ift6266: writeup/techreport.tex annotate

annotate writeup/techreport.tex @ 456:66b05c6077c7

Ajout d'option pour choisir l'ensemble de donnees (train/valid/test) ainsi que mettre NIST,P07 et PNIST pour tous les modeles testes

author	SylvainPL <sylvain.pannetier.lebeuf@umontreal.ca>
date	Wed, 26 May 2010 20:24:16 -0400
parents	b0622f78cfec
children	c0f738f0cef0

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}
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	9 \title{Generating and Exploiting Perturbed 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
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	31 and testing on the full NIST test set.
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
a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	36 training from more classes than those of interest in the end.
a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	37 In fact, we find that the SDA reaches human performance as
a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	38 estimated by the Amazon Mechanical Turk on the NIST test characters.
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	39 \end{abstract}
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	40
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	41 \section{Introduction}
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	42
392 5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	43 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	44 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	45 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	46 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	47 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	48 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	49 different representation. In fact,
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	50 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	51 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	52 of visual cortex)~\cite{HonglakL2008}.
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	53 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	54 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	55 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	56 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	57 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	58 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	59 (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	60 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	61 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	62 Learning increases the
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	63 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	64 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	65 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	66 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	67 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	68 variance extant in real data.
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	69
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	70 Whereas a deep architecture can in principle be more powerful than a shallow
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	71 one in terms of representation, depth appears to render the training problem
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	72 more difficult in terms of optimization and local minima.
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	73 It is also only recently that
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	74 successful algorithms were proposed to overcome some of these
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	75 difficulties.
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	76
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	77 \section{Perturbation and Transformation of Character Images}
420 a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	78 This section describes the different transformations we used to generate data, in their order.
428 9fcd0215b8d5 Added text for ratures filter fsavard parents: 427 diff changeset	79 We can differentiate two important parts in the pipeline. The first one, from slant to pinch, performs transformations
9fcd0215b8d5 Added text for ratures filter fsavard parents: 427 diff changeset	80 of the character. The second part, from blur to contrast, adds noise to the image.
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	81
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	82 \subsection{Adding Slant}
420 a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	83 In order to mimic a slant effect, we simply shift each row of the image proportionnaly to its height: $shift = round(slant \times height)$.
a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	84 We round the shift in order to have a discret displacement. We do not use a filter to smooth the result in order to save computing time
a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	85 and also because latter transformations have similar effects.
a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	86
a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	87 The $slant$ coefficient can be negative or positive with equal probability and its value is randomly sampled according to the complexity level.
431 bfa349f567e8 correction in the transformation descripition Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 428 diff changeset	88 In our case we take uniformly a number in the range $[0,complexity]$, so the maximum displacement for the lowest
420 a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	89 or highest pixel line is of $round(complexity \times 32)$.
a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	90
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	91
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	92 \subsection{Changing Thickness}
431 bfa349f567e8 correction in the transformation descripition Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 428 diff changeset	93 To change the thickness of the characters we used morpholigical operators: 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	94
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	95 The basic idea of such transform is, for each pixel, to multiply in the element-wise manner its neighbourhood with a matrix called the structuring element.
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	96 Then for dilation we remplace the pixel value by the maximum of the result, or the minimum for erosion.
431 bfa349f567e8 correction in the transformation descripition Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 428 diff changeset	97 This will dilate or erode objects in the image and the strength of the transform only depends on the structuring element.
420 a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	98
a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	99 We used ten different structural elements with increasing dimensions (the biggest is $5\times5$).
a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	100 for each image, we radomly sample the operator type (dilation or erosion) with equal probability and one structural element
a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	101 from a subset of the $n$ smallest structuring elements where $n$ is $round(10 \times complexity)$ for dilation and $round(6 \times complexity)$ for erosion.
a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	102 A neutral element is always present in the set, if it is chosen the transformation is not applied.
a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	103 Erosion allows only the six smallest structural elements because when the character is too thin it may 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	104
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	105 \subsection{Affine Transformations}
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	106 We generate an affine transform matrix according to the complexity level, then we apply it directly to the image.
