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arXiv · 1910.03561

Deep Network Classification by Scattering and Homotopy Dictionary Learning

John Zarka·Louis Thiry·Tomás Angles·Stéphane Mallat
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Abstract

We introduce a sparse scattering deep convolutional neural network, which provides a simple model to analyze properties of deep representation learning for classification. Learning a single dictionary matrix with a classifier yields a higher classification accuracy than AlexNet over the ImageNet 2012 dataset. The network first applies a scattering transform that linearizes variabilities due to geometric transformations such as translations and small deformations. A sparse $\ell^1$ dictionary coding reduces intra-class variability while preserving class separation through projections over unions of linear spaces. It is implemented in a deep convolutional network with a homotopy algorithm having an exponential convergence. A convergence proof is given in a general framework that includes ALISTA. Classification results are analyzed on ImageNet.

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John Zarka, Louis Thiry, Tomás Angles, Stéphane Mallat. 2019-10-08. Deep Network Classification by Scattering and Homotopy Dictionary Learning. https://arxiv.org/abs/1910.03561

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