Tensor Graph Research Articles

Effective Incomplete Multi-View Clustering via Low-Rank Graph Tensor Completion

In the past decade, multi-view clustering has received a lot of attention due to the popularity of multi-view data. However, not all samples can be observed from every view due to some unavoidable factors, resulting in the incomplete multi-view clustering (IMC) problem. Up until now, most efforts for the IMC problem have been made on the learning of consensus representations or graphs, while many missing views are ignored, making it impossible to capture the information hidden in the missing view. To overcome this drawback, we first analyzed the low-rank relationship existing inside each graph and among all graphs, and then propose a novel method for the IMC problem via low-rank graph tensor completion. Specifically, we first stack all similarity graphs into a third-order graph tensor and then exploit the low-rank relationship from each mode using the matrix nuclear norm. In this way, the connection hidden between the missing and available instances can be recovered. The consensus representation can be learned from all completed graphs via multi-view spectral clustering. To obtain the optimal multi-view clustering result, incomplete graph recovery and consensus representation learning are integrated into a joint framework for optimization. Extensive experimental results on several incomplete multi-view datasets demonstrate that the proposed method can obtain a better clustering performance in comparison with state-of-the-art incomplete multi-view clustering methods.

A Novel Time-Domain Graph Tensor Attention Network for Specific Emitter Identification

Specific emitter identification (SEI) is significant in military communication scenarios, cognitive radio and self-organized networks. However, these methods only consider the feature of signals or the feature after signal transformation. In other words, the time-domain correlation of each feature and relationships between features are seldom taken into account. A novel method is therefore proposed, which includes a transformation to convert the specific emitter signal into a graph tensor and a model named time domain graph tensor attention network (TDGTAN) to encode graph tensors for SEI. Specifically, the model includes two main parts. The first part is intra graph propagation, which uses the relationship between different sampling points through message propagation in each graph. The other part is inter propagation, which propagates cross layer messages between different graphs at the same sampling point, so as to realize the use of the relationship between different features. Extensive experiments are conducted on real-world dataset, and the result shows that the proposed approach acquires higher accuracy and intriguing anti-interference performance. In addition, the proposed model also has higher parameter utilization and calculation efficiency.

Spatial–Temporal Tensor Graph Convolutional Network for Traffic Speed Prediction

Accurate traffic speed prediction is crucial for the guidance and management of urban traffic, which at the same time requires a model with a satisfactory computational burden and memory space in applications. In this paper, we propose a factorized Spatial-Temporal Tensor Graph Convolutional Network for traffic speed prediction. Traffic networks are modeled and unified into a graph tensor that integrates spatial and temporal information simultaneously. We extend graph convolution into tensor space and propose a tensor graph convolution network to extract more discriminating features from spatial-temporal graph data. We further introduce Tucker decomposition and derive a factorized tensor convolution to reduce the computational burden, which performs separate filtering in small-scale space, time, and feature modes. Besides, we can benefit from noise suppression of traffic data when discarding those trivial components in the process of tensor decomposition. Extensive experiments on the three real-world datasets demonstrate that our method is more effective than traditional prediction methods, and achieves state-of-the-art performance.

Multirelational Tensor Graph Attention Networks for Knowledge Fusion in Smart Enterprise Systems

Augmented Intelligence of Things empowered by knowledge graph drives cognitive intelligence for smart enterprise management systems (EMS). Knowledge fusion technology can effectively integrate knowledge from different sources, thereby improving the accuracy and richness of the knowledge graph, which is of great significance to the sustainable development of smart EMS. Traditional machine learning methods on graphs face challenges in the fusion of complex and multirelational enterprise knowledge graphs due to inherent defects in relation semantic and local structure information capturing. In order to break through these limitations and improve EMS knowledge graphs, we propose tensor-based graph attention networks for multirelational graph representation learning (MR-GAT), and apply it to the critical tasks in knowledge fusion: Entity and relation alignment. Specifically, we innovatively adopt tensor operations to adequately model the interactions between entities and relations in EMS knowledge graph to learn more accurate representations. Additionally, we propose a relation attention mechanism, which focuses on assigning weights in the process of aggregating local semantic information for relation learning in an EMS knowledge graph. Furthermore, we develop a joint entity and relation alignment framework by utilizing the proposed multirelational graph attention networks to improve the accuracy of knowledge fusion. Experimental evaluations on three datasets present that the proposed approach outperforms the baseline models by about 1.4% on average in terms of the mean reciprocal rank metric, which demonstrates the superior ability of the proposed MR-GAT in representation learning for knowledge fusion in smart EMS.

