High-dimensional Data Analysis

High-dimensional data are everywhere: texts, sounds, spectra, images, etc. However, many data analysis tools (coming from statistics, artificial intelligence, etc.) were designed for low-dimensional data. Many of the assumptions behind data analysis tools are not transposable to high-dimensional data. For instance, the Euclidean distance concentrates in high-dimensional spaces; all distances seem identical! It furthermore does not distinguish between relenvant and irrelevant features. In Part One of the book, the phenomenon of the concentration of the distances is considered, and its consequences on data analysis tools are studied. Part Two focuses on the problem of feature selection in the case of a large number of initial features. Most of the concepts studied and presented in this thesis are illustrated on chemometric data, and more particularly on spectral data, with the objective of inferring a physical or chemical property of a material by analysis the spectrum of the light it reflects.