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Vanishing component analysis (VCA) computes approximate generators ofvanishing ideals of samples, which are further used for extracting nonlinearfeatures of the samples. Recent studies have shown that normalization ofapproximate generators plays an important role and different normalizationleads to generators of different properties. In this paper, inspired by recentself-supervised frameworks, we propose a contrastive normalization method forVCA, where we impose the generators to vanish on the target samples and to benormalized on the transformed samples. We theoretically show that a contrastivenormalization enhances the discriminative power of VCA, and provide thealgebraic interpretation of VCA under our normalization. Numerical experimentsdemonstrate the effectiveness of our method. This is the first study to tailorthe normalization of approximate generators of vanishing ideals to obtaindiscriminative features.

Vanishing Component Analysis with Contrastive Normalization