An Integrated Graph-of-Words with Tensor Graph Neural Network Learning Paradigm for Text Classification

In recent years, with tremendous progresses of deep learning in multiple disciplines, there are several advanced sequential neural-network (NN) based architectures (e.g., recurrent neural network—RNN, Auto-Encoding—AE, transformer, etc.) have been proposed. Recently, there are several well-known GNN-based architectures like as graph convolutional network (GNN) have been proposed to deal with challenges related to the global representation preservation of text. However, most of recent proposed GNN-based text-embedding models still be unable to integrate the global structure with the semantic sequential representations of words/sentences into the unified textual embedding space. Moreover, they are also considered as unable to learn the rich context-varied representations of words. In order to tackle aforementioned challenges, in this paper we proposed a novel integrated text graph representation learning approach, named as: GOWSeqGCN. Our proposed GOWSeqGCN is an integrated semantic graph-of-words sequential textual representation under the graph convolutional network framework. In order to demonstrate for the effectiveness of our proposed GOWSeqGCN model in comparing with recent state-of-the-art text representation learning baselines, we conducted extensive experiments in benchmark textual datasets. The experimental outputs showed the outperformances and necessary of our proposed ideas in this paper.

One-step incomplete multiview clustering with low-rank tensor graph learning

Incomplete multiview clustering (IMVC) has attracted extensive attention in the field of machine learning due to its excellent performance in handling incomplete multiview data (IMVD). However, existing IMVC methods often use spectral clustering or k-means on the obtained affinity matrices to obtain the final clustering results, that is, the affinity matrices learning process and clustering process are separated. In this paper, we propose a new ingenious IMVC method, one-step incomplete multiview clustering with low-rank tensor graph learning (OIMVC/LTGL), to solve the problem. This method combines graph learning, low-rank tensor constraint, common representation learning and clustering into a unified optimization framework. First, we utilize the adjacency relationship between views to complete the similarity graph matrices. Second, we stack all similarity graph matrices into a third-order tensor. To mine higher-order correlations among different views, we impose a low-rank tensor constraint, the tensor nuclear norm (TNN), into the constructed tensor. Third, to explore consistent information between views, we introduce a common representation learning term to learn the optimal consensus representation. Last, we introduce spectral rotation to the consensus representation matrices to directly obtain the clustering labels. These steps promote each other for better clustering performance. We solve the optimization problem by using the augmented Lagrange multiplier (ALM) method. Experiments based on five well-known datasets show the superiority of our method.

Auto-weighted Tensor Schatten p-Norm for Robust Multi-view Graph Clustering

Recently, tensor-singular value decomposition based tensor-nuclear norm (t-TNN) has achieved impressive performance for multi-view graph clustering. This primarily ascribes the superiority of t-TNN in exploring high-order structure information among views. However, 1) t-TNN cannot ideally approximate to the original rank minimization, which produces the suboptimal graph tensor; in addition, t-TNN treats different singular values equally, such that the larger singular values corresponding to certain significant feature information (i.e., prior information) has not been utilized fully; 2) the data of original high-dimensional space are often corrupted by noise and outliers, which always makes adaptive neighbors graph learning (ANGL) generate low-quality affinity graphs. To address these issues, we propose a novel multi-view graph clustering method termed auto-weighted tensor Schatten p-norm (t-ATSN) for robust multi-view graph clustering (t-ATSN-RMGC). Concretely, we first propose t-SVD based t-ATSN with 0<p<1 to make the learned graph tensor better approximate the target rank than t-TNN. Meanwhile, it can also automatically and appropriately shrink singular values for constructing a more refined graph tensor, so as to fully capture spatial structure in the graph tensor. Moreover, we introduce the Geman McClure loss function to enhance the robustness of ANGL for noise and outliers. Experimental results on benchmarks across different scenarios and sizes show that the proposed method consistently outperforms state-of-the-art methods.

