Search Results (37)

Graph-based multi-view clustering has gained significant attention in recent years due to its superior ability to reveal clustering structures. However, existing methods often incur high computational costs when capturing local information and overlook the higher-order correlations between multiple views. To address these issues, we propose Tensorized Consensus Graph Learning for Incomplete Multi-View Clustering with Confidence Integration (TCGL). This approach constructs adjacency and local heat kernel graphs by filtering missing samples to better capture local structures while leveraging a t-SVD-based weighted tensor nuclear norm sparsification method to reduce noise. Additionally, we introduce a matrix energy-based adjacency graph normalization strategy that utilizes common nearest neighbors to generate probability matrices, enhancing noise resistance and improving structural exploration. Experimental results demonstrate that TCGL effectively handles incomplete data and significantly outperforms state-of-the-art approaches across multiple datasets. Full article

Recently, a growing number of researchers have focused on multi-view subspace clustering (MSC) due to its potential for integrating heterogeneous data. However, current MSC methods remain challenged by limited robustness and insufficient exploitation of cross-view high-order latent information for clustering advancement. To address these challenges, we develop a novel MSC framework termed TMSC-TNNBDR, a tensorized MSC framework that leverages t-SVD based tensor nuclear norm (TNN) regularization and block diagonal representation (BDR) learning to unify view consistency and structural sparsity. Specifically, each subspace representation matrix is constrained by a block diagonal regularizer to enforce cluster structure, while all matrices are aggregated into a tensor to capture high-order interactions. To efficiently optimize the model, we developed an optimization algorithm based on the inexact augmented Lagrange multiplier (ALM). The TMSC-TNNBDR exhibits both optimized block-diagonal structure and low-rank properties, thereby enabling enhanced mining of latent higher-order inter-view correlations while demonstrating greater resilience to noise. To investigate the capability of TMSC-TNNBDR, we conducted several experiments on certain datasets. Benchmarking on circumscribed datasets demonstrates our method’s superior clustering performance over comparative algorithms while maintaining competitive computational overhead. Full article

Inpainting noisy remote-sensing images can reduce the cost of acquiring remote-sensing images (RSIs). Since RSIs contain complex land structure features and concentrated obscured areas, existing inpainting methods often produce color inconsistency and structural smoothing when applied to RSIs with a high missing ratio. To address these problems, inspired by tensor recovery, a lightweight image Inpainting Generative Adversarial Network (GAN) method combining low-rankness and local-smoothness (IGLL) is proposed. IGLL utilizes the low-rankness and local-smoothness characteristics of RSIs to guide the deep-learning inpainting. Based on the strong low rankness characteristic of the RSIs, IGLL fully utilizes the background information for foreground inpainting and constrains the consistency of the key ranks. Based on the low smoothness characteristic of the RSIs, learnable edges and structure priors are designed to enhance the non-smoothness of the results. Specifically, the generator of IGLL consists of a pixel-level reconstruction net (PIRN) and a perception-level reconstruction net (PERN). In PIRN, the proposed global attention module (GAM) establishes long-range pixel dependencies. GAM performs precise normalization and avoids overfitting. In PERN, the proposed flexible feature similarity module (FFSM) computes the similarity between background and foreground features and selects a reasonable feature for recovery. Compared with existing works, FFSM improves the fineness of feature matching. To avoid the problem of local-smoothness in the results, both the generator and discriminator utilize the structure priors and learnable edges to regularize large concentrated missing regions. Additionally, IGLL incorporates mathematical constraints into deep-learning models. A singular value decomposition (SVD) loss item is proposed to model the low-rankness characteristic, and it constrains feature consistency. Extensive experiments demonstrate that the proposed IGLL performs favorably against state-of-the-art methods in terms of the reconstruction quality and computation costs, especially on RSIs with high mask ratios. Moreover, our ablation studies reveal the effectiveness of GAM, FFSM, and SVD loss. Source code is publicly available on GitHub. Full article

Machine learning (ML) technologies are currently widely used in many domains of science and technology, to discover models that transform input data into output data. The main advantages of such a procedure are the generality and simplicity of the learning process, while their weaknesses remain the required amount of data needed to perform the training and the recurrent difficulties to explain the involved rationale. At present, a panoply of ML techniques exist, and the selection of a method or another depends, in general, on the type and amount of data being considered. This paper proposes a procedure which provides not a field or an image as an output, but its singular value decomposition (SVD), or an SVD-like decomposition, while injecting as input data scalars or the SVD decomposition of an input field. The result is a tensor-to-tensor decomposition, without the need for the full fields, or an input to an output SVD-like decomposition. The proposed method works for the non-hyper-parallepipedic domain, and for any space dimensionality. The results show the ability of the proposed architecture to link the input filed and output field, without requiring access to full space reconstruction. Full article

