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/}
}