L1-norm projection pursuit principal component analysis
L1-norm projection pursuit principal component analysis
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DOI：
10.1016/j.csda.2005.01.009
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发表时间：
2006-03-10
影响因子：
1.8
通讯作者：
Choulakian, V
中科院分区：
文献类型：
--
作者：
Choulakian, V
我们开发了一种基于 L-1 范数投影追踪方法的鲁棒主成分分析新方法。本文的目的有三个。首先，我们提出了基本的数学理论，并表明它与计算主成分的旧质心方法密切相关。其次，我们提出三种算法来执行所需的计算。第三，我们使用Benzecri对主轴上点影响的几何相对测度来定义异常值识别的切点，并迭代地使用它来消除异常值并获得鲁棒的L-1范数投影追踪主成分。提供了两个众所周知的数据集的例子。 (c) 2005 Elsevier B.V. 保留所有权利。
We develop a new method of robust principal component analysis based on the L-1-norm projection pursuit approach. The aim of the paper is threefold. First, we present the underlying mathematical theory and show that it is closely related to the old centroid method of calculating principal components. Second, we present three algorithms to perform the required calculations. Third, we use Benzecri's geometric relative measure of the influence of a point on a principal axis to define cutpoints for the identification of outliers, and iteratively use it to eliminate outliers and obtain robust L-1-norm projection pursuit principal components. Two examples of well-known data sets are provided. (c) 2005 Elsevier B.V. All rights reserved.