Neural networks have become a cornerstone of computer vision applications, with tasks ranging from image classification to object detection. However, challenges such as hyperparameter optimization (HPO) and model compression remain critical for improving performance and deploying models on resource-constrained devices. In this work, we address these challenges using Tensor Network-based methods. For HPO, we propose and evaluate the TetraOpt algorithm against various optimization algorithms. These evaluations were conducted on subsets of the NATS-Bench dataset, including CIFAR-10, CIFAR-100, and ImageNet subsets. TetraOpt consistently demonstrated superior performance, effectively exploring the global optimization space and identifying configurations with higher accuracies. For model compression, we introduce a novel iterative method that combines CP, SVD, and Tucker tensor decompositions. Applied to ResNet-18 and ResNet-152, we evaluated our method on the CIFAR-10 and Tiny ImageNet datasets. Our method achieved compression ratios of up to $14.5\times$ for ResNet-18 and $2.5\times$ for ResNet-152. Additionally, the inference time for processing an image on a CPU remained largely unaffected, demonstrating the practicality of the method. Full article

Employing low tensor rank decomposition in image inpainting has attracted increasing attention. This study exploited novel tensor arrangement schemes to transform an image (a low-order tensor) to a higher-order tensor without changing the total number of pixels. The developed arrangement schemes enhanced the low rankness of images under three tensor decomposition methods: matrix SVD, tensor train (TT) decomposition, and tensor singular value decomposition (t-SVD). By exploiting the schemes, we solved the image inpainting problem with three low-rank constrained models that use the matrix rank, TT rank, and tubal rank as constrained priors. The tensor tubal rank and tensor train multi-rank were developed from t-SVD and TT decomposition, respectively. Then, ADMM algorithms were efficiently exploited for solving the three models. Experimental results demonstrate that our methods are effective for image inpainting and superior to numerous close methods. Full article

In the context of hybrid twins, a data-driven enrichment is added to the physics-based solution to represent with higher accuracy the reference solution assumed to be known at different points in the physical domain. Such an approach enables better predictions. However, the data-driven enrichment is usually represented by a regression, whose main drawbacks are (i) the difficulty of understanding the subjacent physics and (ii) the risks induced by the data-driven model extrapolation. This paper proposes a procedure enabling the extraction of a differential operator associated with the enrichment provided by the data-driven regression. For that purpose, a sparse Singular Value Decomposition, SVD, is introduced. It is then employed, first, in a full operator representation regularized optimization problem, where sparsity is promoted, leading to a linear programming problem, and then in a tensor decomposition of the operator’s identification procedure. The results show the ability of the method to identify the exact missing operators from the model. The regularized optimization problem was also able to identify the weights of the missing terms with a relative error of about 10% on average, depending on the selected use case. Full article

Cooperative MIMO communication systems play an important role in the development of future sixth-generation (6G) wireless systems incorporating new technologies such as massive MIMO relay systems, dual-polarized antenna arrays, millimeter-wave communications, and, more recently, communications assisted using intelligent reflecting surfaces (IRSs), and unmanned aerial vehicles (UAVs). In a companion paper, we provided an overview of cooperative communication systems from a tensor modeling perspective. The objective of the present paper is to provide a comprehensive tutorial on semi-blind receivers for MIMO one-way two-hop relay systems, allowing the joint estimation of transmitted symbols and individual communication channels with only a few pilot symbols. After a reminder of some tensor prerequisites, we present an overview of tensor models, with a detailed, unified, and original description of two classes of tensor decomposition frequently used in the design of relay systems, namely nested CPD/PARAFAC and nested Tucker decomposition (TD). Some new variants of nested models are introduced. Uniqueness and identifiability conditions, depending on the algorithm used to estimate the parameters of these models, are established. Two families of algorithms are presented: iterative algorithms based on alternating least squares (ALS) and closed-form solutions using Khatri–Rao and Kronecker factorization methods, which consist of SVD-based rank-one matrix or tensor approximations. In a second part of the paper, the overview of cooperative communication systems is completed before presenting several two-hop relay systems using different codings and configurations in terms of relaying protocol (AF/DF) and channel modeling. The aim of this presentation is firstly to show how these choices lead to different nested tensor models for the signals received at destination. Then, by capitalizing on these models and their correspondence with the generic models studied in the first part, we derive semi-blind receivers to jointly estimate the transmitted symbols and the individual communication channels for each relay system considered. In a third part, extensive Monte Carlo simulation results are presented to compare the performance of relay systems and associated semi-blind receivers in terms of the symbol error rate (SER) and channel estimate normalized mean-square error (NMSE). Their computation time is also compared. Finally, some perspectives are drawn for future research work. Full article

