A Generalization of Principal Components 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 Exponen- tial 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 func- tions, and give examples on simulated data.

Cite

Text

Collins et al. "A Generalization of Principal Components Analysis to the Exponential Family." Neural Information Processing Systems, 2001.

Markdown

[Collins et al. "A Generalization of Principal Components Analysis to the Exponential Family." Neural Information Processing Systems, 2001.](https://mlanthology.org/neurips/2001/collins2001neurips-generalization/)

BibTeX

@inproceedings{collins2001neurips-generalization,
  title     = {{A Generalization of Principal Components Analysis to the Exponential Family}},
  author    = {Collins, Michael and Dasgupta, S. and Schapire, Robert E.},
  booktitle = {Neural Information Processing Systems},
  year      = {2001},
  pages     = {617-624},
  url       = {https://mlanthology.org/neurips/2001/collins2001neurips-generalization/}
}