Robust sparse principal component analysis: situation of full sparseness

IF 0.3 Q4 MATHEMATICS, APPLIED Journal of Applied Mathematics Statistics and Informatics Pub Date : 2022-05-01 DOI:10.2478/jamsi-2022-0001
B. Alkan, I. Ünaldi
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Abstract

Abstract Principal Component Analysis (PCA) is the main method of dimension reduction and data processing when the dataset is of high dimension. Therefore, PCA is a widely used method in almost all scientific fields. Because PCA is a linear combination of the original variables, the interpretation process of the analysis results is often encountered with some difficulties. The approaches proposed for solving these problems are called to as Sparse Principal Component Analysis (SPCA). Sparse approaches are not robust in existence of outliers in the data set. In this study, the performance of the approach proposed by Croux et al. (2013), which combines the advantageous properties of SPCA and Robust Principal Component Analysis (RPCA), will be examined through one real and three artificial datasets in the situation of full sparseness. In the light of the findings, it is recommended to use robust sparse PCA based on projection pursuit in analyzing the data. Another important finding obtained from the study is that the BIC and TPO criteria used in determining lambda are not much superior to each other. We suggest choosing one of these two criteria that give an optimal result.
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鲁棒稀疏主成分分析:全稀疏情况
摘要主成分分析(PCA)是高维数据集降维和数据处理的主要方法。因此,主成分分析是一种在几乎所有科学领域都广泛使用的方法。由于主成分分析是原始变量的线性组合,因此在解释过程中经常会遇到一些困难。为解决这些问题而提出的方法被称为稀疏主成分分析(SPCA)。稀疏方法在数据集中存在异常值的情况下是不稳健的。在本研究中,Croux等人(2013)提出的方法结合了SPCA和鲁棒主成分分析(RPCA)的优势特性,将在完全稀疏的情况下通过一个真实数据集和三个人工数据集来检验该方法的性能。根据研究结果,建议在分析数据时使用基于投影寻踪的稳健稀疏PCA。从该研究中获得的另一个重要发现是,用于确定lambda的BIC和TPO标准并不比其他标准优越多少。我们建议从这两个标准中选择一个,以获得最佳结果。
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0.00%
发文量
8
审稿时长
20 weeks
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