Mirror symmetry was first observed in worldsheet string constructions, and was shown to have profound implications in the Effective Field Theory (EFT) limit of string compactifications, and for the properties of Calabi–Yau manifolds. It opened up a new field in pure mathematics, and was utilised in the area of enumerative geometry. Spinor–Vector Duality (SVD) is an extension of mirror symmetry. This can be readily understood in terms of the moduli of toroidal compactification of the Heterotic String, which includes the metric the antisymmetric tensor field and the Wilson line moduli. In terms of the toroidal moduli, mirror symmetry corresponds to mappings of the internal space moduli, whereas Spinor–Vector Duality corresponds to maps of the Wilson line moduli. In the past few of years, we demonstrated the existence of Spinor–Vector Duality in the effective field theory compactifications of string theories. This was achieved by starting with a worldsheet orbifold construction that exhibited Spinor–Vector Duality and resolving the orbifold singularities, hence generating a smooth, effective field theory limit with an imprint of the Spinor–Vector Duality. Just like mirror symmetry, the Spinor–Vector Duality can be used to study the properties of complex manifolds with vector bundles. Spinor–Vector Duality offers a top-down approach to the “Swampland” program, by exploring the imprint of the symmetries of the ultra-violet complete worldsheet string constructions in the effective field theory limit. The SVD suggests a demarcation line between (2,0) EFTs that possess an ultra-violet complete embedding versus those that do not. Full article

The cerebral small vessel disease (cSVD) is one of the main causes of vascular and mixed cognitive impairment (CI), and it is associated, in particular, with brain ageing. An understanding of structural tissue changes in an intact cerebral white matter in cSVD might allow one to develop the sensitive biomarkers for early diagnosis and monitoring of disease progression. Purpose of the study: to evaluate microstructural changes in the corpus callosum (CC) using diffusion MRI (D-MRI) approaches in cSVD patients with different severity of CI and reveal the most sensitive correlations of diffusion metrics with CI. Methods: the study included 166 cSVD patients (51.8% women; 60.4 ± 7.6 years) and 44 healthy volunteers (65.9% women; 59.6 ± 6.8 years). All subjects underwent D-MRI (3T) with signal (diffusion tensor and kurtosis) and biophysical (neurite orientation dispersion and density imaging, NODDI, white matter tract integrity, WMTI, multicompartment spherical mean technique, MC-SMT) modeling in three CC segments as well as a neuropsychological assessment. Results: in cSVD patients, microstructural changes were found in all CC segments already at the subjective CI stage, which was found to worsen into mild CI and dementia. More pronounced changes were observed in the forceps minor. Among the signal models FA, MD, MK, RD, and RK, as well as among the biophysical models, MC-SMT (EMD, ETR) and WMTI (AWF) metrics exhibited the largest area under the curve (>0.85), characterizing the loss of microstructural integrity, the severity of potential demyelination, and the proportion of intra-axonal water, respectively. Conclusion: the study reveals the relevance of advanced D-MRI approaches for the assessment of brain tissue changes in cSVD. The identified diffusion biomarkers could be used for the clarification and observation of CI progression. Full article

Hyperspectral images (HSIs) possess an inherent three-order structure, prompting increased interest in extracting 3D features. Tensor analysis and low-rank representations, notably truncated higher-order SVD (T-HOSVD), have gained prominence for this purpose. However, determining the optimal order and addressing sensitivity to changes in data distribution remain challenging. To tackle these issues, this paper introduces an unsupervised Superpixelwise Multiscale Adaptive T-HOSVD (SmaT-HOSVD) method. Leveraging superpixel segmentation, the algorithm identifies homogeneous regions, facilitating the extraction of local features to enhance spatial contextual information within the image. Subsequently, T-HOSVD is adaptively applied to the obtained superpixel blocks for feature extraction and fusion across different scales. SmaT-HOSVD harnesses superpixel blocks and low-rank representations to extract 3D features, effectively capturing both spectral and spatial information of HSIs. By integrating optimal-rank estimation and multiscale fusion strategies, it acquires more comprehensive low-rank information and mitigates sensitivity to data variations. Notably, when trained on subsets comprising 2%, 1%, and 1% of the Indian Pines, University of Pavia, and Salinas datasets, respectively, SmaT-HOSVD achieves impressive overall accuracies of 93.31%, 97.21%, and 99.25%, while maintaining excellent efficiency. Future research will explore SmaT-HOSVD’s applicability in deep-sea HSI classification and pursue additional avenues for advancing the field. Full article

