A Dimension-Independent Generalization Bound for Kernel Supervised Principal Component Analysis

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Hassan Ashtiani, Ali Ghodsi ;
Proceedings of the 1st International Workshop on Feature Extraction: Modern Questions and Challenges at NIPS 2015, PMLR 44:19-29, 2015.

Abstract

Kernel supervised principal component analysis (KSPCA) is a computationally efficient supervised feature extraction method that can learn non-linear transformations. We start the study of the statistical properties of KSPCA, providing the first bound on its sample complexity. This bound is dimension-independent, which justifies the good performance of KSPCA on high-dimensional data. Another observation is that in the kernelized version, the number of parameters of KSPCA grows linearly with the sample size. While this potentially increases the risk of over-fitting, KSPCA works well in practice. In this work, we justify this compelling characteristic of KSPCA by providing a guarantee indicating that KSPCA generalizes well even when the number of parameters is large, as long as they have small norms.

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