FAQ

Question: What is Probabilistic PCA, and what is wrong with standard PCA
Answer: Probabilistic PCA (PPCA) is a formulation of PCA that has a clear probabilistic interpretation. It has been proposed by Tipping and Bishop (cf. Tipping et al. 1999) and has later been applied to Statistical Shape Models by Lüthi et al. (cf. Luethi et al. 2009). Standard PCA Models, as they are typically used for shape modeling, only provide a probabilistic interpretation for the PCA space (a hyperplane defined by the example data). The probability of a shape that does not lie on this plane is undefined. In practice, such a shape is assigned the same probability as its projection onto the PCA space, or sometimes even a probability of 0. In Probabilistic PCA, the probability is extended to the whole space, which provides a well defined probability for all the shapes. While the practical differences are minor (in fact, standard PCA is simply a degenerate case of probabilistic PCA), PPCA is conceptually cleaner and greatly simplifies the (probabilistic) reasoning.