Blind source separation for nonstationary tensor-valued time series

Abstract

Two standard assumptions of the classical blind source separation (BSS) theory are frequently violated by modern data sets. First, the majority of the existing methodology assumes vector-valued signals while data exhibiting a natural tensor structure is frequently observed. Second, many typical BSS applications exhibit serial dependence which is usually modeled using second order stationarity assumptions, which is however often quite unrealistic. To address these two issues we extend three existing methods of nonstationary blind source separation to tensor-valued time series. The resulting methods naturally factor in the tensor form of the observations without resorting to vectorization of the signals. Additionally, the methods allow for two types of nonstationarity, either the source series are blockwise second order weak stationary or their variances change smoothly in time. A simulation study and an application to video data show that the proposed extensions outperform their vectorial counterparts and successfully identify source series of interest.