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arXiv · 2301.01410

Kernel Subspace and Feature Extraction

Xiangxiang Xu·Lizhong Zheng
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Abstract

We study kernel methods in machine learning from the perspective of feature subspace. We establish a one-to-one correspondence between feature subspaces and kernels and propose an information-theoretic measure for kernels. In particular, we construct a kernel from Hirschfeld--Gebelein--R\'{e}nyi maximal correlation functions, coined the maximal correlation kernel, and demonstrate its information-theoretic optimality. We use the support vector machine (SVM) as an example to illustrate a connection between kernel methods and feature extraction approaches. We show that the kernel SVM on maximal correlation kernel achieves minimum prediction error. Finally, we interpret the Fisher kernel as a special maximal correlation kernel and establish its optimality.

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Xiangxiang Xu, Lizhong Zheng. 2023-01-04. Kernel Subspace and Feature Extraction. https://arxiv.org/abs/2301.01410

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