431 bfa349f567e8 correction in the transformation descripition Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 428 diff changeset	107 The matrix is of size $2 \times 3$, so we can represent it by six parameters $(a,b,c,d,e,f)$.
bfa349f567e8 correction in the transformation descripition Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 428 diff changeset	108 Formally, for each pixel $(x,y)$ of the output image,
bfa349f567e8 correction in the transformation descripition Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 428 diff changeset	109 we give the value of the pixel nearest to : $(ax+by+c,dx+ey+f)$, in the input image.
bfa349f567e8 correction in the transformation descripition Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 428 diff changeset	110 This allows to produce scaling, translation, rotation and shearing variances.
bfa349f567e8 correction in the transformation descripition Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 428 diff changeset	111
bfa349f567e8 correction in the transformation descripition Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 428 diff changeset	112 The sampling of the parameters $(a,b,c,d,e,f)$ have been tuned by hand to forbid important rotations (not to confuse classes) but to give good variability of the transformation. For each image we sample uniformly the parameters in the following ranges:
bfa349f567e8 correction in the transformation descripition Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 428 diff changeset	113 $a$ and $d$ in $[1-3 \times complexity,1+3 \times complexity]$, $b$ and $e$ in $[-3 \times complexity,3 \times complexity]$ and $c$ and $f$ in $[-4 \times complexity, 4 \times complexity]$.
bfa349f567e8 correction in the transformation descripition Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 428 diff changeset	114
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	115
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	116 \subsection{Local Elastic Deformations}
416 5f9d04dda707 Correction d'une erreur pour pinch et ajout d'une ref bibliographique fsavard parents: 415 diff changeset	117 This filter induces a "wiggly" effect in the image. The description here will be brief, as the algorithm follows precisely what is described in \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	118
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	119 The general idea is to generate two "displacements" fields, for horizontal and vertical displacements of pixels. Each of these fields has the same size as the original image.
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	120
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	121 When generating the transformed image, we'll loop over the x and y positions in the fields and select, as a value, the value of the pixel in the original image at the (relative) position given by the displacement fields for this x and y. If the position we'd retrieve is outside the borders of the image, we use a 0 value instead.
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	122
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	123 To generate a pixel in either field, first a value between -1 and 1 is chosen from a uniform distribution. Then all the pixels, in both fields, is multiplied by a constant $\alpha$ which controls the intensity of the displacements (bigger $\alpha$ translates into larger wiggles).
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	124
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	125 As a final step, each field is convoluted with a Gaussian 2D kernel of standard deviation $\sigma$. Visually, this results in a "blur" filter. This has the effect of making values next to each other in the displacement fields similar. In effect, this makes the wiggles more coherent, less noisy.
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	126
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	127 As displacement fields were long to compute, 50 pairs of fields were generated per complexity in increments of 0.1 (50 pairs for 0.1, 50 pairs for 0.2, etc.), and afterwards, given a complexity, we selected randomly among the 50 corresponding pairs.
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	128
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	129 $\sigma$ and $\alpha$ were linked to complexity through the formulas $\alpha = \sqrt[3]{complexity} \times 10.0$ and $\sigma = 10 - 7 \times \sqrt[3]{complexity}$.
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	130
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	131
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	132 \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	133
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	134 This is another GIMP filter we used. The filter is in fact named "Whirl and pinch", but we don't use the "whirl" part (whirl is set to 0). As described in GIMP, a pinch is "similar to projecting the image onto an elastic surface and pressing or pulling on the center of the surface".
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	135
416 5f9d04dda707 Correction d'une erreur pour pinch et ajout d'une ref bibliographique fsavard parents: 415 diff changeset	136 Mathematically, for a square input image, think of drawing a circle of radius $r$ around a center point $C$. Any point (pixel) $P$ belonging to that disk (region inside circle) will have its value recalculated by taking the value of another "source" pixel in the original image. The position of that source pixel is found on the line thats goes through $C$ and $P$, but at some other distance $d_2$. Define $d_1$ to be the distance between $P$ and $C$. $d_2$ is given by $d_2 = sin(\frac{\pi{}d_1}{2r})^{-pinch} \times d_1$, where $pinch$ is a parameter to the filter.