Technological developments coupled with socioeconomic changes are driving a rapid transformation of the fifth-generation (5G) cellular network landscape. This evolution has led to versatile applications with fast data-transfer capabilities. The integration of 5G with wireless sensor networks (WSNs) has rendered the Internet of Things (IoTs) crucial for measurement and sensing. Although 5G-enabled IoTs are vital, they face challenges in data integrity, such as mixed noise, outliers, and missing values, owing to various transmission issues. Traditional methods such as the tensor robust principal component analysis (TRPCA) have limitations in preserving essential data. This study introduces an enhanced approach, the weighted robust tensor principal component analysis (WRTPCA), combined with weighted tensor completion (WTC). The new method enhances data recovery using tensor singular value decomposition (t-SVD) to separate regular and abnormal data, preserve significant components, and robustly address complex data corruption issues, such as mixed noise, outliers, and missing data, with the globally optimal solution determined through the alternating direction method of multipliers (ADMM). Our study is the first to address complex corruption in multivariate data using the WTRPCA. The proposed approach outperforms current techniques. In all corrupted scenarios, the normalized mean absolute error (NMAE) of the proposed method is typically less than 0.2, demonstrating strong performance even in the most challenging conditions in which other models struggle. This highlights the effectiveness of the proposed approach in real-world 5G-enabled IoTs. Full article

We investigate and discuss in detail the structure of the restricted singular value decomposition for a tensor triplet under t-product (T-RSVD). The algorithm is provided with a numerical example illustrating the main result. For applications, we consider color image watermarking processing with T-RSVD. Full article

Integration of gene expression (GE) and protein–protein interaction (PPI) is not straightforward because the former is provided as a matrix, whereas the latter is provided as a network. In many cases, genes processed with GE analysis are refined further based on a PPI network or vice versa. This is hardly regarded as a true integration of GE and PPI. To address this problem, we proposed a tensor decomposition (TD)-based method that can integrate GE and PPI prior to any analyses where PPI is also formatted as a matrix to which singular value decomposition (SVD) is applied. Integrated analyses with TD improved the coincidence between vectors attributed to samples and class labels over 27 cancer types retrieved from The Cancer Genome Atlas Program (TCGA) toward five class labels. Enrichment using genes selected with this strategy was also improved with the integration using TD. The PPI network associated with the information on the strength of the PPI can improve the performance than PPI that stores only if the interaction exists in individual pairs. In addition, even restricting genes to the intersection of GE and PPI can improve coincidence and enrichment. Full article

Reconfigurable intelligent surface (RIS)-assisted millimeter-wave (mmWave) communication systems relying on hybrid beamforming structures are capable of achieving high spectral efficiency at a low hardware complexity and with low power consumption. Tensor-based joint beamforming with low-cost ultrasonic and RIS-assisted Dual-Hop Hybrid free space optical (FSO) mm Wave massive Multiple Input Multiple Output (MIMO) of vehicle-to-everything (V2X) is proposed. To address the occlusion problem for high-speed mobility of the vehicle, an RIS-assisted mixed FSO-MIMO V2X system is proposed. The low-cost ultrasonic array signal model is developed to solve the accurate direction-of-arrival (DOA) estimation. The ultrasonic-assisted RIS phase shift matrix based on subspace self-organizing iterations is designed to track the beam direction between RIS and vehicle. Specifically, the associated bandwidth-efficiency maximization problem is transformed into a series of subproblems, where the subarray of phase shifters and RIS elements is jointly optimized to maximize each subarray’s rate. The vehicle motion state is transformed into a two-dimensional model for prior distribution to calculate the particle weights of the RIS phase. Multi-vehicle Tucker tensor decomposition is used to describe the high-dimensional beam space. We conceive a multi-vehicle joint optimization method for designing the hybrid beamforming matrix of the base station (BS) and the passive beamforming matrix of the RIS. A cascaded channel decomposition method based on Singular Value Decomposition (SVD) is used to obtain the combined matrix beamforming of BS and vehicle. Our simulation results demonstrate the superiority of the proposed method compared to its traditional counterparts. Full article