $\pm$.14\% & 65.2\%$\pm$.34\% & 97.45\%$\pm$.06\% & 2.7\% $\pm$.14\%\\ \hline
c0f738f0cef0 added many results Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 452 diff changeset	560 SDA1 & 17.1\% $\pm$.13\% & 29.7\%$\pm$.3\% & 29.7\%$\pm$.3\% & 1.4\% $\pm$.1\%\\ \hline
c0f738f0cef0 added many results Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 452 diff changeset	561 SDA2 & 18.7\% $\pm$.13\% & 33.6\%$\pm$.3\% & 39.9\%$\pm$.17\% & 1.7\% $\pm$.1\%\\ \hline
460 fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	562 MLP0 & 24.2\% $\pm$.15\% & 68.8\%$\pm$.33\% & 78.70\%$\pm$.14\% & 3.45\% $\pm$.15\% \\ \hline
458 c0f738f0cef0 added many results Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 452 diff changeset	563 MLP1 & 23.0\% $\pm$.15\% & 41.8\%$\pm$.35\% & 90.4\%$\pm$.1\% & 3.85\% $\pm$.16\% \\ \hline
460 fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	564 MLP2 & 24.3\% $\pm$.15\% & 46.0\%$\pm$.35\% & 54.7\%$\pm$.17\% & 4.85\% $\pm$.18\% \\ \hline
461 9609c5cf9b6b lit. results Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 460 diff changeset	565 [5] & & & & 4.95\% $\pm$.18\% \\ \hline
9609c5cf9b6b lit. results Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 460 diff changeset	566 [2] & & & & 3.71\% $\pm$.16\% \\ \hline
9609c5cf9b6b lit. results Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 460 diff changeset	567 [3] & & & & 2.4\% $\pm$.13\% \\ \hline
9609c5cf9b6b lit. results Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 460 diff changeset	568 [4] & & & & 2.1\% $\pm$.12\% \\ \hline
392 5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	569 \end{tabular}
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	570 \end{center}
438 a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	571 \end{table}
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	572
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	573 \subsection{Perturbed Training Data More Helpful for SDAE}
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	574
460 fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	575 \begin{table}
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	576 \caption{Relative change in error rates due to the use of perturbed training data,
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	577 either using NISTP, for the MLP1/SDA1 models, or using P07, for the MLP2/SDA2 models.
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	578 A positive value indicates that training on the perturbed data helped for the
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	579 given test set (the first 3 columns on the 62-class tasks and the last one is
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	580 on the clean 10-class digits). Clearly, the deep learning models did benefit more
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	581 from perturbed training data, even when testing on clean data, whereas the MLP
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	582 trained on perturbed data performed worse on the clean digits and about the same
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	583 on the clean characters. }
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	584 \label{tab:sda-vs-mlp-vs-humans}
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	585 \begin{center}
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	586 \begin{tabular}{\|l\|r\|r\|r\|r\|} \hline
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	587 & NIST test & NISTP test & P07 test & NIST test digits \\ \hline
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	588 SDA0/SDA1-1 & 38\% & 84\% & 228\% & 93\% \\ \hline
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	589 SDA0/SDA2-1 & 27\% & 94\% & 144\% & 59\% \\ \hline
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	590 MLP0/MLP1-1 & 5.2\% & 65\% & -13\% & -10\% \\ \hline
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	591 MLP0/MLP2-1 & -0.4\% & 49\% & 44\% & -29\% \\ \hline
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	592 \end{tabular}
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	593 \end{center}
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	594 \end{table}
458 c0f738f0cef0 added many results Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 452 diff changeset	595
460 fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	596
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	597 \subsection{Multi-Task Learning Effects}
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	598
460 fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	599 As previously seen, the SDA is better able to benefit from the
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	600 transformations applied to the data than the MLP. In this experiment we
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	601 define three tasks: recognizing digits (knowing that the input is a digit),
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	602 recognizing upper case characters (knowing that the input is one), and
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	603 recognizing lower case characters (knowing that the input is one). We
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	604 consider the digit classification task as the target task and we want to
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	605 evaluate whether training with the other tasks can help or hurt, and
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	606 whether the effect is different for MLPs versus SDAs. The goal is to find
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	607 out if deep learning can benefit more (or less) from multiple related tasks
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	608 (i.e. the multi-task setting) compared to a corresponding purely supervised
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	609 shallow learner.
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	610
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	611 We use a single hidden layer MLP with 1000 hidden units, and a SDA
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	612 with 3 hidden layers (1000 hidden units per layer), pre-trained and
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	613 fine-tuned on NIST.
437 479f2f518fc9 added Training with More Classes than Necessary Guillaume Sicard <guitch21@gmail.com> parents: 434 diff changeset	614
460 fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	615 Our results show that the MLP benefits marginally from the multi-task setting
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	616 in the case of digits (5\% relative improvement) but is actually hurt in the case
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	617 of characters (respectively 3\% and 4\% worse for lower and upper class characters).
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	618 On the other hand the SDA benefitted from the multi-task setting, with relative
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	619 error rate improvements of 27\%, 15\% and 13\% respectively for digits,
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	620 lower and upper case characters, as shown in Table~\ref{tab:multi-task}.
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	621
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	622 \begin{table}
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	623 \caption{Test error rates and relative change in error rates due to the use of
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	624 a multi-task setting, i.e., training on each task in isolation vs training
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	625 for all three tasks together, for MLPs vs SDAs. The SDA benefits much
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	626 more from the multi-task setting. All experiments on only on the
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	627 unperturbed NIST data, using validation error for model selection.
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	628 Relative improvement is 1 - single-task error / multi-task error.}
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	629 \label{tab:multi-task}
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	630 \begin{center}
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	631 \begin{tabular}{\|l\|r\|r\|r\|} \hline
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	632 & single-task & multi-task & relative \\
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	633 & setting & setting & improvement \\ \hline
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	634 MLP-digits & 3.77\% & 3.99\% & 5.6\% \\ \hline
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	635 MLP-lower & 17.4\% & 16.8\% & -4.1\% \\ \hline
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	636 MLP-upper & 7.84\% & 7.54\% & -3.6\% \\ \hline
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	637 SDA-digits & 2.6\% & 3.56\% & 27\% \\ \hline
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	638 SDA-lower & 12.3\% & 14.4\% & 15\% \\ \hline
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	639 SDA-upper & 5.93\% & 6.78\% & 13\% \\ \hline
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	640 \end{tabular}
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	641 \end{center}
fe292653a0f8 ajoute dernier tableau de resultats Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 458 diff changeset	642 \end{table}
437 479f2f518fc9 added Training with More Classes than Necessary Guillaume Sicard <guitch21@gmail.com> parents: 434 diff changeset	643
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	644 \section{Conclusions}
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	645
407 fe2e2964e7a3 description des transformations en cours ajout d un fichier special.bib pour des references specifiques Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 393 diff changeset	646 \bibliography{strings,ml,aigaion,specials}
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	647 \bibliographystyle{mlapa}
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	648
407 fe2e2964e7a3 description des transformations en cours ajout d un fichier special.bib pour des references specifiques Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 393 diff changeset	649 \end{document}

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