Spatio-temporal grey model based on tensor Tucker decomposition for traffic flow prediction

Shared subspace learning via partial Tucker decomposition for hyperspectral image classification.

To address the challenges that rolling bearing vibration signals are easily affected by noise and that traditional single-channel methods cannot fully exploit multi-channel information, this paper proposes a multi-channel fault diagnosis method combining Whale Optimization Algorithm-assisted Variational Mode Decomposition (WOA-VMD) with Tucker tensor decomposition. In this method, multi-channel vibration signals are first adaptively decomposed using WOA-VMD, with optimized decomposition parameters to effectively extract weak fault features. The resulting intrinsic mode functions (IMFs) are then structured into a third-order tensor to preserve inter-channel correlations. Tucker decomposition is subsequently applied to extract robust feature vectors from the tensor factor matrices, achieving dimensionality reduction, redundancy suppression, and enhanced noise mitigation. Finally, statistical features such as standard deviation, kurtosis, and waveform factor are computed from the denoised signals and fed into a Support Vector Machine (SVM) classifier for precise fault identification. Experimental results show that the proposed method outperforms traditional approaches in extracting weak fault features, effectively leveraging correlations among multi-channel signals to extract meaningful features from noise-corrupted signals, and achieving efficient and reliable fault diagnosis.

In this work, we describe the rank-reduced variant of the equation-of-motion coupled cluster theory with complete inclusion of single, double, and triple excitations. The advantage of the proposed formalism, in comparison with the canonical theory, stems from the application of Tucker decomposition format to the ground- and excited-states triply excited amplitude tensors. By exploiting the linear scaling of the dimension of the decomposed amplitudes with respect to the system size N, one can reduce the computational cost of the method to the level of N6 and storage requirements to N4. While, in practice, the proposed rank-reduced formalism introduces an error, we show that it is several times smaller than the inherent error of the parent theory with the proposed default settings for a wide range of problems. A higher level of accuracy can be achieved by increasing the value of a single parameter present in this formulation, recovering the canonical method in an appropriate limit. We illustrate the accuracy and performance of the proposed method by calculations for a group of molecules with excited states of different character─from dominated by single excitations with respect to the reference determinant to states with moderate and large contributions of double and higher excitations. We report calculations of potential energy curves and related spectroscopic parameters for the first four singlet excited states of magnesium dimer, as well as the potential energy curve for the excited state of charge-transfer character in the NH3-F2 complex as a function of intermolecular separation.

Collaborative clustering is an ensemble technique that enhances clustering performance by simultaneously and synergistically processing multiple data dimensions or tasks. This is an active research area in artificial intelligence, machine learning, and data mining. A common approach to co-clustering is based on non-negative matrix factorization (NMF). While widely used, NMF-based co-clustering is limited by its bilinear nature and fails to capture the multilinear structure of data. With the objective of enhancing the effectiveness of non-negative Tucker decomposition (NTD) in image clustering tasks, in this paper, we propose a dual-graph constrained sparse non-negative Tucker decomposition NTD (GDSNTD) model for co-clustering. It integrates graph regularization, the Frobenius norm, and an l1 norm constraint to simultaneously optimize the objective function. The GDSNTD mode, featuring graph regularization on both factor matrices, more effectively discovers meaningful latent structures in high-order data. The addition of the l1 regularization constraint on the factor matrices may help identify the most critical original features, and the use of the Frobenius norm may produce a more highly stable and accurate solution to the optimization problem. Then, the convergence of the proposed method is proven, and the detailed derivation is provided. Finally, experimental results on public datasets demonstrate that the proposed model outperforms state-of-the-art methods in image clustering, achieving superior scores in accuracy and Normalized Mutual Information.

