Reduced rank vector generalized linear models for feature extraction

Supervised linear feature extraction can be achieved by fitting a reduced rank multivariate model. This paper studies rank penalized and rank constrained vector generalized linear models. From the perspective of thresholding rules, we build a framework for fitting singular value penalized models and use it for feature extraction. Through solving the rank constraint form of the problem, we propose progressive feature space reduction for fast computation in high dimensions with little performance loss. A novel projective cross-validation is proposed for parameter tuning in such nonconvex setups. Real data applications are given to show the power of the methodology in supervised dimension reduction and feature extraction.

Keywords

reduced rank regression, generalized linear models, feature extraction, projective crossvalidation, progressive dimension reduction

2010 Mathematics Subject Classification

Primary 62H30, 62J12. Secondary 62H12.

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Published 10 May 2013