Robust Principal Component Analysis Using Statistical Estimators

TL;DR

This paper introduces a robust PCA method that employs statistical estimators like median and Huber M-estimator to effectively handle outliers, improving accuracy and reducing computational cost compared to traditional PCA and Kernel PCA.

Contribution

The paper presents a novel robust PCA technique using statistical estimators to enhance outlier resistance and computational efficiency over existing methods.

Findings

Outperforms traditional PCA in outlier handling.

Achieves comparable accuracy to Kernel PCA with lower computation.

Effective on multiple real-world datasets.

Abstract

Principal Component Analysis (PCA) finds a linear mapping and maximizes the variance of the data which makes PCA sensitive to outliers and may cause wrong eigendirection. In this paper, we propose techniques to solve this problem; we use the data-centering method and reestimate the covariance matrix using robust statistic techniques such as median, robust scaling which is a booster to data-centering and Huber M-estimator which measures the presentation of outliers and reweight them with small values. The results on several real world data sets show that our proposed method handles outliers and gains better results than the original PCA and provides the same accuracy with lower computation cost than the Kernel PCA using the polynomial kernel in classification tasks.