Fengyu Cong

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.

Haihua Luo, Xuming Ran, Tommi Kärkkäinen et al.

The dynamic evolution of real-world necessitates model editing within Large Language Models. While existing methods explore modular isolation or parameter-efficient strategies, they still suffer from semantic drift or knowledge forgetting due to continual updating. To address these challenges, we propose SoLA, a Semantic routing-based LoRA framework for lifelong model editing. In SoLA, each edit is encapsulated as an independent LoRA module, which is frozen after training and mapped to input by semantic routing, allowing dynamic activation of LoRA modules via semantic matching. This mechanism avoids semantic drift caused by cluster updating and mitigates catastrophic forgetting from parameter sharing. More importantly, SoLA supports precise revocation of specific edits by removing key from semantic routing, which restores model's original behavior. To our knowledge, this reversible rollback editing capability is the first to be achieved in existing literature. Furthermore, SoLA integrates decision-making process into edited layer, eliminating the need for auxiliary routing networks and enabling end-to-end decision-making process. Extensive experiments demonstrate that SoLA effectively learns and retains edited knowledge, achieving accurate, efficient, and reversible lifelong model editing.

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.

Deqing Wang, Fengyu Cong, Tapani Ristaniemi

Nonnegative CANDECOMP/PARAFAC (NCP) decomposition is an important tool to process nonnegative tensor. Sometimes, additional sparse regularization is needed to extract meaningful nonnegative and sparse components. Thus, an optimization method for NCP that can impose sparsity efficiently is required. In this paper, we construct NCP with sparse regularization (sparse NCP) by l1-norm. Several popular optimization methods in block coordinate descent framework are employed to solve the sparse NCP, all of which are deeply analyzed with mathematical solutions. We compare these methods by experiments on synthetic and real tensor data, both of which contain third-order and fourth-order cases. After comparison, the methods that have fast computation and high effectiveness to impose sparsity will be concluded. In addition, we proposed an accelerated method to compute the objective function and relative error of sparse NCP, which has significantly improved the computation of tensor decomposition especially for higher-order tensor.

Xiao-Feng Gong, Qiu-Hua Lin, Feng-Yu Cong et al.

Joint blind source separation (J-BSS) is an emerging data-driven technique for multi-set data-fusion. In this paper, J-BSS is addressed from a tensorial perspective. We show how, by using second-order multi-set statistics in J-BSS, a specific double coupled canonical polyadic decomposition (DC-CPD) problem can be formulated. We propose an algebraic DC-CPD algorithm based on a coupled rank-1 detection mapping. This algorithm converts a possibly underdetermined DC-CPD to a set of overdetermined CPDs. The latter can be solved algebraically via a generalized eigenvalue decomposition based scheme. Therefore, this algorithm is deterministic and returns the exact solution in the noiseless case. In the noisy case, it can be used to effectively initialize optimization based DC-CPD algorithms. In addition, we obtain the determini- stic and generic uniqueness conditions for DC-CPD, which are shown to be more relaxed than their CPD counterpart. Experiment results are given to illustrate the superiority of DC-CPD over standard CPD based BSS methods and several existing J-BSS methods, with regards to uniqueness and accuracy.

Tuomo Sipola, Fengyu Cong, Tapani Ristaniemi et al.

Functional magnetic resonance imaging (fMRI) produces data about activity inside the brain, from which spatial maps can be extracted by independent component analysis (ICA). In datasets, there are n spatial maps that contain p voxels. The number of voxels is very high compared to the number of analyzed spatial maps. Clustering of the spatial maps is usually based on correlation matrices. This usually works well, although such a similarity matrix inherently can explain only a certain amount of the total variance contained in the high-dimensional data where n is relatively small but p is large. For high-dimensional space, it is reasonable to perform dimensionality reduction before clustering. In this research, we used the recently developed diffusion map for dimensionality reduction in conjunction with spectral clustering. This research revealed that the diffusion map based clustering worked as well as the more traditional methods, and produced more compact clusters when needed.