Christopher G. Baker
MSc Computer Science

A Block Incremental Algorithm for Computing Dominant Singular Subspaces

The Singular Value Decomposition is one of the most useful matrix decompositions, having applications in virtually every scientific and engineering discipline. However, its computation is expensive, prohibiting its use for many large problems. Incremental methods help to lessen this cost by processing the data in groups of vectors, computing an approximation of the dominant singular value decomposition.

My research unifies the previous methods incremental methods for tracking dominant singular subspaces. This general presentation exposes a new algorithm, with a lower complexity and better runtime performance than previous methods, over a broader range of algorithm parameters. I also explore the effect of block size on accuracy of the method. I propose "second pass" algorithms. These techniques improve the approximation to the dominant SVD computed by incremental algorithms by making multiple passes through the data. Finally, I explore the application of the proposed algorithms to a problem in face recognition and image compression.

Courses taken outside of major
Numerical Linear Algebra I, II
Computational Methods in Statistics I, II
Quantum Computation
Scientific Visualization
Photorealistic Computer Graphics

Florida State University