## Theses

#### 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, EMG 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 method for SVD based on a L1-norm (sum of absolute values) formulation, namely L1-norm compact Singular-Value Decomposition (L1-cSVD). We then propose a closed-form algorithm to solve this problem and find the robust singular values with cost $\mathcal{O}(N^3K^2)$. Accordingly, the proposed method demonstrates sturdy resistance against outliers, especially for singular values estimation, and can facilitate more reliable data analysis and processing in a wide range of engineering applications.

4-2022

Thesis

#### Degree Name

Electrical Engineering (MS)

#### Department, Program, or Center

Electrical Engineering (KGCOE)

Panos P. Markopoulos

Sohail A. Dianat