Bayesian lower bounds for dense or sparse (Outlier) noise in the RMT framework
Principal Component Analysis, when formulated as a probabilistic model, can be made robust to outliers by using a Student-t assumption on the noise distribution instead of a Gaussian one. On the other hand, mixtures of PCA is a model aimed to discover nonlinear dependencies in data by finding clusters and identifying local linear submanifolds. This paper shows how mixtures of PCA can be made robust to outliers too. Using a hierarchical probabilistic model, parameters are set by likelihood maximization. The method is shown to be effectively robust to outliers, even in the context of high-dimensional data.