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Nonnegative tensor decomposition has been widely applied in signal processingand neuroscience, etc. When it comes to group analysis of multi-block tensors,traditional tensor decomposition is insufficient to utilize the shared/similarinformation among tensors. In this study, we propose a coupled nonnegativeCANDECOMP/PARAFAC decomposition algorithm optimized by the alternating proximalgradient method (CoNCPDAPG), which is capable of a simultaneous decompositionof tensors from different samples that are partially linked and a simultaneousextraction of common components, individual components and core tensors. Due tothe low optimization efficiency brought by the nonnegative constraint and thehigh-dimensional nature of the data, we further propose the lraCoNCPD-APGalgorithm by combining low-rank approximation and the proposed CoNCPD-APGmethod. When processing multi-block large-scale tensors, the proposedlraCoNCPD-APG algorithm can greatly reduce the computational load withoutcompromising the decomposition quality. Experiment results of couplednonnegative tensor decomposition problems designed for synthetic data,real-world face images and event-related potential data demonstrate thepracticability and superiority of the proposed algorithms.

Fast Learnings of Coupled Nonnegative Tensor Decomposition Using Optimal Gradient and Low-rank Approximation