Generalized low rank models

Abstract/Contents

Abstract

Principal components analysis (PCA) is a well-known technique for approximating a tabular data set by a low rank matrix. This dissertation extends the idea of PCA to handle arbitrary data sets consisting of numerical, Boolean, categorical, ordinal, and other data types. This framework encompasses many well known techniques in data analysis, such as nonnegative matrix factorization, matrix completion, sparse and robust PCA, k-means, k-SVD, and maximum margin matrix factorization. The method handles heterogeneous data sets, and leads to coherent schemes for compressing, denoising, and imputing missing entries across all data types simultaneously. It also admits a number of interesting interpretations of the low rank factors, which allow clustering of examples or of features. We propose several parallel algorithms for fitting generalized low rank models, and describe implementations and numerical results.

Description

Type of resource	text
Form	electronic; electronic resource; remote
Extent	1 online resource.
Publication date	2015
Issuance	monographic
Language	English

Creators/Contributors

Associated with	Udell, Madeleine
Associated with	Stanford University, Institute for Computational and Mathematical Engineering.
Primary advisor	Boyd, Stephen P
Thesis advisor	Boyd, Stephen P
Thesis advisor	Mackey, Lester
Thesis advisor	Van Roy, Benjamin
Advisor	Mackey, Lester
Advisor	Van Roy, Benjamin

Subjects

Genre	Theses

Bibliographic information

Statement of responsibility	Madeleine Udell.
Note	Submitted to the Institute for Computational and Mathematical Engineering.
Thesis	Thesis (Ph.D.)--Stanford University, 2015.
Location	electronic resource

Access conditions

Copyright

© 2015 by Madeleine Richards Udell

License

This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).

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