Vanishing Component Analysis with Contrastive Normalization

TL;DR

This paper introduces a contrastive normalization technique for vanishing component analysis (VCA) that enhances the discriminative power of nonlinear features by tailoring generator normalization, supported by theoretical and experimental validation.

Contribution

It proposes the first contrastive normalization method for VCA, improving the discriminative ability of the generated features with theoretical insights and numerical experiments.

Findings

Contrastive normalization improves discriminative features in VCA.

Theoretical analysis shows enhanced algebraic properties of normalized generators.

Numerical experiments confirm the effectiveness of the proposed method.

Abstract

Vanishing component analysis (VCA) computes approximate generators of vanishing ideals of samples, which are further used for extracting nonlinear features of the samples. Recent studies have shown that normalization of approximate generators plays an important role and different normalization leads to generators of different properties. In this paper, inspired by recent self-supervised frameworks, we propose a contrastive normalization method for VCA, where we impose the generators to vanish on the target samples and to be normalized on the transformed samples. We theoretically show that a contrastive normalization enhances the discriminative power of VCA, and provide the algebraic interpretation of VCA under our normalization. Numerical experiments demonstrate the effectiveness of our method. This is the first study to tailor the normalization of approximate generators of vanishing ideals to obtain discriminative features.