Regularisation for PCA- and SVD-type matrix factorisations

2021/06/24 by Abdolrahman Khoshrou, Khoshrou, Abdolrahman, Eric Pauwels +1
Computer Science · Engineering · #Blind Source Separation Techniques #Computational Engineering #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #Finance #Matrix Theory and Algorithms #Sparse and Compressive Sensing Techniques #and Science (cs.CE)

paper · pdf · doi:10.48550/arxiv.2106.12955

openalex publication_date 2021/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Singular Value Decomposition (SVD) and its close relative, Principal Component Analysis (PCA), are well-known linear matrix decomposition techniques that are widely used in applications such as dimension reduction and clustering. However, an important limitation of SVD/PCA is its sensitivity to noise in the input data. In this paper, we take another look at the problem of regularisation and show that different formulations of the minimisation problem lead to qualitatively different solutions.

Citations

• The Approximation of One Matrix by Another of Lower Rank
• Robust principal component analysis?

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