Xiulin Wang

Carla Schenker, Xiulin Wang, Evrim Acar

Coupled matrix and tensor factorizations (CMTF) have emerged as an effective data fusion tool to jointly analyze data sets in the form of matrices and higher-order tensors. The PARAFAC2 model has shown to be a promising alternative to the CANDECOMP/PARAFAC (CP) tensor model due to its flexibility and capability to handle irregular/ragged tensors. While fusion models based on a PARAFAC2 model coupled with matrix/tensor decompositions have been recently studied, they are limited in terms of possible regularizations and/or types of coupling between data sets. In this paper, we propose an algorithmic framework for fitting PARAFAC2-based CMTF models with the possibility of imposing various constraints on all modes and linear couplings, using Alternating Optimization (AO) and the Alternating Direction Method of Multipliers (ADMM). Through numerical experiments, we demonstrate that the proposed algorithmic approach accurately recovers the underlying patterns using various constraints and linear couplings.

Xiulin Wang, Jing Liu, Fengyu Cong

Tensor decomposition is a fundamental technique widely applied in signal processing, machine learning, and various other fields. However, traditional tensor decomposition methods encounter limitations when jointly analyzing multi-block tensors, as they often struggle to effectively explore shared information among tensors. In this study, we first introduce a novel coupled nonnegative CANDECOMP/PARAFAC decomposition algorithm optimized by the alternating proximal gradient method (CoNCPD-APG). This algorithm is specially designed to address the challenges of jointly decomposing different tensors that are partially or fully linked, while simultaneously extracting common components, individual components and, core tensors. Recognizing the computational challenges inherent in optimizing nonnegative constraints over high-dimensional tensor data, we further propose the lraCoNCPD-APG algorithm. By integrating low-rank approximation with the proposed CoNCPD-APG method, the proposed algorithm can significantly decrease the computational burden without compromising decomposition quality, particularly for multi-block large-scale tensors. Simulation experiments conducted on synthetic data, real-world face image data, and two kinds of electroencephalography (EEG) data demonstrate the practicality and superiority of the proposed algorithms for coupled nonnegative tensor decomposition problems. Our results underscore the efficacy of our methods in uncovering meaningful patterns and structures from complex multi-block tensor data, thereby offering valuable insights for future applications.

Yukai Cai, Hang Liu, Xiulin Wang et al.

In the field of brain science, data sharing across servers is becoming increasingly challenging due to issues such as industry competition, privacy security, and administrative procedure policies and regulations. Therefore, there is an urgent need to develop new methods for data analysis and processing that enable scientific collaboration without data sharing. In view of this, this study proposes to study and develop a series of efficient non-negative coupled tensor decomposition algorithm frameworks based on federated learning called FCNCP for the EEG data arranged on different servers. It combining the good discriminative performance of tensor decomposition in high-dimensional data representation and decomposition, the advantages of coupled tensor decomposition in cross-sample tensor data analysis, and the features of federated learning for joint modelling in distributed servers. The algorithm utilises federation learning to establish coupling constraints for data distributed across different servers. In the experiments, firstly, simulation experiments are carried out using simulated data, and stable and consistent decomposition results are obtained, which verify the effectiveness of the proposed algorithms in this study. Then the FCNCP algorithm was utilised to decompose the fifth-order event-related potential (ERP) tensor data collected by applying proprioceptive stimuli on the left and right hands. It was found that contralateral stimulation induced more symmetrical components in the activation areas of the left and right hemispheres. The conclusions drawn are consistent with the interpretations of related studies in cognitive neuroscience, demonstrating that the method can efficiently process higher-order EEG data and that some key hidden information can be preserved.

Carla Schenker, Xiulin Wang, David Horner et al.

Data fusion models based on Coupled Matrix and Tensor Factorizations (CMTF) have been effective tools for joint analysis of data from multiple sources. While the vast majority of CMTF models are based on the strictly multilinear CANDECOMP/PARAFAC (CP) tensor model, recently also the more flexible PARAFAC2 model has been integrated into CMTF models. PARAFAC2 tensor models can handle irregular/ragged tensors and have shown to be especially useful for modelling dynamic data with unaligned or irregular time profiles. However, existing PARAFAC2-based CMTF models have limitations in terms of possible regularizations on the factors and/or types of coupling between datasets. To address these limitations, in this paper we introduce a flexible algorithmic framework that fits PARAFAC2-based CMTF models using Alternating Optimization (AO) and the Alternating Direction Method of Multipliers (ADMM). The proposed framework allows to impose various constraints on all modes and linear couplings to other matrix-, CP- or PARAFAC2-models. Experiments on various simulated and a real dataset demonstrate the utility and versatility of the proposed framework as well as its benefits in terms of accuracy and efficiency in comparison with state-of-the-art methods.