Large 00022

Classification with Sparse Depp Scattering Networks

St├ęphane Mallat

Recorded 08 July 2013 in Lausanne, Vaud, Switzerland

Event: Spars 2013 - Signal Processing with Adaptive Sparse Structured Representations

Abstract

Deep neural networks are remarkably successful classi?ers, ?rst trained on large data bases of unlabeled examples, and then optimized with fewer labeled examples. They provide state of the art results in computer vision, speech recognition, music and bio-medical classi?cation, but with little mathematical understanding of their performance. We introduce a mathematical model of deep neural networks with scattering transforms, which cascades complex valued unitary operators and contractive modulus. We show that unsupervised learning optimizes a contraction of the space, and amounts to ?nd unitary operators providing sparse representations of unlabeled examples. Wavelet operators appear to be nearly optimal for the ?rst network layers of many audio and image classi?cation problems. Classi?cation applications will be discussed and shown on images and sounds.

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