Phase-Locked Matrix Factorization with Estimation of the Common Oscillation

Phase-Locked Matrix Factorization (PLMF) is an algorithm to perform separation of synchronous sources. Such a problem cannot be addressed by orthodox methods such as Independent Component Analysis, because synchronous sources are highly mutually dependent. PLMF separates available data into the mixing matrix and the sources; the sources are then decomposed into amplitude and phase components. Previously, PLMF was applicable only if the oscillatory component, common to all synchronized sources, was known, which is clearly a restrictive assumption. The main goal of this paper is to present a version of PLMF where this assumption is no longer needed-the oscillatory component can be estimated alongside all the other variables, thus making PLMF much more applicable to real-world data. Furthermore, the optimization procedures in the original PLMF are improved. Results on simulated data illustrate that this new approach successfully estimates the oscillatory component, together with the remaining variables, showing that the general problem of separation of synchronous sources can now be tackled.