An Adaptive Algorithm for Tracking Third-Order Coupled Canonical Polyadic Decomposition

Coupled canonical polyadic decomposition (C-CPD) of multiple tensors is a fundamental tool for multi-set data fusion. Existing C-CPD works are mainly limited to batch processing techniques for stationary models, yet in practice the C-CPD model may be dynamic and thus adaptive C-CPD tracking techniques are in urgent need. In this paper, we consider the problem of adaptive tracking of a time-varying third-order C-CPD model, and propose a recursive least squares based adaptive tracking algorithm. Theoretical and experimental results are provided to show the merits of the proposed C-CPD tracking algorithm over batch C-CPD algorithm and CPD tracking algorithm, in terms of improved accuracy, reduced complexity, and more relaxed working conditions.