Vanishing Component Analysis with Contrastive Normalization
This work addresses a domain-specific issue in machine learning for feature extraction, representing an incremental improvement over existing VCA methods.
The paper tackles the problem of improving the discriminative power of vanishing component analysis (VCA) by proposing a contrastive normalization method for approximate generators, which theoretically enhances feature extraction and is validated through numerical experiments.
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.