Robust Singular Values based on L1-norm PCA

Duc Le; Panos P. Markopoulos

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arXiv · 2210.12097

Robust Singular Values based on L1-norm PCA

Duc Le·Panos P. Markopoulos

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Abstract

Singular-Value Decomposition (SVD) is a ubiquitous data analysis method in engineering, science, and statistics. Singular-value estimation, in particular, is of critical importance in an array of engineering applications, such as channel estimation in communication systems, electromyography signal analysis, and image compression, to name just a few. Conventional SVD of a data matrix coincides with standard Principal-Component Analysis (PCA). The L2-norm (sum of squared values) formulation of PCA promotes peripheral data points and, thus, makes PCA sensitive against outliers. Naturally, SVD inherits this outlier sensitivity. In this work, we present a novel robust non-parametric method for SVD and singular-value estimation based on a L1-norm (sum of absolute values) formulation, which we name L1-cSVD. Accordingly, the proposed method demonstrates sturdy resistance against outliers and can facilitate more reliable data analysis and processing in a wide range of engineering applications.

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Duc Le, Panos P. Markopoulos. 2022-10-21. Robust Singular Values based on L1-norm PCA. https://arxiv.org/abs/2210.12097

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