稳健稀疏主成分分析法及其实证研究

Robust Sparce Principal Component Analysis and Its Empirical Study

主成分分析是多元统计分析中一种非常经典的降维技术。然而,经典主成分分析却是对离群值非常敏感的,常因离群值的存在导致结果与实际不相符。另一方面,当主成分分析用于综合评价时,主成分的含义常因载荷间绝对值大小不分明而含糊不清,从而导致综合评价难以展开。本文通过使用稳健稀疏主成分分析法进行模拟实验和实证分析,结果表明:该方法不仅能很好地抵抗离群值的影响,而且还能准确地识别出离群样本。通过该方法得出的主成分的含义也较经典主成分分析和稳健主成分分析更加地明确和贴近实际。

Principal component analysis(PCA) is a classical dimensionality reduction method in multivariable analysis.However,classical PCA is so sensitive to outliers that usually the results are not in line with the reality.Besides,when PCA is applied to overall evaluation,the meanings of principal components are confusing for the absolute values of big loadings and small loadings being too close.This makes it difficult to do overall evaluation.In this paper,simulations and empirical study on the robust sparse principal component analysis are conducted,the results of which show that this method is highly resistant to outliers and is able to detect the outlying samples precisely.Also,by applying this method,the meanings of the principal components are more clear and fit the reality better,compared to classical PCA and robust PCA.