Parametric Scattering Networks

TL;DR

This paper explores learning parameters of wavelet filters in scattering transforms, demonstrating that data-driven filter design can outperform traditional fixed filterbanks, especially in small-sample classification tasks.

Contribution

It introduces a method to learn scales, orientations, and aspect ratios of Morlet wavelets within scattering transforms, challenging the necessity of fixed filterbank constructions.

Findings

Learned scattering transforms outperform standard ones in small-sample classification.

Traditional filterbank assumptions may not always be optimal for scattering transforms.

Empirical results show significant performance gains with learned filter parameters.

Abstract

The wavelet scattering transform creates geometric invariants and deformation stability. In multiple signal domains, it has been shown to yield more discriminative representations compared to other non-learned representations and to outperform learned representations in certain tasks, particularly on limited labeled data and highly structured signals. The wavelet filters used in the scattering transform are typically selected to create a tight frame via a parameterized mother wavelet. In this work, we investigate whether this standard wavelet filterbank construction is optimal. Focusing on Morlet wavelets, we propose to learn the scales, orientations, and aspect ratios of the filters to produce problem-specific parameterizations of the scattering transform. We show that our learned versions of the scattering transform yield significant performance gains in small-sample classification settings over the standard scattering transform. Moreover, our empirical results suggest that traditional filterbank constructions may not always be necessary for scattering transforms to extract effective representations.