Low-rank tucker decomposition for multi-view outlier detection based on meta-learning

In this article, we present the dynamic graph mixer (DGM), a novel model for learning spatiotemporal-individual coupled features from high-dimensional and incomplete (HDI) tensors, which frequently represent dynamic interactions among real-world data samples. In contrast to existing methods, the proposed DGM possesses the following three advantages when learning representations from HDI tensors. First, it performs light graph message passing based on the conjoint attentions learned by jointly modeling latent features and implicit structures to extract the high-order connectivity. Second, a multilayer nonlinear tensor neural network (TNN) is adopted to learn the intricate attribute features of node-node-time from different views. Third, it follows the Tucker decomposition paradigm in a data density-oriented modeling mechanism to integrate node representations, preserving the overall multidimensional interaction patterns. In addition, we provide theoretical evidence that the key components in DGM can significantly improve expressiveness. Extensive experiments conducted on eight testing datasets of HDI tensors demonstrate that DGM outperforms state-of-the-art methods in both learning accuracy and efficiency.

ABSTRACT Sparse tensors have become prevalent data structures in multiple applications, such as medical imaging and machine learning, making operations that decompose them, that is, creating smaller structures that retain most of the original information, essential. Two of the most commonly used tensor decomposition methods are the Canonical Polyadic and Tucker Decomposition, with the most time‐consuming operations being the MTTKRP and TTM‐chain, respectively. Modern computing platforms combine multiple devices with different architectures to achieve unprecedented levels of performance, creating an environment where portability is as important as performance. To tackle this challenge, this work proposes SYCL‐based MTTKRP and TTM‐chain approaches for sparse tensors, which are portable to any CPU or GPU, extending previous literature by handling mode‐4 and mode‐5 tensors and tackling the TTM‐chain operation as a whole, allowing for further optimizations. The experimental results show that the proposed approaches present linear to superlinear scalability as the problem size grows and outperform the portable state‐of‐the‐art by 4.9× on average.

Understanding and interpreting human emotions through neurophysiological signals has become a central goal in affective computing. This paper presents a focused survey of recent advances in emotion recognition using tensor factorization techniques specifically applied to functional Near-Infrared Spectroscopy (fNIRS) data. We examine how tensor-based frameworks have been leveraged to capture the temporal, spatial, and spectral characteristics of fNIRS brain signals, enabling effective dimensionality reduction and latent pattern extraction. Focusing on third-order tensor constructions (trials × channels × time), we compare the use of Canonical Polyadic (CP) and Tucker decompositions in isolating components representative of emotional states. The review further evaluates the performance of extracted features when classified by conventional machine learning models such as Random Forests and Support Vector Machines. Emphasis is placed on comparative accuracy, interpretability, and the advantages of tensor methods over traditional approaches for distinguishing arousal and valence levels. We conclude by discussing the relevance of these methods for the development of real-time, explainable, emotion-aware systems in wearable neurotechnology, with a particular focus on medical applications such as mental health monitoring, early diagnosis of affective disorders, and personalized neurorehabilitation.

When an arrhythmia occurs in the heart, all electrocardiogram (ECG) leads show evidence of it, but it is more prominent in some leads. This medical fact serves as the foundation for the knowledge distillation (KD) model proposed in this paper, which aims to enhance weak leads by leveraging information from stronger ones. The model employs single-lead signals for the student network and twelve-lead signals for the teacher network. Tucker decomposition is used in this KD model to decompose the teacher's feature maps. According to evaluations, the student model achieves an accuracy of 96.48% on the Chapman ECG dataset classification task.

Gradient neural network models for approximate Tucker decomposition of time-dependent tensors

The efficiency of the Tucker decomposition of amplitude tensors within the single-reference relativistic coupled cluster method with single and double excitations was studied in a series of benchmark calculations for (AuCl)n chains, Aun clusters, and the cluster model of solid YbCl2. The 1kJ/mol level of accuracy for correlation energy estimates of moderate-size systems and typical reaction energies can be achieved with relatively high compression rates of amplitude tensors via rejecting singular values smaller than ∼10-4. For the most extensive system studied (the YbCl7 cluster used for modeling of the ytterbium center in the ytterbium dichloride crystal), only ∼3% of compressed double amplitudes were shown to be significant. Thus, the rank reduction for the relativistic coupled cluster method with single and double theory, improving its computational scaling, is feasible. The advantage (if not necessity) of using the Goldstone diagrammatic technique rather than the "antisymmetrized" Brandow one is underlined. The proposed approach is promising for high-precision modeling of relatively large systems with heavy atoms.

