ML Anthology

EM Algorithms for PCA and SPCA

Sam T. Roweis
NeurIPS 1997 pp. 626-632
/neurips/1997/roweis1997neurips-em/

Abstract

I present an expectation-maximization (EM) algorithm for principal component analysis (PCA). The algorithm allows a few eigenvectors and eigenvalues to be extracted from large collections of high dimensional data. It is computationally very efficient in space and time. It also natu(cid:173) rally accommodates missing infonnation. I also introduce a new variant of PC A called sensible principal component analysis (SPCA) which de(cid:173) fines a proper density model in the data space. Learning for SPCA is also done with an EM algorithm. I report results on synthetic and real data showing that these EM algorithms correctly and efficiently find the lead(cid:173) ing eigenvectors of the covariance of datasets in a few iterations using up to hundreds of thousands of datapoints in thousands of dimensions.

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Text

Roweis. "EM Algorithms for PCA and SPCA." Neural Information Processing Systems, 1997.

Markdown

[Roweis. "EM Algorithms for PCA and SPCA." Neural Information Processing Systems, 1997.](https://mlanthology.org/neurips/1997/roweis1997neurips-em/)

BibTeX

@inproceedings{roweis1997neurips-em,
  title     = {{EM Algorithms for PCA and SPCA}},
  author    = {Roweis, Sam T.},
  booktitle = {Neural Information Processing Systems},
  year      = {1997},
  pages     = {626-632},
  url       = {https://mlanthology.org/neurips/1997/roweis1997neurips-em/}
}