Classification with Invariant Scattering Representations

TL;DR

This paper introduces a scattering transform for signal representation that is invariant to translations and deformations, enabling effective classification of complex signals and textures with low-dimensional models.

Contribution

It presents a novel scattering transform based on wavelet and modulus operators, improving invariance and stability for classification tasks.

Findings

Achieved state-of-the-art results in handwritten digit recognition with small training sets.

Successfully classified textures using low-dimensional affine models in the scattering domain.

Demonstrated Lipschitz continuity to deformations for robust signal representation.

Abstract

A scattering transform defines a signal representation which is invariant to translations and Lipschitz continuous relatively to deformations. It is implemented with a non-linear convolution network that iterates over wavelet and modulus operators. Lipschitz continuity locally linearizes deformations. Complex classes of signals and textures can be modeled with low-dimensional affine spaces, computed with a PCA in the scattering domain. Classification is performed with a penalized model selection. State of the art results are obtained for handwritten digit recognition over small training sets, and for texture classification.