Estimation of common subspace order across multiple datasets: Application to multi-subject fMRI data

The success of many joint blind source separation techniques is dependent upon accurate estimation of the common signal subspace order across multiple datasets. This has stimulated the development of techniques to estimate the number of common signals across two datasets, in particular, a method that uses information theoretic criteria using the canonical correlation coefficients in the likelihood formulation and a method based upon a two stage procedure, principal component analysis and canonical correlation analysis. However, these methods are limited to two datasets. In this paper, we propose a method based on multiset canonical correlation analysis followed by knee point detection (MCCA-KPD) to estimate the common subspace order across more than two datasets. We present a detailed comparison of the order estimation methods using simulated examples as well as real functional magnetic resonance imaging data. We demonstrate the superior performance of MCCA-KPD in terms of estimating the true common subspace order across multiple datasets.