Determining the number of signals correlated across multiple data sets for small sample support

This paper presents a detection scheme for determining the number of signals that are correlated across multiple data sets when the sample size is small compared to the dimensions of the data sets. To accommodate the sample-poor regime, we decouple the problem into several independent two-channel order-estimation problems that may be solved separately by a combination of principal component analysis (PCA) and canonical correlation analysis (CCA). Since the signals that are correlated across all data sets must be a subset of the signals that are correlated between any pair of data sets, we keep only the correlated signals for each pair of data sets. Then, a criterion inspired by a traditional information-theoretic criterion is applied to estimate the number of signals correlated across all data sets. The performance of the proposed scheme is verified by simulations.