论文标题
与归一化的消失组件分析
Vanishing Component Analysis with Contrastive Normalization
论文作者
论文摘要
消失的组件分析（VCA）计算出消失的样品理想的近似发生器，这些形式进一步用于提取样品的非线性特征。最近的研究表明，近似发电机的归一化起着重要作用，不同的归一化导致不同性质的发生器。在本文中，受到最新自我监督框架的启发，我们提出了一种对VCA的对比标准化方法，在该方法中，我们强加了发电机在目标样本上消失，并在转化的样品上进行标准化。从理论上讲，我们表明，对比标准化增强了VCA的判别能力，并在我们的归一化下提供了VCA的代数解释。数值实验证明了我们方法的有效性。这是第一个定制消失理想的近似发生器的归一化以获得歧视特征的研究。
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.
