Sequentially-fit alternating least squares algorithms in nonnegative matrix factorization

Lorenz, Florian M.

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https://hdl.handle.net/2142/16196 Copy

Description

Title

Sequentially-fit alternating least squares algorithms in nonnegative matrix factorization

Author(s)

Lorenz, Florian M.

Issue Date

2010-05-19T18:40:22Z

Director of Research (if dissertation) or Advisor (if thesis)

• Hubert, Lawrence J.
• Hong, Sungjin

Department of Study

Psychology

Discipline

Psychology

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

M.A.

Degree Level

Thesis

Keyword(s)

• Nonnegative Matrix Factorization (NMF)
• Sequential Fitting (SEFIT)
• Alternating Least Squares (ALS)
• Nonnegative Least Squares (NNLS)

Abstract

Nonnegative matrix factorization (NMF) and nonnegative least squares regression (NNLS regression) are widely used in the physical sciences; this thesis explores the often-overlooked origins of NMF in the psychometrics literature. Another method originating in psychometrics is sequentially-fit factor analysis (SEFIT). SEFIT was used to provide faster solutions to NMF, using both alternating least squares (ALS) with zero-substitution of negative values and NNLS. In a simulation using SEFIT for NMF, differences in fit between the ALS-based solution and the NNLS-based solution were minimal; both solutions were substantially faster than standard whole matrix based approaches to NMF.

Graduation Semester

2010-5

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http://hdl.handle.net/2142/16196

Copyright and License Information

Copyright 2010 Florian Markus Lorenz. All rights reserved.

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