A generalization of principal component analysis to the exponential family

Michael Collins; Sanjoy Dasgupta; Robert E. Schapire

A generalization of principal component analysis to the exponential family

Michael Collins, Sanjoy Dasgupta, Robert E. Schapire

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

Principal component analysis (PCA) is a commonly applied technique for dimensionality reduction. PCA implicitly minimizes a squared loss function, which may be inappropriate for data that is not real-valued, such as binary-valued data. This paper draws on ideas from the Exponential family, Generalized linear models, and Bregman distances, to give a generalization of PCA to loss functions that we argue are better suited to other data types. We describe algorithms for minimizing the loss functions, and give examples on simulated data.

Original language	English (US)
Title of host publication	Advances in Neural Information Processing Systems 14 - Proceedings of the 2001 Conference, NIPS 2001
Publisher	Neural information processing systems foundation
ISBN (Print)	0262042088, 9780262042086
State	Published - 2002
Externally published	Yes
Event	15th Annual Neural Information Processing Systems Conference, NIPS 2001 - Vancouver, BC, Canada Duration: Dec 3 2001 → Dec 8 2001

Publication series

Name	Advances in Neural Information Processing Systems
ISSN (Print)	1049-5258

Other

Other	15th Annual Neural Information Processing Systems Conference, NIPS 2001
Country/Territory	Canada
City	Vancouver, BC
Period	12/3/01 → 12/8/01

All Science Journal Classification (ASJC) codes

Computer Networks and Communications
Information Systems
Signal Processing

Cite this

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title = "A generalization of principal component analysis to the exponential family",

abstract = "Principal component analysis (PCA) is a commonly applied technique for dimensionality reduction. PCA implicitly minimizes a squared loss function, which may be inappropriate for data that is not real-valued, such as binary-valued data. This paper draws on ideas from the Exponential family, Generalized linear models, and Bregman distances, to give a generalization of PCA to loss functions that we argue are better suited to other data types. We describe algorithms for minimizing the loss functions, and give examples on simulated data.",

author = "Michael Collins and Sanjoy Dasgupta and Schapire, {Robert E.}",

year = "2002",

language = "English (US)",

isbn = "0262042088",

series = "Advances in Neural Information Processing Systems",

publisher = "Neural information processing systems foundation",

booktitle = "Advances in Neural Information Processing Systems 14 - Proceedings of the 2001 Conference, NIPS 2001",

note = "15th Annual Neural Information Processing Systems Conference, NIPS 2001 ; Conference date: 03-12-2001 Through 08-12-2001",

}

Collins, M, Dasgupta, S & Schapire, RE 2002, A generalization of principal component analysis to the exponential family. in Advances in Neural Information Processing Systems 14 - Proceedings of the 2001 Conference, NIPS 2001. Advances in Neural Information Processing Systems, Neural information processing systems foundation, 15th Annual Neural Information Processing Systems Conference, NIPS 2001, Vancouver, BC, Canada, 12/3/01.

A generalization of principal component analysis to the exponential family. / Collins, Michael; Dasgupta, Sanjoy; Schapire, Robert E.
Advances in Neural Information Processing Systems 14 - Proceedings of the 2001 Conference, NIPS 2001. Neural information processing systems foundation, 2002. (Advances in Neural Information Processing Systems).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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T1 - A generalization of principal component analysis to the exponential family

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AU - Dasgupta, Sanjoy

AU - Schapire, Robert E.

PY - 2002

Y1 - 2002

N2 - Principal component analysis (PCA) is a commonly applied technique for dimensionality reduction. PCA implicitly minimizes a squared loss function, which may be inappropriate for data that is not real-valued, such as binary-valued data. This paper draws on ideas from the Exponential family, Generalized linear models, and Bregman distances, to give a generalization of PCA to loss functions that we argue are better suited to other data types. We describe algorithms for minimizing the loss functions, and give examples on simulated data.

AB - Principal component analysis (PCA) is a commonly applied technique for dimensionality reduction. PCA implicitly minimizes a squared loss function, which may be inappropriate for data that is not real-valued, such as binary-valued data. This paper draws on ideas from the Exponential family, Generalized linear models, and Bregman distances, to give a generalization of PCA to loss functions that we argue are better suited to other data types. We describe algorithms for minimizing the loss functions, and give examples on simulated data.

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M3 - Conference contribution

AN - SCOPUS:84899014910

SN - 0262042088

SN - 9780262042086

T3 - Advances in Neural Information Processing Systems

BT - Advances in Neural Information Processing Systems 14 - Proceedings of the 2001 Conference, NIPS 2001

PB - Neural information processing systems foundation

T2 - 15th Annual Neural Information Processing Systems Conference, NIPS 2001

Y2 - 3 December 2001 through 8 December 2001

ER -

A generalization of principal component analysis to the exponential family

Abstract

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All Science Journal Classification (ASJC) codes

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