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:信号处理和神经科学等广泛应用了无偏向性沙尘变分解法。当涉及多区块抗拉器的分组分析时,传统的抗拉分解法不足以利用不同区块之间的共享/类似信息。在本研究中,我们建议采用一种由交替性准梯度法优化的混合非阴性CANDECOMP/PARAFAC分解算法(CONCPDAPG),这种法能够同时从部分相连的不同样品中分离气分解气分解,同时提取共同部件、个别部件和核心气分解器。由于非阴性制约和数据的高度性质带来的优化效率低,我们进一步建议采用低级别近似率和拟议的CONCPD-APG方法相结合的LACF算法。在处理多区块大型抗拉CONCPD-APG算法时,拟议的LaraCOCPD-APG算法可以大大减少计算负荷,但不会损害分解质量。由于数据的不相邻性抗体分解,因此,我们进一步建议采用LACO-PGPG的算法方法,以综合数据、真实性图像和潜在数据。