On Column Selection in Approximate Kernel Canonical Correlation Analysis

Weiran Wang

doi:10.48550/arxiv.1602.02172

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On Column Selection in Approximate Kernel Canonical Correlation Analysis

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On Column Selection in Approximate Kernel Canonical Correlation Analysis

Weiran Wang

arXiv (Cornell University)

02/05/2016

DOI: 10.48550/arxiv.1602.02172

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https://doi.org/10.48550/arXiv.1602.02172View

Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

We study the problem of column selection in large-scale kernel canonical correlation analysis (KCCA) using the Nyström approximation, where one approximates two positive semi-definite kernel matrices using "landmark" points from the training set. When building low-rank kernel approximations in KCCA, previous work mostly samples the landmarks uniformly at random from the training set. We propose novel strategies for sampling the landmarks non-uniformly based on a version of statistical leverage scores recently developed for kernel ridge regression. We study the approximation accuracy of the proposed non-uniform sampling strategy, develop an incremental algorithm that explores the path of approximation ranks and facilitates efficient model selection, and derive the kernel stability of out-of-sample mapping for our method. Experimental results on both synthetic and real-world datasets demonstrate the promise of our method.

Computer Science - Learning

Statistics - Machine Learning

Details

Title: Subtitle: On Column Selection in Approximate Kernel Canonical Correlation Analysis
Creators: Weiran Wang
Resource Type: Preprint
Publication Details: arXiv (Cornell University)
DOI: 10.48550/arxiv.1602.02172
eISSN: 2331-8422
Language: English
Date posted: 02/05/2016
Academic Unit: Computer Science
Record Identifier: 9984696868702771

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