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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.
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