Altered topological properties of white matter structural network in adults with autism spectrum disorder.

Autism spectrum disorder (ASD) is a complex developmental disability and is currently viewed as a disorder of brain connectivity in which white matter abnormalities. However, the majority of the research to date has focused on children with ASD. Understanding the topological organization of the white matter structural network in adults may help uncover the nature of ASD pathology in adulthood. This study investigated the topological properties of white matter structural network using diffusion tensor imaging and graph theory analysis in a sample of 32 adults with ASD compared to 35 matched typically developing (TD) controls. Group differences in global and nodal topological metrics were compared. The relationships between the altered network metrics and the severity of clinical symptoms were calculated. Compared to TD controls, ASD patients exhibited decreased small-worldness and increased global efficiency. In addition, the reduced nodal efficiency and increased nodal degree were found in the frontal (e.g., the inferior frontal gyrus) and parietal (e.g., postcentral gyrus) regions. Furthermore, the altered topological metrics (e.g., increased global efficiency and reduced nodal efficiency) were correlated with the severity of ASD symptoms. These results indicated that the complicatedly topological organization of the white matter structural network was abnormal and may play an essential role in the underlying pathological mechanism of ASD in adults.

Tensor Graph Attention Network for Knowledge Reasoning in Internet of Things

Knowledge graph builds the bridge from massive data generated by the interaction and communication between various objects to intelligent applications and services in Internet of Things. The graph representation learning technology represented by graph neural networks plays an essential role in the understanding and reasoning of the knowledge graph with complicated internal structure. Although they are capable of assigning different attention weights to neighbors, the graph attention network (GAT) and its variants are inherently flawed and inadequate in modeling high-order knowledge graphs with high heterogeneity. Therefore, we propose a novel multirelational GAT framework in this article for knowledge reasoning over heterogeneous graphs by employing tensor and tensor operations. Specifically, we formulate the general high-order heterogeneous knowledge graph first. Then, the tensor GAT (TGAT), composed of three components: 1) heterogeneous information propagation; 2) multimodal semantic-aware attention; and 3) knowledge aggregation, is developed to simulate rich interactions between mixed triples, entities, and relationships when aggregating local information. What is more, we utilize the Tucker model to compress the parameters of TGAT and further reduce the storage and calculation consumption of the intermediate calculation process on the premise of maintaining the expressive power. We conduct extensive experiments to solve the link prediction task on four real-world heterogeneous graphs, and the results demonstrate that the TGAT model proposed in this article remarkably outperforms state-of-the-art competitors and improves the hits@1 accuracy by up to 7.6%.

Topologic Reorganization of White Matter Connectivity Networks in Early-Blind Adolescents.

Blindness studies are important models for the comprehension of human brain development and reorganization, after visual deprivation early in life. To investigate the global and local topologic alterations and to identify specific reorganized neural patterns in early-blind adolescents (EBAs), we applied diffusion tensor tractography and graph theory to establish and analyze the white matter connectivity networks in 21 EBAs and 22 age- and sex-matched normal-sighted controls (NSCs). The network profiles were compared between the groups using a linear regression model, and the associations between clinical variables and network profiles were analyzed. Graph theory analysis revealed “small-world” attributes in the structural connection networks of both EBA and NSC cohorts. The EBA cohort exhibited significant lower network density and global and local efficiency, as well as significantly elevated shortest path length, compared to the NSC group. The network efficiencies were markedly reduced in the EBA cohort, with the largest alterations in the default-mode, visual, and limbic areas. Moreover, decreased regional efficiency and increased nodal path length in some visual and default-mode areas were strongly associated with the period of blindness in EBA cohort, suggesting that the function of these areas would gradually weaken in the early-blind brains. Additionally, the differences in hub distribution between the two groups were mainly within the occipital and frontal areas, suggesting that neural reorganization occurred in these brain regions after early visual deprivation during adolescence. This study revealed that the EBA brain structural network undergoes both convergent and divergent topologic reorganizations to circumvent early visual deprivation. Our research will add to the growing knowledge of underlying neural mechanisms that govern brain reorganization and development, under conditions of early visual deprivation.