5f9d04dda707 Correction d'une erreur pour pinch et ajout d'une ref bibliographique fsavard parents: 415 diff changeset	137
417 0282882aa91f Completed the pinch transformation text fsavard parents: 416 diff changeset	138 If the region considered is not square then, before computing $d_2$, the smallest dimension (x or y) is stretched such that we may consider the region as if it was square. Then, after $d_2$ has been computed and corresponding components $d_2\_x$ and $d_2\_y$ have been found, the component corresponding to the stretched dimension is compressed back by an 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	139
417 0282882aa91f Completed the pinch transformation text fsavard parents: 416 diff changeset	140 The actual value is given by bilinear interpolation considering the pixels around the (non-integer) source position thus found.
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	141
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	142 The value for $pinch$ in our case was given by sampling from an uniform distribution over the range $[-complexity, 0.7 \times complexity]$.
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	143
426 a7fab59de174 change order of transformations Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 425 diff changeset	144 \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	145
426 a7fab59de174 change order of transformations Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 425 diff changeset	146 This is a GIMP filter we applied, a "linear motion blur" in GIMP 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	147
426 a7fab59de174 change order of transformations Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 425 diff changeset	148 This algorithm has two input parameters, $length$ and $angle$. The value of a pixel in the final image is the mean value of the $length$ first pixels found by moving in the $angle$ direction. An approximation of this idea is used, as we won't fall onto precise pixels by following that 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	149
426 a7fab59de174 change order of transformations Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 425 diff changeset	150 The angle, in our case, is chosen from a uniform distribution over $[0,360]$ degrees. The length, though, depends on the complexity; it's sampled from a Gaussian distribution of mean 0 and standard deviation $\sigma = 3 \times complexity$.
420 a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	151
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	152 \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	153
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	154 This filter selects random parts of other (hereafter "occlusive") letter images and places them over the original letter (hereafter "occluded") image. To be more precise, having selected a subregion of the occlusive image and a desination position in the occluded image, to determine the final value for a given overlapping pixel, it selects whichever pixel is the lightest. As a reminder, the background value is 0, black, so the value nearest to 1 is selected.
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	155
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	156 To select a subpart of the occlusive image, four numbers are generated. For compability with the code, we'll call them "haut", "bas", "gauche" and "droite" (respectively meaning top, bottom, left and right). Each of these numbers is selected according to a Gaussian distribution of mean $8 \times complexity$ and standard deviation $2$. This means the largest the complexity is, the biggest the occlusion will be. The absolute value is taken, as the numbers must be positive, and the maximum value is capped at 15.
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	157
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	158 These four sizes collectively define a window centered on the middle pixel of the occlusive image. This is the part that will be extracted as the occlusion.
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	159
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	160 The next step is to select a destination position in the occluded image. Vertical and horizontal displacements $y\_arrivee$ and $x\_arrivee$ are selected according to Gaussian distributions of mean 0 and of standard deviations of, respectively, 3 and 2. Then an horizontal placement mode, $endroit$ (meaning location), is selected to be of three values meaning left, middle or right.
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	161
416 5f9d04dda707 Correction d'une erreur pour pinch et ajout d'une ref bibliographique fsavard parents: 415 diff changeset	162 If $endroit$ is "middle", the occlusion will be horizontally centered around the horizontal middle of the occluded image, then shifted according to $x\_arrivee$. If $endroit$ is "left", it will be placed on the left of the occluded image, then displaced right according to $x\_arrivee$. The contrary happens if $endroit$ is $right$.
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	163
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	164 In both the horizontal and vertical positionning, the maximum position in either direction is such that the selected occlusion won't go beyond the borders of the occluded image.
