Determining the number of components in a factor model from limited noisy data

Determining the number of components in a linear mixture model is a fundamental problem in many scientific fields, including chemometrics and signal processing. In this paper we present a new method to automatically determine the number of components from a limited number of (possibly) high dimensional noisy samples. The proposed method, based on the eigenvalues of the sample covariance matrix, combines a matrix perturbation approach for the interaction of signal and noise eigenvalues, with recent results from random matrix theory regarding the behavior of noise eigenvalues. We present the theoretical derivation of the algorithm and an analysis of its consistency and limit of detection. Results on simulated data show that under a wide range of conditions our method compares favorably with other common algorithms.