A study of dimensionality reduction as subspace data embedding linked by multidimensional scaling.

Abstract

Some state-of-the-art dimensionality reduction techniques are reviewed and investigated in this thesis. Dimensionality reduction techniques can be catego- rized into two serving different purposes. The first category is to mitigate the computational load and to address the Curse-of-Dimensionality, and the second category is to model the data spread or manifold. ISOMAP and LLE tech- niques are developed for the second purpose, and both of them are embedding techniques. By means of embedding, some data points in a higher dimensional space can be mapped into a lower dimensional space, provided that the pairwise distances are kept unchanged or within a small tolerant range. Some conven- tional category one techniques, such as Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA), are developed from variance analysis, but they also can be interpreted as embedding techniques through links to the metric Multidimensional Scaling (MDS).