Multivariate Data Analysis on Matrix Manifolds

Nickolay T. Trendafilov is Reader of Computational Statistics in the School of Mathematics and Statistics, Open University, UK. He received MSc and PhD in the Department of Mathematics and Informatics, University of Sofia “St. Kl. Ohridski”, and then joined the Laboratory of Computational Stochastic, Bulgarian Academy of Sciences. He held research and visiting positions in a number of universities in Belgium, Italy, Japan and USA. His interests are in the computational aspects of multivariate data analysis and interpretation. Other activities include elected memberships in the International Statistical Institute (ISI), the Royal Statistical Society's (RSS) Computing Section, and the Board of Directors, European Regional Section of the International Association for Statistical Computing (IASC). Michele Gallo is Professor in the Department of Human and Social Sciences at the University of Naples – L’Orientale. He received his PhD degree in Total Quality Management from the University of Naples – Federico II, in 2000. His current research interest is in Multivariate Data Analysis, Compositional and Ordinal Data, Rasch Analysis. He has published more than 90 research articles. He is Associate-Editor of the journal Computational Statistics.

• Introduction.- Matrix analysis and differentiation.- Matrix manifolds in MDA.- Principal component analysis (PCA).- Factor analysis (FA).- Procrustes analysis (PA).- Linear discriminant analysis (LDA).- Canonical correlation analysis (CCA).- Common principal components (CPC).- Metric multidimensional scaling (MDS) and related methods.- Data analysis on simplexes.