Robust Singular Values based on L1-norm PCA
This work addresses outlier sensitivity in SVD for engineering applications like communication systems and image compression, offering a robust alternative to conventional methods.
The authors tackled the problem of outlier sensitivity in Singular-Value Decomposition (SVD) by proposing L1-cSVD, a robust non-parametric method based on L1-norm PCA, which demonstrates sturdy resistance against outliers for more reliable data analysis.
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.