Fast Implementation of Double-coupled Nonnegative Canonical Polyadic Decomposition

Abstract

Real-world data exhibiting high order/dimensionality and various couplings are linked to each other since they share some common characteristics. Coupled tensor decomposition has become a popular technique for group analysis in recent years, especially for simultaneous analysis of multi-block tensor data with common information. To address the multiblock tensor data, we propose a fast double-coupled nonnegative Canonical Polyadic Decomposition (FDC-NCPD) algorithm in this study, based on the linked CP tensor decomposition (LCPTD) model and fast Hierarchical Alternating Least Squares (Fast-HALS) algorithm. The proposed FDCNCPD algorithm enables simultaneous extraction of common components, individual components and core tensors from tensor blocks. Moreover, time consumption is greatly reduced without compromising the decomposition quality when handling large-scale tensor blocks. Simulation experiments of synthetic and real-world data are conducted to demonstrate the superior performance of the proposed algorithm.