Linear Dimensionality Reduction

These notes are an overview of some classical linear methods in Multivariate Data Analysis. This is an good old domain, well established since the 60's, and refreshed timely as a key step in statistical learning. It can be presented as part of statistical learning, or as dimensionality reduction with a geometric flavor. Both approaches are tightly linked: it is easier to learn patterns from data in low dimensional spaces than in high-dimensional spaces. It is shown how a diversity of methods and tools boil down to a single core methods, PCA with SVD, such that the efforts to optimize codes for analyzing massive data sets can focus on this shared core method, and benefit to all methods. An extension to the study of several arrays is presented (Canonical Analysis).