While linear discriminant analysis (LDA) is a widely used classification method, it is highly affected by outliers which commonly occur in various real datasets. Therefore, several robust LDA methods have been proposed. However, they either rely on robust estimation of the sample means and covariance matrix which may have noninvertible Hessians or can only handle binary classes or low dimensional cases. The proposed robust discriminant analysis is a multi-directional projection-pursuit approach which can classify multiple classes without estimating the covariance or Hessian matrix and work for high dimensional cases. The weight function effectively gives smaller weights to the points more deviant from the class center. The discriminant vectors and scoring vectors are solved by the proposed iterative algorithm. It inherits good properties of the weight function and multi-directional projection pursuit for reducing the influence of outliers on estimating the discriminant directions and producing robust classification which is less sensitive to outliers. We show that when a weight function is appropriately chosen, then the influence function is bounded and discriminant vectors and scoring vectors are both consistent as the percentage of outliers goes to zero. The experimental results show that the robust optimal scoring discriminant analysis is effective and efficient.

尽管线性判别分析（LDA）是一种广泛使用的分类方法，但它受到异常值的强烈影响，这些异常值通常出现在各种实际数据集中。因此，已经提出了几种鲁棒的LDA方法。但是，它们要么依赖于对样本均值和协方差矩阵的稳健估计，而后者可能具有不可逆的Hessian或只能处理二进制类或低维情况。提出的鲁棒判别分析是一种多方向投影－追踪方法，可以在不估计协方差或Hessian矩阵的情况下对多个类别进行分类，并且适用于高维情况。权重函数有效地将较小的权重赋予与班级中心更偏离的点。通过所提出的迭代算法来求解判别向量和得分向量。它继承了权重函数和多方向投影追踪的良好特性，可减少离群值对判别方向的影响，并产生对离群值不敏感的可靠分类。我们表明，当一个权重函数进行适当的选择，那么影响函数是有界和判别向量和得分向量都一致为异常的比例变为零。实验结果表明，鲁棒的最优评分判别分析是有效的。然后影响函数是有界的，当离群值的百分比变为零时，判别向量和评分向量都一致。实验结果表明，鲁棒的最优评分判别分析是有效的。然后影响函数是有界的，当离群值的百分比变为零时，判别向量和评分向量都一致。实验结果表明，鲁棒的最优评分判别分析是有效的。