Determining the number of factors in a linear mixture model from limited noisy data
Seminar Room 2, Newton Institute Gatehouse
Determining the number of signals (sources / components) in a linear mixture model is a fundamental problem in many scientific fields, including signal processing and analytical chemistry. While most methods in signal processing are based on information-theoretic criteria, in this talk we'll describe a novel non-parametric estimation method based on a sequence of hypothesis tests. The proposed method uses the eigenvalues of the sample covariance matrix, and combines a matrix perturbation approach with recent results from random matrix theory regarding the behaviour of noise eigenvalues. We'll present the theoretical derivation of the method, analysis of its consistency and limit of detection. As we'll show in simulations, under a wide range of conditions our method compares favourably with other common methods
Joint work with Shira Kritchman (Weizmann).