Robust discriminant analysis using multi-directional projection pursuit

Robust discriminant analysis using multi-directional projection pursuit
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DOI：
10.1016/j.patrec.2020.09.013
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发表时间：
2020-09
期刊：
Pattern Recognit. Lett.
影响因子：
--
通讯作者：
Hsin-Hsiung Huang;Teng Zhang
Hsin-Hsiung Huang;Teng Zhang
中科院分区：
其他
文献类型：
--
作者：
Hsin-Hsiung Huang;Teng Zhang

文献摘要

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线性判别分析（LDA）是一种应用广泛的分类方法，但它受离群值的影响很大，离群值在各种真实数据集中都很常见。因此，提出了几种鲁棒LDA方法。然而，它们要么依赖于样本均值和协方差矩阵的鲁棒估计，这些估计可能具有不可逆的Hessians，要么只能处理二分类或低维情况。所提出的鲁棒判别分析是一种多向投影-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。权重函数有效地给偏离类中心的点更小的权重。判别向量和评分向量采用迭代算法求解。它继承了权函数和多向投影追踪的良好特性，降低了异常值对判别方向估计的影响，实现了对异常值不敏感的鲁棒分类。我们表明，当适当选择权重函数时，则影响函数是有界的，并且随着离群值的百分比趋于零，判别向量和评分向量都是一致的。实验结果表明，鲁棒最优评分判别分析是有效的。
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.