Robust Singular Values based on L1-norm PCA

TL;DR

This paper introduces L1-cSVD, a robust non-parametric SVD method based on L1-norm PCA, designed to improve resistance to outliers in data analysis tasks across various engineering fields.

Contribution

The paper presents a novel L1-norm based SVD approach that enhances robustness against outliers, addressing limitations of traditional L2-norm PCA-based SVD.

Findings

L1-cSVD shows increased robustness to outliers.

The method improves reliability in data analysis.

Applicable to diverse engineering applications.

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.