Abstract
Optimal scoring (OS), an equivalent form of linear discriminant analysis (LDA), is an important supervised learning method and dimensionality reduction tool. However, it is still a challenge for the classical OS on small sample size (SSS) datasets. In this paper, to find sparse discriminant vectors, we propose a unified model for sparse optimal scoring (SOS) by virtue of the generalized ℓq-norm (0≤q≤1). To overcome the difficulty in treating the generalized ℓq-norm, we propose an efficient alternative direction method of multipliers (ADMM), where proximity operator of ℓq-norm is employed for different q values. Meanwhile, the convergence results of our method are also established. Numerical experiments on artificial and benchmark datasets demonstrate the effectiveness and feasibility of our proposed method.
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