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arXiv · 1702.04570

Main and Interaction Effects Selection for Quadratic Discriminant Analysis via Penalized Linear Regression

Deqiang Zheng·Jinzhu Jia·Xiangzhong Fang·Xiuhua Guo
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Abstract

Discriminant analysis is a useful classification method. Variable selection for discriminant analysis is becoming more and more im- portant in a high-dimensional setting. This paper is concerned with the binary-class problems of main and interaction effects selection for the quadratic discriminant analysis. We propose a new penalized quadratic discriminant analysis (QDA) for variable selection in binary classification. Under sparsity assumption on the relevant variables, we conduct a penalized liner regression to derive sparse QDA by plug- ging the main and interaction effects in the model. Then the QDA problem is converted to a penalized sparse ordinary least squares op- timization by using the composite absolute penalties (CAP). Coor- dinate descent algorithm is introduced to solve the convex penalized least squares. The penalized linear regression can simultaneously se- lect the main and interaction effects, and also conduct classification. Compared with the existing methods of variable selection in QDA, the extensive simulation studies and two real data analyses demon- strate that our proposed method works well and is robust in the performance of variable selection and classification.

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Deqiang Zheng, Jinzhu Jia, Xiangzhong Fang, Xiuhua Guo. 2017-02-15. Main and Interaction Effects Selection for Quadratic Discriminant Analysis via Penalized Linear Regression. https://arxiv.org/abs/1702.04570

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