Tucker tensor decomposition offers a more effective representation for multiway data compared to the widely used PARAFAC model. However, its flexibility brings the challenge of selecting the appropriate latent multi-rank. To overcome the issue of pre-selecting the latent multi-rank, we introduce a Bayesian adaptive Tucker decomposition model that infers the multi-rank automatically via an infinite increasing shrinkage prior. The model introduces local sparsity in the core tensor, inducing rich and at the same time parsimonious dependency structures. Posterior inference proceeds via an efficient adaptive Gibbs sampler, supporting both continuous and binary data and allowing for straightforward missing data imputation when dealing with incomplete multiway data. We discuss fundamental properties of the proposed modeling framework, providing theoretical justification. Simulation studies and applications to chemometrics and complex ecological data offer compelling evidence of its advantages over existing tensor factorization methods. Supplementary materials for this article are available online.

ABSTRACT Revealing spatial clustering patterns among urban geographic units is crucial for synergistic regional development and integrated urban management. Existing clustering methods neglect the intrinsic relationships between different features and spatiotemporal interactions among units, leading to a biased comprehension of urban clusters. This study develops a Graph-Laplacian Coupled Non-negative Tucker Decomposition (GCNTD) model to recognize multi-scale urban clusters in planar and network urban spaces. First, we construct spatiotemporal feature tensors of mobility flows and spatially couple them to capture the intrinsic correlations among multi-view features. Then, we propose an enhanced gravity model to represent spatial interactions among geographic units under free and constrained flows, and embed it into the coupled tensors using Graph-Laplacian regularization. Based on the decomposed spatiotemporal factors, we analyze the dynamic characteristics of geographic units and utilize hierarchical clustering to identify urban spatial clusters. Using human flow data in China, the inter-city experiments revealed clustering patterns among 366 cities and extracted 11 urban clusters. The total flow within clusters accounted for 41.40% of national mobility, while inter-cluster flows represented 8.87%. Intra-city experiments were conducted in Wuhan, where 152 fine-grained nodes were categorized into 4 clusters representing stable volume-travel time, high daytime volume, high nighttime volume, and high travel time.

A faster heterogeneous parallel computing method for Tucker decomposition

Magnetic resonance images (MRI) denoising aims to obtain clean image for further treatment by doctors. Recently, low-rank tensor methods have achieved amazing results in MRI denoising. Nevertheless, imbalanced matricization from Tucker decomposition and nuclear norm penalty mechanism are incapable of fully characterizing the internal structure information of 3D MR image. To mitigate these matters, a novel framework, which combines non-local self-similarity technique and low-rank tensor regularization from tensor train decomposition with balanced matricization, is proposed to noise removal. The constructed fourth-order tensor from non-local self-similarity technique is conducted by tensor train regularization with weighted Schatten-p norm function. The designed method not only considers structural correlation across different dimensions for 3D MR images, but also takes the importance of various singular values into account. Experimental results over synthetic and real images demonstrate that our proposal achieves competitive performance with respect to the state-of-the-art MR images denoising filters (ANLM3D, BM4D, WNNM3D, NLM-tSVD and HOSVD-R) both visually and quantitatively.

The murals in Shaanxi temples and monasteries, with their long history and diverse styles, are invaluable yet non-renewable cultural heritage. However, prolonged environmental exposure has led to severe damage, including cracking, mold growth, and large-scale detachment, creating an urgent need for restoration. Traditional restoration methods struggle with reconstructing complex structures and patterns due to their neglect of the murals’ global structure. To address this, we propose a novel diffusion model guided by global low-rank structure for mural restoration. By leveraging the inherent low-rank prior of mural images, our model explicitly captures non-local similarities within murals. To enhance computational efficiency, we incorporate orthogonal Tucker decomposition, reducing the complexity of low-rank solutions. Comprehensive experiments and ablation studies validate the effectiveness of the low-rank prior, demonstrating that our model achieves state-of-the-art performance and provides significant advancements in digital restoration of ancient murals.

