Sparse Dimensionality Reduction Methods: Algorithms and Applications

Abstract

In this thesis, we propose some sparse dimensionality reduction methods, which aim to find optimal mappings to project high-dimensional data into low-dimensional spaces and at the same time incorporate sparsity into the mappings. These methods have many applications, including bioinformatics, text processing and computer vision. We address the problem of deriving sparse version of some widely used dimensionality reduction methods, specifically, Linear Discriminant Analysis (LDA), Canonical Correlation Analysis (CCA) and its kernel extension Kernel Canonical Correlation Analysis (kernel CCA). Numerical results with synthetic and real-world data sets validate the efficiency of the proposed methods, and comparison with existing state-of-the-art algorithms shows that our algorithms are competitive.