Exploring the Optimality of Tight-Frame Scattering Networks

Shanel Gauthier, Benjamin Thérien, Laurent Alsène-Racicot, Muawiz Sajjad Chaudhary, Irina Rish, Eugene Belilovsky, Michael Eickenberg, Guy Wolf

Keywords: Scattering Transforms, Wavelets, Few-sample learning

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 if such a tight frame 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 tight-frames may not always be necessary for scattering transforms to extract effective representations.

One-sentence Summary: A parametrized 2D Scattering transform is proposed and used to study the importance of the wavelet tight frame construction and improve results in few sample datasets.