Nonnegative tensor decomposition has been widely applied in signal processing and neuroscience, etc. When it comes to group analysis of multi-block tensors, traditional tensor decomposition is insufficient to utilize the shared/similar information among tensors. In this study, we propose a coupled nonnegative CANDECOMP/PARAFAC decomposition algorithm optimized by the alternating proximal gradient method (CoNCPDAPG), which is capable of a simultaneous decomposition of tensors from different samples that are partially linked and a simultaneous extraction of common components, individual components and core tensors. Due to the low optimization efficiency brought by the nonnegative constraint and the high-dimensional nature of the data, we further propose the lraCoNCPD-APG algorithm by combining low-rank approximation and the proposed CoNCPD-APG method. When processing multi-block large-scale tensors, the proposed lraCoNCPD-APG algorithm can greatly reduce the computational load without compromising the decomposition quality. Experiment results of coupled nonnegative tensor decomposition problems designed for synthetic data, real-world face images and event-related potential data demonstrate the practicability and superiority of the proposed algorithms.

翻译：非负张量分解已被广泛应用于信号处理和神经科学等领域。在处理多块张量的群体分析时，传统张量分解难以充分利用张量间的共享/相似信息。本研究提出一种由交替近端梯度法优化的耦合非负CANDECOMP/PARAFAC分解算法（CoNCPD-APG），该算法能够对来自不同样本且部分关联的张量进行同步分解，并同时提取公共成分、个体成分和核心张量。针对非负约束与数据高维特性导致的优化效率低下问题，我们进一步结合低秩逼近与所提CoNCPD-APG方法，提出lraCoNCPD-APG算法。在处理多块大规模张量时，所提lraCoNCPD-APG算法可在不降低分解质量的前提下大幅减少计算负荷。针对合成数据、真实人脸图像及事件相关电位数据设计的耦合非负张量分解问题实验结果表明，所提算法具有实用性与优越性。