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eRPCA: Robust Principal Component Analysis for Exponential Family Distributions.

Authors :
Zheng, Xiaojun
Mak, Simon
Xie, Liyan
Xie, Yao
Source :
Statistical Analysis & Data Mining. Apr2024, Vol. 17 Issue 2, p1-20. 20p.
Publication Year :
2024

Abstract

Robust principal component analysis (RPCA) is a widely used method for recovering low‐rank structure from data matrices corrupted by significant and sparse outliers. These corruptions may arise from occlusions, malicious tampering, or other causes for anomalies, and the joint identification of such corruptions with low‐rank background is critical for process monitoring and diagnosis. However, existing RPCA methods and their extensions largely do not account for the underlying probabilistic distribution for the data matrices, which in many applications are known and can be highly non‐Gaussian. We thus propose a new method called RPCA for exponential family distributions (eRPCA$$ {e}^{\mathrm{RPCA}} $$), which can perform the desired decomposition into low‐rank and sparse matrices when such a distribution falls within the exponential family. We present a novel alternating direction method of multiplier optimization algorithm for efficient eRPCA$$ {e}^{\mathrm{RPCA}} $$ decomposition, under either its natural or canonical parametrization. The effectiveness of eRPCA$$ {e}^{\mathrm{RPCA}} $$ is then demonstrated in two applications: the first for steel sheet defect detection and the second for crime activity monitoring in the Atlanta metropolitan area. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
19321864
Volume :
17
Issue :
2
Database :
Academic Search Index
Journal :
Statistical Analysis & Data Mining
Publication Type :
Academic Journal
Accession number :
176813020
Full Text :
https://doi.org/10.1002/sam.11670