Robust PCA: Optimization of the Robust Reconstruction Error over the\n Stiefel Manifold

2015/05/31 by Anastasia Podosinnikova, Podosinnikova, Anastasia, Simon Setzer +3
Computer Science · Engineering · #Anomaly Detection Techniques and Applications #Blind Source Separation Techniques #FOS: Computer and information sciences #Industrial Vision Systems and Defect Detection #Machine Learning (cs.LG) #Machine Learning (stat.ML)

paper · pdf · doi:10.48550/arxiv.1506.00323

openalex publication_date 2015/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is well known that Principal Component Analysis (PCA) is strongly affected\nby outliers and a lot of effort has been put into robustification of PCA. In\nthis paper we present a new algorithm for robust PCA minimizing the trimmed\nreconstruction error. By directly minimizing over the Stiefel manifold, we\navoid deflation as often used by projection pursuit methods. In distinction to\nother methods for robust PCA, our method has no free parameter and is\ncomputationally very efficient. We illustrate the performance on various\ndatasets including an application to background modeling and subtraction. Our\nmethod performs better or similar to current state-of-the-art methods while\nbeing faster.\n

Related

• Robust Orthogonal Complement Principal Component Analysis
• Robust PCA by Manifold Optimization
• Cellwise robust and sparse principal component analysis
• Pseudo-Bayesian Robust PCA: Algorithms and Analyses
• Robust Principal Component Analysis: A Construction Error Minimization Perspective