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	165
416 5f9d04dda707 Correction d'une erreur pour pinch et ajout d'une ref bibliographique fsavard parents: 415 diff changeset	166 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	167
426 a7fab59de174 change order of transformations Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 425 diff changeset	168
442 d5b2b6397a5a added permut pixel Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 431 diff changeset	169 \subsection{Pixel permutation}
d5b2b6397a5a added permut pixel Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 431 diff changeset	170
d5b2b6397a5a added permut pixel Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 431 diff changeset	171 This filter permuts neighbouring pixels. It selects first $\frac{complexity}{3}$ pixels randomly in the image. Each of them are then sequentially
d5b2b6397a5a added permut pixel Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 431 diff changeset	172 exchanged to one other pixel in its $V4$ neighbourhood. Number of exchanges to the left, right, top, bottom are equal or does not differ from more than 1
444 18841eeb433f small syntax fix Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 443 diff changeset	173 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	174
d5b2b6397a5a added permut pixel Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 431 diff changeset	175 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	176
d5b2b6397a5a added permut pixel Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 431 diff changeset	177
426 a7fab59de174 change order of transformations Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 425 diff changeset	178 \subsection{Distorsion gauss}
a7fab59de174 change order of transformations Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 425 diff changeset	179
a7fab59de174 change order of transformations Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 425 diff changeset	180 This filter simply adds, to each pixel of the image independently, a gaussian noise of mean $0$ and standard deviation $\frac{complexity}{10}$.
a7fab59de174 change order of transformations Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 425 diff changeset	181
a7fab59de174 change order of transformations Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 425 diff changeset	182 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	183
a7fab59de174 change order of transformations Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 425 diff changeset	184
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	185 \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	186
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	187 This transformation adds a random background behind the letter. The background is chosen by first selecting, at random, an image from a set of images. Then we choose a 32x32 subregion of that image as the background image (by sampling x and y positions uniformly while making sure not to cross image borders).
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	188
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	189 To combine the original letter image and the background image, contrast adjustments are made. We first get the maximal values (i.e. maximal intensity) for both the original image and the background image, $maximage$ and $maxbg$. We also have a parameter, $contrast$, given by sampling from a uniform distribution over $[complexity, 1]$.
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	190
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	191 Once we have all these numbers, we first adjust the values for the background image. Each pixel value is multiplied by $\frac{max(maximage - contrast, 0)}{maxbg}$. Therefore the higher the contrast, the darkest the background will be.
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 The final image is found by taking the brightest (i.e. value nearest to 1) pixel from either the background image or the corresponding pixel in the original image.
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
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	195 \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	196
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	197 This filter adds noise to the image by randomly selecting a certain number of them and, for those selected pixels, assign a random value according to a uniform distribution over the $[0,1]$ ranges. This last distribution does not change according to complexity. Instead, the number of selected pixels does: the proportion of changed pixels corresponds to $complexity / 5$, which means, as a maximum, 20\% of the pixels will be randomized. On the lowest extreme, no pixel is changed.
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	198
420 a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	199 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	200
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	201 \subsection{Spatially Gaussian Noise}
426 a7fab59de174 change order of transformations Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 425 diff changeset	202
420 a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	203 The aim of this transformation is to filter, with a gaussian kernel, different regions of the image. In order to save computing time
a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	204 we decided to convolve the whole image only once with a symmetric gaussian kernel of size and variance choosen uniformly in the ranges:
a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	205 $[12,12 + 20 \times complexity]$ and $[2,2 + 6 \times complexity]$. The result is normalized between $0$ and $1$.
a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	206 We also create a symmetric averaging window, of the kernel size, with maximum value at the center.
a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	207 For each image we sample uniformly from $3$ to $3 + 10 \times complexity$ pixels that will be averaging centers
a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	208 between the original image and the filtered one.
a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	209 We initialize to zero a mask matrix of the image size. For each selected pixel we add to the mask the averaging window centered to it.
444 18841eeb433f small syntax fix Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 443 diff changeset	210 The final image is computed from the following element-wise operation: $\frac{image + filtered image \times mask}{mask+1}$.
420 a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	211
a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	212 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	213
428 9fcd0215b8d5 Added text for ratures filter fsavard parents: 427 diff changeset	214 \subsection{"Ratures"}
9fcd0215b8d5 Added text for ratures filter fsavard parents: 427 diff changeset	215
9fcd0215b8d5 Added text for ratures filter fsavard parents: 427 diff changeset	216 The ratures ("scratches") filter places line-like white patches on the image. The lines are in fact heavily transformed images of the digit "1" (one), chosen at random among five thousands such start images of this digit.
