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description des transformations en cours ajout d un fichier special.bib pour des references specifiques
author Xavier Glorot <glorotxa@iro.umontreal.ca>
date Wed, 28 Apr 2010 14:35:01 -0400
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children 6330298791fb
rev   line source
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1 \documentclass[12pt,letterpaper]{article}
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2 \usepackage[utf8]{inputenc}
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3 \usepackage{graphicx}
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4 \usepackage{times}
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5 \usepackage{mlapa}
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6
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7 \begin{document}
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8 \title{Generating and Exploiting Perturbed Training Data for Deep Architectures}
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9 \author{The IFT6266 Gang}
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10 \date{April 2010, Technical Report, Dept. IRO, U. Montreal}
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11
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12 \maketitle
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13
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14 \begin{abstract}
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15 Recent theoretical and empirical work in statistical machine learning has
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16 demonstrated the importance of learning algorithms for deep
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17 architectures, i.e., function classes obtained by composing multiple
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18 non-linear transformations. In the area of handwriting recognition,
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19 deep learning algorithms
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20 had been evaluated on rather small datasets with a few tens of thousands
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21 of examples. Here we propose a powerful generator of variations
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22 of examples for character images based on a pipeline of stochastic
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23 transformations that include not only the usual affine transformations
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24 but also the addition of slant, local elastic deformations, changes
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25 in thickness, background images, color, contrast, occlusion, and
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26 various types of pixel and spatially correlated noise.
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27 We evaluate a deep learning algorithm (Stacked Denoising Autoencoders)
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28 on the task of learning to classify digits and letters transformed
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29 with this pipeline, using the hundreds of millions of generated examples
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30 and testing on the full NIST test set.
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31 We find that the SDA outperforms its
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32 shallow counterpart, an ordinary Multi-Layer Perceptron,
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33 and that it is better able to take advantage of the additional
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34 generated data.
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35 \end{abstract}
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36
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37 \section{Introduction}
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38
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39 Deep Learning has emerged as a promising new area of research in
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40 statistical machine learning (see~\emcite{Bengio-2009} for a review).
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41 Learning algorithms for deep architectures are centered on the learning
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42 of useful representations of data, which are better suited to the task at hand.
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43 This is in great part inspired by observations of the mammalian visual cortex,
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44 which consists of a chain of processing elements, each of which is associated with a
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45 different representation. In fact,
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46 it was found recently that the features learnt in deep architectures resemble
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47 those observed in the first two of these stages (in areas V1 and V2
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48 of visual cortex)~\cite{HonglakL2008}.
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49 Processing images typically involves transforming the raw pixel data into
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50 new {\bf representations} that can be used for analysis or classification.
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51 For example, a principal component analysis representation linearly projects
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52 the input image into a lower-dimensional feature space.
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53 Why learn a representation? Current practice in the computer vision
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54 literature converts the raw pixels into a hand-crafted representation
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55 (e.g.\ SIFT features~\cite{Lowe04}), but deep learning algorithms
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56 tend to discover similar features in their first few
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57 levels~\cite{HonglakL2008,ranzato-08,Koray-08,VincentPLarochelleH2008-very-small}.
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58 Learning increases the
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59 ease and practicality of developing representations that are at once
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60 tailored to specific tasks, yet are able to borrow statistical strength
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61 from other related tasks (e.g., modeling different kinds of objects). Finally, learning the
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62 feature representation can lead to higher-level (more abstract, more
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63 general) features that are more robust to unanticipated sources of
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64 variance extant in real data.
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65
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66 Whereas a deep architecture can in principle be more powerful than a shallow
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67 one in terms of representation, depth appears to render the training problem
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68 more difficult in terms of optimization and local minima.
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69 It is also only recently that
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70 successful algorithms were proposed to overcome some of these
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71 difficulties.
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72
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73 \section{Perturbation and Transformation of Character Images}
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74
407
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75 \subsection{Adding Slant}
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76 In order to mimic a slant effect, we simply shift each row of the image proportionnaly to its height.
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77 The coefficient is randomly sampled according to the complexity level and can be negatif or positif with equal probability.
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78
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79 \subsection{Changing Thickness}
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80 To change the thickness of the characters we used morpholigical operators: dilation and erosion~\cite{Haralick87,Serra82}.
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81 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.
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82 Then for dilation we remplace the pixel value by the maximum of the result, or the minimum for erosion.
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83 This will dilate or erode objects in the image, the strength of the transform only depends on the structuring element.
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84 We used ten different structural elements with various shapes (the biggest is $5\times5$).
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85 for each image, we radomly sample the operator type (dilation or erosion) and one structural element
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86 from a subset depending of the complexity (the higher the complexity, the biggest the structural element can be).
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87 Erosion allows only the five smallest structural elements because when the character is too thin it may erase it completly.
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88
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89 \subsection{Affine Transformations}
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90 We generate an affine transform matrix according to the complexity level, then we apply it directly to the image.
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91 This allows to produce scaling, translation, rotation and shearing variances. We took care that the maximum rotation applied
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92 to the image is low enough not to confuse classes.
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93
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94 \subsection{Local Elastic Deformations}
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95 \subsection{GIMP transformation}
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96 \subsection{Occlusion}
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97 \subsection{Background Images}
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98 \subsection{Salt and Pepper Noise}
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99 \subsection{Spatially Gaussian Noise}
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100 \subsection{Color and Contrast Changes}
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101
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102 \begin{figure}[h]
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103 \resizebox{.99\textwidth}{!}{\includegraphics{images/example_t.png}}\\
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104 \caption{Illustration of the pipeline of stochastic
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105 transformations applied to the image of a lower-case t
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106 (the upper left image). Each image in the pipeline (going from
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107 left to right, first top line, then bottom line) shows the result
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108 of applying one of the modules in the pipeline. The last image
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109 (bottom right) is used as training example.}
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110 \label{fig:pipeline}
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111 \end{figure}
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112
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113 \section{Learning Algorithms for Deep Architectures}
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114
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115 \section{Experimental Setup}
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116
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117 \subsection{Training Datasets}
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118
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119 \subsubsection{Data Sources}
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120
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121 \begin{itemize}
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122 \item {\bf NIST}
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123 \item {\bf Fonts}
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124 \item {\bf Captchas}
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125 \item {\bf OCR data}
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126 \end{itemize}
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127
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128 \subsubsection{Data Sets}
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129 \begin{itemize}
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130 \item {\bf NIST}
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131 \item {\bf P07}
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132 \item {\bf NISTP} {\em ne pas utiliser PNIST mais NISTP, pour rester politically correct...}
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133 \end{itemize}
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134
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135 \subsection{Models and their Hyperparameters}
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136
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137 \subsubsection{Multi-Layer Perceptrons (MLP)}
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138
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139 \subsubsection{Stacked Denoising Auto-Encoders (SDAE)}
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140
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141 \section{Experimental Results}
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142
392
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143 \subsection{SDA vs MLP}
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144
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145 \begin{center}
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146 \begin{tabular}{lcc}
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147 & train w/ & train w/ \\
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148 & NIST & P07 + NIST \\ \hline
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149 SDA & & \\ \hline
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150 MLP & & \\ \hline
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151 \end{tabular}
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152 \end{center}
379
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153
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154 \subsection{Perturbed Training Data More Helpful for SDAE}
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155
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156 \subsection{Training with More Classes than Necessary}
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157
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158 \section{Conclusions}
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159
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160 \bibliography{strings,ml,aigaion,specials}
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161 \bibliographystyle{mlapa}
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162
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163 \end{document}