Dual-symmetric Parallel Factor analysis using Procrustes estimation and Khatri-Rao factorization

The higher-order tensor analysis of multi-channel signals and systems has developed to one of the key signal processing areas over the past few years. In this contribution we present a new algorithm for the Parallel Factor (PARAFAC) analysis of tensors obeying a special kind of symmetry, which we refer to as dual-symmetry. This iterative algorithm is based on alternating Procrustes estimation and Khatri-Rao factorization (ProKRaft). The PARAFAC analysis of dual-symmetric tensors is of high interest for every correlation-based multi-channel algorithm, such as analytical channel models. It can also be used for the computation of the Independent Component Analysis (ICA), which is one of the most frequently applied methods in signal processing. Based on Monte-Carlo simulations we show that the new algorithm outperforms other state-of-the-art approaches while being very robust with respect to outliers. Furthermore, we evaluate its performance for the computation of the ICA also in comparison to other ICA algorithms.