Kernel Subspace and Feature Extraction

• URL: http://arxiv.org/abs/2301.01410v2
• Date: Thu, 11 May 2023 00:37:47 GMT
• Title: Kernel Subspace and Feature Extraction
• Authors: Xiangxiang Xu, Lizhong Zheng
• Abstract summary: We study kernel methods in machine learning from the perspective of feature subspace. We construct a kernel from Hirschfeld--Gebelein--R'enyi maximal correlation functions, coined the maximal correlation kernel, and demonstrate its information-theoretic optimality.
• Score: 7.424262881242935
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• 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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