9fcd0215b8d5 Added text for ratures filter fsavard parents: 427 diff changeset	217
9fcd0215b8d5 Added text for ratures filter fsavard parents: 427 diff changeset	218 Once the image is selected, the transformation begins by finding the first $top$, $bottom$, $right$ and $left$ non-zero pixels in the image. It is then cropped to the region thus delimited, then this cropped version is expanded to 32x32 again. It is then rotated by a random angle having a Gaussian distribution of mean 90 and standard deviation $100 \times complexity$ (in degrees). The rotation is done with bicubic interpolation.
9fcd0215b8d5 Added text for ratures filter fsavard parents: 427 diff changeset	219
9fcd0215b8d5 Added text for ratures filter fsavard parents: 427 diff changeset	220 The rotated image is then resized to 50x50, with anti-aliasing. In that image, we crop the image again by selecting a region delimited horizontally to $left$ to $left+32$ and vertically by $top$ to $top+32$.
9fcd0215b8d5 Added text for ratures filter fsavard parents: 427 diff changeset	221
9fcd0215b8d5 Added text for ratures filter fsavard parents: 427 diff changeset	222 Once this is done, two passes of a greyscale morphological erosion filter are applied. Put briefly, this erosion filter reduces the width of the line by a certain $smoothing$ amount. For small complexities (< 0.5), $smoothing$ is 6, so the line is very small. For complexities ranging from 0.25 to 0.5, $smoothing$ is 5. It is 4 for complexities 0.5 to 0.75, and 3 for higher complexities.
9fcd0215b8d5 Added text for ratures filter fsavard parents: 427 diff changeset	223
9fcd0215b8d5 Added text for ratures filter fsavard parents: 427 diff changeset	224 To compensate for border effects, the image is then cropped to 28x28 by removing two pixels everywhere on the borders, then expanded to 32x32 again. The pixel values are then linearly expanded such that the minimum value is 0 and the maximal one is 1. Then, 50\% of the time, the image is vertically flipped.
9fcd0215b8d5 Added text for ratures filter fsavard parents: 427 diff changeset	225
9fcd0215b8d5 Added text for ratures filter fsavard parents: 427 diff changeset	226 This filter is only applied only 15\% of the time. When it is applied, 50\% of the time, only one patch image is generated and applied. In 30\% of cases, two patches are generated, and otherwise three patches are generated. The patch is applied by taking the maximal value on any given 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	227
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	228 \subsection{Color and Contrast Changes}
426 a7fab59de174 change order of transformations Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 425 diff changeset	229
420 a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	230 This filter changes the constrast and may invert the image polarity (white on black to black on white). The contrast $C$ is defined here as the difference
424 6e5f0f50ddab Fix latex syntax in 2.12 (would not compile otherwise). Arnaud Bergeron <abergeron@gmail.com> parents: 423 diff changeset	231 between the maximum and the minimum pixel value of the image. A contrast value is sampled uniformly between $1$ and $1-0.85 \times complexity$
420 a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	232 (this insure a minimum constrast of $0.15$). We then simply normalize the image to the range $[\frac{1-C}{2},1-\frac{1-C}{2}]$. The polarity
a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	233 is inverted with $0.5$ probability.
a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	234
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	235
393 4c840798d290 added examples of figure and table of results Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 392 diff changeset	236 \begin{figure}[h]
4c840798d290 added examples of figure and table of results Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 392 diff changeset	237 \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	238 \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	239 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	240 (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	241 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	242 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	243 (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	244 \label{fig:pipeline}
4c840798d290 added examples of figure and table of results Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 392 diff changeset	245 \end{figure}
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	246
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	247 \section{Learning Algorithms for Deep Architectures}
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	248
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	249 Learning for deep network has long been a problem since well-known learning algorithms do not generalize well on deep architectures.
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	250 Using these training algorithms on deep network usually yields to a worse generalization than on shallow networks.
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	251 Recently, new initialization techniques have been discovered that enable better generalization overall.
