Influence function and robust variant of kernel canonical correlation analysis

NEUROCOMPUTING

卷:304

Article

Alam, Md Ashad^1,3  Fukumizu, Kenji²  Wang, Yu-Ping¹ 

[1] Tulane Univ, Dept Biomed Engn, New Orleans, LA 70118 USA

[2] Inst Stat Math, Tachikawa, Tokyo 1908562, Japan

[3] Hajee Mohammad Danesh Sci & Technol Univ, Dept Stat, Dinajpur 5200, Bangladesh

关键词: Robustness;    Influence function;    Kernel (coss-) covariance operator;    Kernel methods;    Imaging genetics analysis;   

DOI  :  10.1016/j.neucom.2018.04.008

来源: Elsevier

【 摘 要 】

Many unsupervised kernel methods rely on the estimation of kernel covariance operator (kernel CO) or kernel cross-covariance operator (kernel CCO). Both are sensitive to contaminated data, even when bounded positive definite kernels are used. To the best of our knowledge, there are few well-founded robust kernel methods for statistical unsupervised learning. In addition, while the influence function (IF) of an estimator can characterize its robustness, asymptotic properties and standard error, the IF of a standard kernel canonical correlation analysis (standard kernel CCA) has not been derived yet. To fill this gap, we first propose a robust kernel covariance operator (robust kernel CO) and a robust kernel cross-covariance operator (robust kernel CCO) based on a generalized loss function instead of the quadratic loss function. Second, we derive the IF for robust kernel CCO and standard kernel CCA. Using the IF of the standard kernel CCA, we can detect influential observations from two sets of data. Finally, we propose a method based on the robust kernel CO and the robust kernel CCO, called robust kernel CCA, which is less sensitive to noise than the standard kernel CCA. The introduced principles can also be applied to many other kernel methods involving kernel CO or kernel CCO. Our experiments on both synthesized and imaging genetics data demonstrate that the proposed IF of standard kernel CCA can identify outliers. It is also seen that the proposed robust kernel CCA method performs better for ideal and contaminated data than the standard kernel CCA. (c) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

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