Date of Award

2022

Document Type

Masters Thesis

Degree Name

M.S.

Organizational Unit

Daniel Felix Ritchie School of Engineering and Computer Science, Electrical and Computer Engineering

First Advisor

Zhihui Zhu

Second Advisor

Margareta Stefanovic

Third Advisor

Rui Fan

Fourth Advisor

Mei Yin

Keywords

Electrical engineering

Abstract

Efficiently computing an (approximate) orthonormal basis and low-rank approximation for the input data X plays a crucial role in data analysis. One of the most efficient algorithms for such tasks is the randomized algorithm, which proceeds by computing a projection XA with a random projection matrix A of much smaller size, and then computing the orthonormal basis as well as low-rank factorizations of the tall matrix XA. While a random matrix A is the de facto choice, in this work, we improve upon its performance by utilizing a learning approach to find an adaptive projection matrix A from a set of training data. We derive a closed-form formulation for the gradient of the training problem, enabling us to use efficient gradient-based algorithms. Experiments show that the learned dense matrix trained by eight different objective functions achieves better performance than a random one. We also extend this approach for learning structured projection matrix, such as the sketching matrix that performs as selecting a few number of representative columns from the input data. Our experiments on both synthetical and real data show that both learned dense and sketch projection matrices outperform the random ones in finding the approximate orthonormal basis and low-rank approximations. We conclude the thesis by discussing possible approaches for generalization analysis.

Publication Statement

Copyright is held by the author. User is responsible for all copyright compliance.

Rights Holder

Haiyan Yu

Provenance

Received from ProQuest

File Format

application/pdf

Language

en

File Size

52 pgs

Discipline

Electrical engineering

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