Sparse multivariate analyses via ℓ1-regularized optimization problems solved with Bregman Iterative Techniques
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In this dissertation we propose Split Bregman algorithms for several multivariate analytic techniques for dimensionality reduction and feature selection including Sparse Principal Components Analysis, Bisparse Singular Value Decomposition (BSSVD) and Bisparse Singular Value Decomposition with an ℓ1-constrained classifier BSSVDℓ1. For each of these problems we construct and solve a new optimization problem using these Bregman iterative techniques. Each of the proposed optimization problems contain one or more ℓ1-regularization terms to enforce sparsity in the solutions. The use of the ℓ1-norm to ...