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	252
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	253 One of these initialization techniques is denoising auto-encoders.
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	254 The principle is that each layer starting from the bottom is trained to encode and decode their input and the encoding part is kept as initialization for the weights and bias of the network.
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	255 For more details see section \ref{SdA}.
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	256
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	257 After initialization is done, standard training algorithms work.
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	258 In this case, since we have large data sets we use stochastic gradient descent.
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	259 This resemble minibatch training except that the batches are selected at random.
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	260 To speed up computation, we randomly pre-arranged examples in batches and used those for all training experiments.
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	261
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	262 \section{Experimental Setup}
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	263
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	264 \subsection{Training Datasets}
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	265
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	266 \subsubsection{Data Sources}
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	267
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	268 \begin{itemize}
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	269 \item {\bf NIST}
434 310c730516af added description of nist19 and captcha data sources goldfinger parents: 432 diff changeset	270 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	271 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	272 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	273 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	274 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	275 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	276 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	277 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	278
e2fd928a7de0 added description of nist19 and captcha data sources goldfinger parents: 428 diff changeset	279
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	280 \item {\bf Fonts}
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	281 \item {\bf Captchas}
432 e2fd928a7de0 added description of nist19 and captcha data sources goldfinger parents: 428 diff changeset	282 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	283 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	284 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	285 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	286 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	287 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	288 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	289 \item {\bf OCR data}
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	290 \end{itemize}
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	291
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	292 \subsubsection{Data Sets}
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	293 \begin{itemize}
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	294 \item {\bf NIST}
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	295 \item {\bf P07}
420 a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	296 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	297 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	298 $0.25$ 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	299 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	300 \item {\bf NISTP} {\em ne pas utiliser PNIST mais NISTP, pour rester politically correct...}
420 a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	301 NISTP is equivalent to P07 except that we only apply transformations from slant to pinch. Therefore, the character is transformed
a3a4a9c6476d added transformations description and began dataset descriptions Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 417 diff changeset	302 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	303 \end{itemize}
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	304
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	305 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	306 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	307
b0622f78cfec Add a small paragraph mentionning the distribution differences and a figure illustrating the difference. Arnaud Bergeron <abergeron@gmail.com> parents: 444 diff changeset	308 \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	309 \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	310 \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	311 \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	312 \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	313 \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	314 \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	315 \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	316
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	317 \subsection{Models and their Hyperparameters}
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	318
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	319 \subsubsection{Multi-Layer Perceptrons (MLP)}
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	320
410 6330298791fb Description brève de MLP et SdA Arnaud Bergeron <abergeron@gmail.com> parents: 407 diff changeset	321 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	322 $$g(x) = \tanh(b+Wx)$$
6330298791fb Description brève de MLP et SdA Arnaud Bergeron <abergeron@gmail.com> parents: 407 diff changeset	323 The input, $x$, is a $d$-dimension vector.
6330298791fb Description brève de MLP et SdA Arnaud Bergeron <abergeron@gmail.com> parents: 407 diff changeset	324 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	325 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	326 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	327 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	328 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	329 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	330 Here is a common example
6330298791fb Description brève de MLP et SdA Arnaud Bergeron <abergeron@gmail.com> parents: 407 diff changeset	331 $$f(x) = c + V\tanh(b+Wx)$$
6330298791fb Description brève de MLP et SdA Arnaud Bergeron <abergeron@gmail.com> parents: 407 diff changeset	332 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	333 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	334 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	335
6330298791fb Description brève de MLP et SdA Arnaud Bergeron <abergeron@gmail.com> parents: 407 diff changeset	336 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	337 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	338
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	339 \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	340 \label{SdA}
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	341
410 6330298791fb Description brève de MLP et SdA Arnaud Bergeron <abergeron@gmail.com> parents: 407 diff changeset	342 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	343 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	344 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	345 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	346
411 4f69d915d142 Better description of the model parameters. Arnaud Bergeron <abergeron@gmail.com> parents: 410 diff changeset	347 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	348 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	349 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	350 The other parameters are discarded.
