A study of several model selection criteria for determining the number of signals

Addressing the problem of detecting the number of source signals as selecting the hidden dimensionality of Factor Analysis (FA) model, we investigate several model selection criteria via a new empirical analyzing tool that examines the joint effect of signal-noise ratio (SNR) and sample size N on the model selection performance. The contours of the model selection accuracies visualize a three-region partition on the space of SNR andN, and a diminishing marginal effect which trades off SNR and N on the performance. Moreover, the newly derived Variational Bayes algorithm and three variants of Bayesian Ying-Yang (BYY) algorithms are more robust against reducing SNR and N, where the BYY with priors´ hyperparameters updated is the best in general.