Tensor-Based Knowledge Fusion and Reasoning for Cyberphysical-Social Systems: Theory and Framework

Cyberphysical-social systems (CPSS) integrate human, machine, and information into large-scale automated systems and generate complex heterogeneous big data from multiple sources. Knowledge graphs play a pivotal role in energizing the data with huge volume and uneven quality to drive CPSS intelligent applications and services, thus attracting intense research interests from scholars. The Resource Description Framework (RDF) describes knowledge in the form of subject-predicate-object triples and interpreted as directed labeled graphs. However, the graph structure doesn’t have flexible operability and direct computability in the theoretical framework, although it can be understood intuitively. Therefore, we proposed a tensor-based knowledge analysis framework in this article, which supports the representation, fusion, and reasoning of knowledge graphs. First, we employ Boolean tensors to represent heterogeneous knowledge graphs completely. Then, we present a series of graph tensor operations for the modification, extraction, and aggregation of high-order knowledge graphs. Furthermore, we perform tensor 1-mode product operation between the knowledge graph representation tensor and the entity representation tensor to obtain the relation path tensor, so as to infer the relationship between any two entities. Finally, we demonstrate the practicality and effectiveness of the proposed model by implementing a case study.

Cognitive Improvement via Left Angular Gyrus-Navigated Repetitive Transcranial Magnetic Stimulation Inducing the Neuroplasticity of Thalamic System in Amnesic Mild Cognitive Impairment Patients.

Stimulating superficial brain regions highly associated with the hippocampus by repetitive transcranial magnetic stimulation (rTMS) may improve memory of Alzheimer's disease (AD) spectrum patients. We recruited 16 amnesic mild cognitive impairment (aMCI) and 6 AD patients in the study. All the patients were stimulated to the left angular gyrus, which was confirmed a strong link to the hippocampus through neuroimaging studies, by the neuro-navigated rTMS for four weeks. Automated fiber quantification using diffusion tensor imaging metrics and graph theory analysis on functional network were employed to detect the neuroplasticity of brain networks. After neuro-navigated rTMS intervention, the episodic memory of aMCI patients and Montreal Cognitive Assessment score of two groups were significantly improved. Increased FA values of right anterior thalamic radiation among aMCI patients, while decreased functional network properties of thalamus subregions were observed, whereas similar changes not found in AD patients. It is worth noting that the improvement of cognition was associated with the neuroplasticity of thalamic system. We speculated that the rTMS intervention targeting left angular gyrus may be served as a strategy to improve cognitive impairment at the early stage of AD patients, supporting by the neuroplasticity of thalamic system.

Generation of photonic tensor network states with circuit QED

We propose a circuit QED platform and protocol to generate microwave photonic tensor network states deterministically. We first show that using a microwave cavity as ancilla and a transmon qubit as emitter is a good platform to produce photonic matrix product states. The ancilla cavity combines a large controllable Hilbert space with a long coherence time, which we predict translates into a high number of entangled photons and states with a high bond dimension. Going beyond this paradigm, we then consider a natural generalization of this platform, in which several cavity-qubit pairs are coupled to form a chain. The photonic states thus produced feature a two-dimensional entanglement structure and can be interpreted as $\textit{radial plaquette}$ projected entangled pair states [Wei, Malz, and Cirac, Phys. Rev. Lett. 128, 010607 (2022)], which include many paradigmatic states, such as the broad class of isometric tensor network states, graph states, and string-net states.

