EM algorithms for PCA and SPCA
NIPS '97 Proceedings of the 1997 conference on Advances in neural information processing systems 10
Mixtures of probabilistic principal component analyzers
Neural Computation
Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications
Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications
Robust probabilistic projections
ICML '06 Proceedings of the 23rd international conference on Machine learning
Pattern Recognition and Machine Learning (Information Science and Statistics)
Pattern Recognition and Machine Learning (Information Science and Statistics)
A note on variational Bayesian factor analysis
Neural Networks
Practical Approaches to Principal Component Analysis in the Presence of Missing Values
The Journal of Machine Learning Research
Robust principal component analysis?
Journal of the ACM (JACM)
Bayesian Robust Principal Component Analysis
IEEE Transactions on Image Processing
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We present a probabilistic model for robust factor analysis and principal component analysis in which the observation noise is modeled by Student-t distributions in order to reduce the negative effect of outliers. The Student-t distributions are modeled independently for each data dimensions, which is different from previous works using multivariate Student-t distributions. We compare methods using the proposed noise distribution, the multivariate Student-t and the Laplace distribution. Intractability of evaluating the posterior probability density is solved by using variational Bayesian approximation methods. We demonstrate that the assumed noise model can yield accurate reconstructions because corrupted elements of a bad quality sample can be reconstructed using the other elements of the same data vector. Experiments on an artificial dataset and a weather dataset show that the dimensional independency and the flexibility of the proposed Student-t noise model can make it superior in some applications.