EM algorithms for PCA and SPCA
NIPS '97 Proceedings of the 1997 conference on Advances in neural information processing systems 10
Proceedings of the 1998 conference on Advances in neural information processing systems II
Proceedings of the 24th international conference on Machine learning
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PCA can be smarter and makes more sensible projections. In this paper, we propose smart PCA, an extension to standard PCA to regularize and incorporate external knowledge into model estimation. Based on the probabilistic interpretation of PCA, the inverse Wishart distribution can be used as the informative conjugate prior for the population covariance, and useful knowledge is carried by the prior hyperparameters. We design the hyperparameters to smoothly combine the information from both the domain knowledge and the data itself. The Bayesian point estimation of principal components is in closed form. In empirical studies, smart PCA shows clear improvement on three different criteria: image reconstruction errors, the perceptual quality of the reconstructed images, and the pattern recognition performance.