Deep Learning Triplet Ordinal Relation Preserving Binary Code for Remote Sensing Image Retrieval Task

As satellite observation technology rapidly develops, the number of remote sensing (RS) images dramatically increases, and this leads RS image retrieval tasks to be more challenging in terms of speed and accuracy. Recently, an increasing number of researchers have turned their attention to this issue, as well as hashing algorithms, which map real-valued data onto a low-dimensional Hamming space and have been widely utilized to respond quickly to large-scale RS image search tasks. However, most existing hashing algorithms only emphasize preserving point-wise or pair-wise similarity, which may lead to an inferior approximate nearest neighbor (ANN) search result. To fix this problem, we propose a novel triplet ordinal cross entropy hashing (TOCEH). In TOCEH, to enhance the ability of preserving the ranking orders in different spaces, we establish a tensor graph representing the Euclidean triplet ordinal relationship among RS images and minimize the cross entropy between the probability distribution of the established Euclidean similarity graph and that of the Hamming triplet ordinal relation with the given binary code. During the training process, to avoid the non-deterministic polynomial (NP) hard problem, we utilize a continuous function instead of the discrete encoding process. Furthermore, we design a quantization objective function based on the principle of preserving triplet ordinal relation to minimize the loss caused by the continuous relaxation procedure. The comparative RS image retrieval experiments are conducted on three publicly available datasets, including UC Merced Land Use Dataset (UCMD), SAT-4 and SAT-6. The experimental results show that the proposed TOCEH algorithm outperforms many existing hashing algorithms in RS image retrieval tasks.

Quantum Machine Learning Algorithm for Knowledge Graphs

Semantic knowledge graphs are large-scale triple-oriented databases for knowledge representation and reasoning. Implicit knowledge can be inferred by modeling the tensor representations generated from knowledge graphs. However, as the sizes of knowledge graphs continue to grow, classical modeling becomes increasingly computationally resource intensive. This article investigates how to capitalize on quantum resources to accelerate the modeling of knowledge graphs. In particular, we propose the first quantum machine learning algorithm for inference on tensorized data, i.e., on knowledge graphs. Since most tensor problems are NP-hard [18], it is challenging to devise quantum algorithms to support the inference task. We simplify the modeling task by making the plausible assumption that the tensor representation of a knowledge graph can be approximated by its low-rank tensor singular value decomposition, which is verified by our experiments. The proposed sampling-based quantum algorithm achieves speedup with a polylogarithmic runtime in the dimension of knowledge graph tensor.

Hybrid node‐based tensor graph convolutional network for aspect‐category sentiment classification of microblog comments

SummaryAspect‐category sentiment classification of microblog comments aims to identify the sentiment polarity of different opinion aspects in microblog comments, which is meaningful for the analysis of public opinion. At present, most of aspect‐category sentiment classification methods need much annotation data, and regard comments as independent samples, without using of the relationship between comments. This article proposes an aspect‐category sentiment classification method based on tensor graph convolutional networks. First, the combination of a comment and its aspect category is regarded as a hybrid node, and the original representation of a hybrid node is encoded by the Bert model. Second, sentiment graph and semantic graph are constructed according to the semantic similarity and sentimental relevance between hybrid nodes, and they are stacked into a tensor. Then two convolution operations, including intra‐graph convolution and inter‐graph convolution, are performed for each layer of graph tensor. In this way, hybrid nodes can learn and merge the heterogeneous information of different graphs. Finally, under the supervision of few labeled comments, the sentiment classification can be completed based on the features of the hybrid nodes. Experimental results on two microblog datasets show that the proposed model can significantly improve the performance of sentiment classification compared with other baseline models.

Disrupted Topological Organization in White Matter Networks in Unilateral Sudden Sensorineural Hearing Loss.

