A central issue in principal component analysis(PCA) is to choose the number of principal components to retain.However,most studies assume a known dimension or determine it heuristically,though there are a number of model selection criteria.In this paper,the probabilistic reformulation of PCA is used and a model selection criterion to determine the intrinsic dimensionality of data including Akaike′s information criterion(AIC),the consistent Akaika′s information criterion(CAIC),and the Bayesian i...