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.
REF introduced a generalization of PCA method to loss function for non real-valued data, such as binary-valued.
A Generalization of Principal Component Analysis to the Exponential Family
Advances in Neural Information Processing Systems
Computer Science