We propose a robust and sparse classification method based on the optimal scoring approach. It is also applicable if the number of variables exceeds the number of observations. The data are first projected into a low dimensional subspace according to an optimal scoring criterion. The projection only includes a subset of the original variables (sparse modeling) and is not distorted by outliers (robust modeling). In this low dimensional subspace classification is performed by minimizing a robust Mahalanobis distance to the group centers. The low dimensional representation of the data is also useful for visualization purposes. We discuss the algorithm for the proposed method in detail. A simulation study illustrates the properties of robust and sparse classification by optimal scoring compared to the non-robust and/or non-sparse alternative methods. Three real data applications are given.

中文翻译：

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通过最佳评分方法进行鲁棒且稀疏的多组分类

我们提出了一种基于最佳评分方法的鲁棒且稀疏的分类方法。如果变量数量超过观察数量，则也适用。首先根据最佳评分标准将数据投影到低维子空间中。投影仅包含原始变量的一个子集（稀疏建模），而不受异常值影响（稳健建模）。在这种低维子空间分类中，通过最小化到群体中心的鲁棒马氏距离进行分类。数据的低维表示形式也可用于可视化目的。我们将详细讨论所提出方法的算法。仿真研究通过与非健壮和/或非稀疏替代方法相比，通过最佳评分说明了健壮和稀疏分类的属性。