Kernel Subspace and Feature Extraction
Kernel Subspace and Feature Extraction
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DOI：
10.1109/isit54713.2023.10206532
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发表时间：
2023-01
期刊：
影响因子：
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通讯作者：
Xiangxiang Xu;Lizhong Zheng
中科院分区：
文献类型：
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作者：
Xiangxiang Xu;Lizhong Zheng
从特征子空间的角度研究了机器学习中的核方法。我们建立了一个一对一的对应关系的特征子空间和内核，并提出了一个信息论的措施内核。特别地，我们构造了一个核从Hirschal-Gebelein-Rényi最大相关函数，创造了最大相关核，并证明了其信息论最优性。我们使用支持向量机（SVM）作为一个例子来说明核方法和特征提取方法之间的联系。我们表明，最大相关核的核支持向量机实现最小的预测误差。最后，我们将Fisher核解释为一种特殊的最大相关核，并证明了它的最优性。
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–Rényi 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.