A generalization of principal component analysis to the exponential family

Michael Collins, Sanjoy Dasgupta, Robert E. Schapire

Research output: Chapter in Book/Report/Conference proceedingConference contribution

126 Scopus citations

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 languageEnglish (US)
Title of host publicationAdvances in Neural Information Processing Systems 14 - Proceedings of the 2001 Conference, NIPS 2001
PublisherNeural information processing systems foundation
ISBN (Print)0262042088, 9780262042086
StatePublished - Jan 1 2002
Externally publishedYes
Event15th Annual Neural Information Processing Systems Conference, NIPS 2001 - Vancouver, BC, Canada
Duration: Dec 3 2001Dec 8 2001

Publication series

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

Other

Other15th Annual Neural Information Processing Systems Conference, NIPS 2001
CountryCanada
CityVancouver, BC
Period12/3/0112/8/01

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing

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  • Cite this

    Collins, M., Dasgupta, S., & Schapire, R. E. (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.