Mercurial > ift6266
annotate writeup/techreport.tex @ 455:09e1c5872c2b
Ajout de trois lignes de code pour le calcul de l'erreur standart
| author | SylvainPL <sylvain.pannetier.lebeuf@umontreal.ca> |
|---|---|
| date | Wed, 26 May 2010 20:23:02 -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 | 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 | 35 generated data, as well as better able to take advantage of |
| 36 training from more classes than those of interest in the end. | |
| 37 In fact, we find that the SDA reaches human performance as | |
| 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 | 79 We can differentiate two important parts in the pipeline. The first one, from slant to pinch, performs transformations |
| 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 | 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 | 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 | 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 | 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 | 214 \subsection{"Ratures"} |
| 215 | |
| 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. | |
| 217 | |
| 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. | |
| 219 | |
| 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 $top+32$. | |
| 221 | |
| 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. | |
| 223 | |
| 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. | |
| 225 | |
| 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 | 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 | 361 We compare here the best MLP (according to validation set error) that we found against |
| 362 the best SDA (again according to validation set error), along with a precise estimate | |
| 363 of human performance obtained via Amazon's Mechanical Turk (AMT) | |
| 364 service\footnote{http://mturk.com}. AMT users are paid small amounts | |
| 365 of money to perform tasks for which human intelligence is required. | |
| 366 Mechanical Turk has been used extensively in natural language | |
| 367 processing \cite{SnowEtAl2008} and vision | |
| 368 \cite{SorokinAndForsyth2008,whitehill09}. AMT users where presented | |
| 369 with 10 character images and asked to type 10 corresponding ascii | |
| 370 characters. Hence they were forced to make a hard choice among the | |
| 371 62 character classes. Three users classified each image, allowing | |
| 372 to estimate inter-human variability (shown as +/- in parenthesis below). | |
| 373 | |
| 374 \begin{table} | |
| 375 \caption{Overall comparison of error rates on 62 character classes (10 digits + | |
| 376 26 lower + 26 upper), except for last columns -- digits only, between deep architecture with pre-training | |
| 377 (SDA=Stacked Denoising Autoencoder) and ordinary shallow architecture | |
| 378 (MLP=Multi-Layer Perceptron). } | |
| 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 | 381 \begin{tabular}{|l|r|r|r|r|} \hline |
| 382 & NIST test & NISTP test & P07 test & NIST test digits \\ \hline | |
| 383 Humans& & & & \\ \hline | |
| 384 SDA & & & &\\ \hline | |
| 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 | 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} |