# Vanishing Component Analysis with Contrastive Normalization

arXiv: https://arxiv.org/abs/2210.16171 · HTML: https://mlsanity.com/paper/2210.16171/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 39 references that are in the map.
- First posted on arXiv 27 Oct 2022.

## Builds on (most cited first, 9 of 9)

- [Deep Anomaly Detection Using Geometric Transformations](https://mlsanity.com/paper/1805.10917/) (2018)
- [Classification-Based Anomaly Detection for General Data](https://mlsanity.com/paper/2005.02359/) (2020)
- [Gradient Boosts the Approximate Vanishing Ideal](https://mlsanity.com/paper/1911.04174/) (2019)
- [Spurious Vanishing Problem in Approximate Vanishing Ideal](https://mlsanity.com/paper/1901.08798/) (2019)
- [Analytic Manifold Learning: Unifying and Evaluating Representations for Continuous Control](https://mlsanity.com/paper/2006.08718/) (2020)
- [Approximate Vanishing Ideal Computations at Scale](https://mlsanity.com/paper/2207.01236/) (2022)
- [Dual-to-kernel learning with ideals](https://mlsanity.com/paper/1402.0099/) (2014)
- [Approximate Vanishing Ideal via Data Knotting](https://mlsanity.com/paper/1801.09367/) (2018)
- [Border basis computation with gradient-weighted normalization](https://mlsanity.com/paper/2101.00401/) (2021)

## Abstract (arXiv)

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.