This book reports on the latest advances in concepts and further development of principal component analysis (PCA), discussing in detail a number of open problems related to dimensional reduction techniques and their extensions. It brings together research findings, previously scattered throughout many scientific journal papers worldwide, and presents them in a methodologically unified form. Offering vital insights into the subject matter in self-contained chapters that balance the theory and concrete applications, and focusing on open problems, it is essential reading for all researchers and practitioners with an interest in PCA.