Aiming at the limitations of existing multisensor fault diagnosis methods for rolling bearings in real industrial scenarios, this paper proposes an innovative intuitionistic fuzzy weighted least squares twin support higher-order tensor machine (IFW-LSTSHTM) model, which realizes a breakthrough in the noise robustness, adaptability to the working conditions, and the class imbalance processing capability. First, the multimodal feature tensor is constructed: the fourier synchro-squeezed transform is used to convert the multisensor time-domain signals into time–frequency images, and then the tensor is reconstructed to retain the three-dimensional structural information of the sensor coupling relationship and time–frequency features. The nonlinear feature mapping strategy combined with Tucker decomposition effectively maintains the high-order correlation of the feature tensor. Second, the adaptive sample-weighting mechanism is developed: an intuitionistic fuzzy membership score assignment scheme with global–local information fusion is proposed. At the global level, the class contribution is assessed based on the relative position of the samples to the classification boundary; at the local level, the topological structural features of the sample distribution are captured by K-nearest neighbor analysis; this mechanism significantly improves the recognition of noisy samples and the handling of class-imbalanced data. Finally, a dual hyperplane classifier is constructed in tensor space: a structural risk regularization term is introduced to enhance the model generalization ability and a dynamic penalty factor is set to set adaptive weights for different categories. A linear equation system solving strategy is adopted: the nonparallel hyperplane optimization is converted into matrix operations to improve the computational efficiency. The extensive experimental results on the two rolling bearing datasets have verified that the proposed method outperforms existing solutions in diagnostic accuracy and stability.

The binary relational knowledge base (KB, a.k.a. knowledge graph), representing real-world knowledge with binary relations and entities, has been an important research topic in artificial intelligence, while, considerable knowledge also involves beyond-binary relations. Recently, the area proposes to model n-ary relational KBs with both binary and beyond-binary relations included. However, most current models are extended from translational distance and neural network models in binary relational KBs, which suffer from weak expressiveness and high complexity, respectively. To overcome such issues, in this work, we propose a novel two-step modeling framework, GETD, generalizing the powerful tensor decomposition technique from binary relational KBs to the n-ary case. For n-ary relational KBs with single-arity relations, the GETD framework introduces Tucker decomposition and Tensor Ring decomposition for expressive and efficient modeling. Furthermore, the framework is technically extended for the representation of n-ary relational KBs with mixed-arity relations. The existing negative sampling technique is also generalized to the n-ary case for GETD. In addition, we theoretically prove that the GETD framework is fully expressive to completely represent any KBs. Empirical results on two representative datasets show that the proposed framework significantly outperforms the state-of-the-art methods, achieving 11–26% and 4–7% improvements on Hits@10 for the single-arity and the mixed-arity cases, respectively.

Recently, tensor singular value decomposition (t-SVD)-based methods were proposed to solve the low-rank tensor completion (LRTC) problem, which has achieved unprecedented success on image and video inpainting tasks. The t-SVD is limited to process third-order tensors. When faced with higher-order tensors, it reshapes them into third-order tensors, leading to the destruction of interdimensional correlations. To address this limitation, this letter introduces a tproductinduced Tucker decomposition (tTucker) model that replaces the mode product in Tucker decomposition with t-product, which jointly extends the ideas of t-SVD and high-order SVD. This letter defines the rank of the tTucker decomposition and presents an LRTC model that minimizes the induced Schatten-p norm. An efficient alternating direction multiplier method (ADMM) algorithm is developed to optimize the proposed LRTC model, and its effectiveness is demonstrated through experiments conducted on both synthetic and real data sets, showcasing excellent performance.