4f69d915d142 Better description of the model parameters. Arnaud Bergeron <abergeron@gmail.com> parents: 410 diff changeset	351
410 6330298791fb Description brève de MLP et SdA Arnaud Bergeron <abergeron@gmail.com> parents: 407 diff changeset	352 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	353 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	354 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	355 For additional details see \cite{vincent:icml08}.
6330298791fb Description brève de MLP et SdA Arnaud Bergeron <abergeron@gmail.com> parents: 407 diff changeset	356
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	357 \section{Experimental Results}
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	358
438 a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	359 \subsection{SDA vs MLP vs Humans}
392 5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	360
438 a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	361 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	362 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	363 of human performance obtained via Amazon's Mechanical Turk (AMT)
a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	364 service\footnote{http://mturk.com}. AMT users are paid small amounts
a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	365 of money to perform tasks for which human intelligence is required.
a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	366 Mechanical Turk has been used extensively in natural language
a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	367 processing \cite{SnowEtAl2008} and vision
a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	368 \cite{SorokinAndForsyth2008,whitehill09}. AMT users where presented
a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	369 with 10 character images and asked to type 10 corresponding ascii
a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	370 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	371 62 character classes. Three users classified each image, allowing
a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	372 to estimate inter-human variability (shown as +/- in parenthesis below).
a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	373
a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	374 \begin{table}
a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	375 \caption{Overall comparison of error rates on 62 character classes (10 digits +
a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	376 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	377 (SDA=Stacked Denoising Autoencoder) and ordinary shallow architecture
a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	378 (MLP=Multi-Layer Perceptron). }
a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	379 \label{tab:sda-vs-mlp-vs-humans}
392 5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	380 \begin{center}
438 a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	381 \begin{tabular}{\|l\|r\|r\|r\|r\|} \hline
a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	382 & NIST test & NISTP test & P07 test & NIST test digits \\ \hline
a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	383 Humans& & & & \\ \hline
a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	384 SDA & & & &\\ \hline
a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	385 MLP & & & & \\ \hline
392 5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	386 \end{tabular}
5f8fffd7347f possible image for illustrating perturbations Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 381 diff changeset	387 \end{center}
438 a6d339033d03 added AMT Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 437 diff changeset	388 \end{table}
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	389
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	390 \subsection{Perturbed Training Data More Helpful for SDAE}
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	391
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	392 \subsection{Training with More Classes than Necessary}
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	393
437 479f2f518fc9 added Training with More Classes than Necessary Guillaume Sicard <guitch21@gmail.com> parents: 434 diff changeset	394 As previously seen, the SDA is better able to benefit from the transformations applied to the data than the MLP. We are now training SDAs and MLPs on single classes from NIST (respectively digits, lower case characters and upper case characters), to compare the test results with those from models trained on the entire NIST database (per-class test error, with an a priori on the desired class). The goal is to find out if training the model with more classes than necessary reduces the test error on a single class, as opposed to training it only with the desired class. We use a single hidden layer MLP with 1000 hidden units, and a SDA with 3 hidden layers (1000 hidden units per layer), pre-trained and fine-tuned on NIST.
479f2f518fc9 added Training with More Classes than Necessary Guillaume Sicard <guitch21@gmail.com> parents: 434 diff changeset	395
440 89258bb41e4c updating values in Training with More Classes than Necessary Guillaume Sicard <guitch21@gmail.com> parents: 438 diff changeset	396 Our results show that the MLP only benefits from a full NIST training on digits, and the test error is only 5\% smaller than a digits-specialized MLP. On the other hand, the SDA always gives better results when it is trained with the entire NIST database, compared to its specialized counterparts (with upper case character, the test errors is 12\% smaller, 27\% smaller on digits, and 15\% smaller on lower case characters).
437 479f2f518fc9 added Training with More Classes than Necessary Guillaume Sicard <guitch21@gmail.com> parents: 434 diff changeset	397
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	398 \section{Conclusions}
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	399
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	400 \bibliography{strings,ml,aigaion,specials}
379 a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	401 \bibliographystyle{mlapa}
a21a174c1c18 added writeup skeleton Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	402
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	403 \end{document}

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