Abstract
SUMMARYSufficient dimension reduction is popular for reducing data dimensionality without stringent model assumptions. However, most existing methods may work poorly for binary classification. For example, sliced inverse regression (Li, 1991) can estimate at most one direction if the response is binary. In this paper we propose principal weighted support vector machines, a unified framework for linear and nonlinear sufficient dimension reduction in binary classification. Its asymptotic properties are studied, and an efficient computing algorithm is proposed. Numerical examples demonstrate its performance in binary classification.
Highlights
Increasing data dimension can pose challenges at various stages of a statistical analysis
We focus on sufficient dimension reduction in binary classification
For model (i), SY |X forms a line since k = 1, and the angles between the estimated and true SY |X are reported as 0·12 and 0·08 radians for sliced inverse regression and the principal weighted support vector machine, respectively
Summary
Increasing data dimension can pose challenges at various stages of a statistical analysis. In the sufficient dimension reduction literature, many estimators rely on inverse regression, whose target is functionals of X given Y They may suffer in binary classification due to the insufficient information provided by the binary response. For model (i), SY |X forms a line since k = 1, and the angles between the estimated and true SY |X are reported as 0·12 and 0·08 radians for sliced inverse regression and the principal weighted support vector machine, respectively. Both approaches perform well in this case, with the principal weighted support vector machine being slightly better. We provide the corresponding 360◦ rotation animation in the Supplementary Material
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