Probabilistic PCA for t distributions

Principal component analysis (PCA) is a popular technique for dimension reduction. Since the scope of its application is limited by its global linearity, several generalizations are proposed in the literature, among which the probabilistic PCA, introduced recently by Tipping and Bishop, is a particularly important one. Based on a probabilistic model, these authors obtained a PCA type projection from a maximum-likelihood procedure. In this paper, we derive the same type PCA and its mixture for data sampled from multivariate t distributions. Our new dimension reduction tool is theoretically a generalization of the above probabilistic PCA; in practice, it requires smaller model size and has better performance as shown by our experimental results.