Sudden sensorineural hearing loss (SSNHL) is a sudden-onset hearing impairment that rapidly develops within 72 h and is mostly unilateral. Only a few patients can be identified with a defined cause by routine clinical examinations. Recently, some studies have shown that unilateral SSNHL is associated with alterations in the central nervous system. However, little is known about the topological organization of white matter (WM) networks in unilateral SSNHL patients in the acute phase. In this study, 145 patients with SSNHL and 91 age-, gender-, and education-matched healthy controls were evaluated using diffusion tensor imaging (DTI) and graph theoretical approaches. The topological properties of WM networks, including global and nodal parameters, were investigated. At the global level, SSNHL patients displayed decreased clustering coefficient, local efficiency, global efficiency, normalized clustering coefficient, normalized characteristic path length, and small-worldness and increased characteristic path length (p < 0.05) compared with healthy controls. At the nodal level, altered nodal centralities in brain regions involved the auditory network, visual network, attention network, default mode network (DMN), sensorimotor network, and subcortical network (p < 0.05, Bonferroni corrected). These findings indicate a shift of the WM network topology in SSNHL patients toward randomization, which is characterized by decreased global network integration and segregation and is reflected by decreased global connectivity and altered nodal centralities. This study could help us understand the potential pathophysiology of unilateral SSNHL.

Multiple Kernel Clustering with Kernel k-Means Coupled Graph Tensor Learning

Kernel k-means (KKM) and spectral clustering (SC) are two basic methods used for multiple kernel clustering (MKC), which have both been widely used to identify clusters that are non-linearly separable. However, both of them have their own shortcomings: 1) the KKM-based methods usually focus on learning a discrete clustering indicator matrix via a combined consensus kernel, but cannot exploit the high-order affinities of all pre-defined base kernels; and 2) the SC-based methods require a robust and meaningful affinity graph in kernel space as input in order to form clusters with desired clustering structure. In this paper, a novel method, kernel k-means coupled graph tensor (KCGT), is proposed to graciously couple KKM and SC for seizing their merits and evading their demerits simultaneously. In specific, we innovatively develop a new graph learning paradigm by leveraging an explicit theoretical connection between clustering indicator matrix and affinity graph, such that the affinity graph propagated from KKM enjoys the valuable block diagonal and sparse property. Then, by using this graph learning paradigm, base kernels can produce multiple candidate affinity graphs, which are stacked into a low-rank graph tensor for capturing the high-order affinity of all these graphs. After that, by averaging all the frontal slices of the tensor, a high-quality affinity graph is obtained. Extensive experiments have shown the superiority of KCGT compared with the state-of-the-art MKC methods.

Multitype branching and graph product theory of infectious disease outbreaks.

The heterogeneity of human populations is a challenge to mathematical descriptions of epidemic outbreaks. Numerical simulations are deployed to account for the many factors influencing the spreading dynamics. Yet, the results from numerical simulations are often as complicated as the reality, leaving us with a sense of confusion about how the different factors account for the simulation results. Here, using a multitype branching together with a graph tensor product approach, I derive a single equation for the effective reproductive number of an infectious disease outbreak. Using this equation I deconvolute the impact of crowd management, targeted testing, contact heterogeneity, stratified vaccination, mask use, and smartphone tracing app use. This equation can be used to gain a basic understanding of infectious disease outbreaks and their simulations.

Discriminant Tensor-Based Manifold Embedding for Medical Hyperspectral Imagery.

Medical hyperspectral imagery has recentlyattracted considerable attention. However, for identification tasks, the high dimensionality of hyperspectral images usually leads to poor performance. Thus, dimensionality reduction (DR) is crucial in hyperspectral image analysis. Motivated by exploiting the underlying structure information of medical hyperspectral images and enhancing the discriminant ability of features, a discriminant tensor-based manifold embedding (DTME) is proposed for discriminant analysis of medical hyperspectral images. Based on the idea of manifold learning, a new discriminant similarity metric is designed, which takes into account the tensor representation, sparsity, low-rank and distribution characteristics. Then, an inter-class tensor graph and an intra-class tensor graph are constructed using the new similarity metric to reveal intrinsic manifold of hyperspectral data. Dimensionality reduction is achieved by embedding this supervised tensor graphs into the low-dimensional tensor subspace. Experimental results on membranous nephropathy and white bloodcells identification tasks demonstrate the potential clinical value of the proposed DTME.