This book provides a comprehensive, modern treatment of Principal Component Analysis (PCA) and its robust extensions for high-dimensional data analysis, with a particular emphasis on image data, machine learning (ML) and artificial intelligence (AI) applications, and optimization-based methods. Classical PCA remains a foundational tool for dimensionality reduction, outlier detection, feature extraction, and data image visualization and reconstruction; however, its sensitivity to outliers, noise, missing data, and gross corruption severely limits its applicability in real-world problems. This book addresses these limitations by developing a unified and rigorous framework for Robust PCA and its advanced variants.
The scope of the book spans from classical PCA to state-of-the-art robust low-rank modelling techniques, including Robust PCA with weighted nuclear norm, norm-based robustness, truncated weighted nuclear norm RPCA, and tensor robust PCA for high-dimensional imaging data.. Particular attention is given to ADMM and related optimization strategies that enable scalable solutions for high-dimensional problems.
The core arguments of the book are threefold. First, robustness is essential not optional in modern data analysis, especially for high-dimensional image and tensor data contaminated by outliers, occlusions, and structured noise. Second, carefully incorporated regularization, such as weighted and truncated nuclear norms and structured sparsity via the  norm, substantially improves recovery accuracy and interpretability compared with standard RPCA. Third, many seemingly distinct methods in machine learning and AI, and low-rank modelling can be understood within a unified optimization framework, enabling principled algorithm design and theoretical insight.

Habte Tadesse Likassa is an Assistant Professor in the College of Health Solutions at Arizona State University, United States. He also serves as an Extraordinary Assistant Professor at the University of South Africa (UNISA) and is affiliated with the Department of Statistics at Addis Ababa University. He previously served at Ambo University; both institutions are in Ethiopia.
Habte Tadesse Likassa’s current research focuses on developing statistical methods and tools, with an emphasis on low-rank and sparse methods. He applies these methods to medical imaging data for the detection of diseases such as cancer, cataracts, glaucoma, and Alzheimer’s disease. His methods are also applied to natural image data for crime detection and security applications. He is also interested in modern robust statistics and in applying existing statistical methods to a wide range of real-world datasets.
His work has been published in reputable journals in the field.

Ding-Geng Chen is a Professor of Biostatistics and Executive Director in the College of Health Solutions at Arizona State University and an internationally recognized researcher in statistical methodology, biostatistics, and data science. His research interests include robust statistical methods, longitudinal and multivariate analysis, high-dimensional data modelling, and computational statistics, with broad applications in health sciences and interdisciplinary research. Dr. Chen has an extensive publication record, having authored and co-authored numerous peer-reviewed journal articles, books, and book chapters in leading statistical and applied journals. He has also served as an editor and editorial board member for several professional journals and has played a significant role in advancing methodological research and graduate education in statistics and biostatistics.