New optimization approaches to matrix factorization problems with connections to natural language processing

In this thesis, we propose novel formulation optimization methods for four matrix factorization problems in depth: sparse principal component analysis, compressed sensing, discrete component analysis, and latent Dirichlet allocation. For each new formulations, we develop efficient solution algorithms using discrete and robust optimization, and demonstrate tractability and effectiveness in computational experiments. In Chapter 1, we develop a framework for matrix factorization problems and provide a technical introduction to topic modeling with examples. Chapter 2, Certifiably optimal sparse principal component analysis, addresses the sparse principal component analysis (SPCA) problem. We propose a tailored branch-and- bound algorithm, Optimal-SPCA, that enables us to solve SPCA to certifiable optimality.

Name thesis:degree_name

Doctoral

Department dc:contributor.department

Massachusetts Institute of Technology. Operations Research Center

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2020

Author dc:creator

• Berk, Lauren Elizabeth.

Advisor dc:contributor.advisor

• Robert Freund.

• Operations Research Center.

Statement dc:rights

• MIT theses may be protected by copyright. Please reuse MIT thesis content according to the MIT Libraries Permissions Policy, which is available through the URL provided.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/127291

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/127291