Tensor-based Approach Research Articles

A Tensor-Based Approach to L-Shaped Arrays Processing With Enhanced Degrees of Freedom

A new tensor-based approach, which is capable of significantly increasing the degrees of freedom (DOF) of an L-shaped array consisting of two orthogonal uniform linear arrays (ULAs), is proposed. By dividing each ULA into some overlapping subarrays and then combining their received signals into a data tensor, a new cross-correlation tensor between the two data tensors from the two ULAs is built. Analyses show that such a cross-correlation tensor can be transformed into an equivalent received data matrix of a virtual uniform rectangular array (URA). Under the constraint of a fixed actual number of physical sensors, the optimal number of the subarrays is found by maximizing the DOF of the URA. It is shown that a virtual URA with approximately 0.34(M + 1)2 DOF can be obtained from an L-shaped array with 2M physical sensors. To exploit the increased DOF for the two dimensional (2-D) DOA estimation without the multidimensional search, a parallel factor (PARAFAC) model of the URA is provided so that the PARAFAC decomposition can be utilized to do the 2-D DOA estimation effectively. Simulation results demonstrate that the proposed method can yield a better estimation performance and resolve more sources than some computationally efficient methods reported in literature.

A Tensor-Based Multiple Clustering Approach With Its Applications in Automation Systems

Multiple clustering analysis has the clear advantages to discover latent data pattern in big data from different views, so it has tremendous practical values in automation industries. However, most of current algorithms are difficult to group heterogeneous data to multiple clusterings according to the requirements of different applications. This paper presents a flexible multiple clustering analytic and service framework, and a novel tensor-based multiple clusterings (TMC) approach. Heterogeneous data objects in cyber-physical-social systems are first represented as low-order tensors and a weight tensor construction approach is proposed to measure the importance of attributes combinations in heterogeneous feature spaces. Then, a selective weighted tensor distance is explored to cluster tensorized data objects for different applications. This paper, through a real-world smart bike maintenance system, illustrates TMC and evaluates its clustering performance. Experimental results reveal TMC can obtain higher quality clustering results but with lower redundancies to meet different requirements of applications in automation systems.

Compressive Sensing of Hyperspectral Images via Joint Tensor Tucker Decomposition and Weighted Total Variation Regularization

In this letter, we consider the problem of compressive sensing of hyperspectral images (HSIs). We propose a novel tensor-based approach by modeling the global spatial–spectral correlation and local smoothness properties hidden in HSIs. Specifically, we use the tensor Tucker decomposition to describe the global spatial–spectral correlation among all HSI bands, and a weighted 3-D total variation to characterize the local smooth structure in both spatial and spectral modes. We then design an efficient algorithm to solve the resulting optimization problem by using the alternating direction method of multipliers. Experimental results on several HSI data sets demonstrate improved reconstruction performance of the proposed approach, as compared with other competing approaches.

Recursive Tensor Subspace Tracking for Dynamic Brain Network Analysis

Recent years have seen a rapid growth in computational methods for a better understanding of functional connectivity brain networks constructed from neuroimaging data. Most of the current work has been limited to static functional connectivity networks (FCNs), where the relationships between different brain regions is assumed to be stationary. Recent work indicates that functional connectivity is a dynamic process over multiple time scales and the dynamic formation and dissolution of connections plays a key role in cognition, memory, and learning. In the proposed work, we introduce a tensor-based approach for tracking dynamic functional connectivity networks. The proposed framework introduces a robust low-rank+sparse structure learning algorithm for tensors to separate the low-rank community structure of connectivity networks from sparse outliers. The proposed framework is used to both identify change points, where the low-rank community structure of the FCN changes significantly, and summarize this community structure within each time interval. The proposed framework is applied to the study of cognitive control from electroencephalogram data during a Flanker task.

Anisotropic elastic-plastic deformation of paper: Out-of-plane model

Laminated paperboard and paper is widely used in packaging products. Its out-of-plane properties play a crucial role in converting paperboard to a carton through the creasing and folding process. The aim of this study is to describe the out-of-plane mechanical response with an elastic-plastic model based on the observed experimental behavior. The model was derived from a thermodynamic framework and was based on the multiplicative split of the deformation gradient in the context of hyperelasticity. A structural tensor-based approach was applied to model the elastic deformation, while a multi-surface based yield criterion was adopted to describe the plastic behavior. The model considers both material densification and internal friction effects, which were observed experimentally. According to the experimental behavior, a quadratic yield locus under pure shear loading was assumed in the model. Finally, the model was validated with a cylinder compression test and found to capture the highly anisotropic, elastic-plastic behavior accurately.

Higher-order singular value decomposition-based discrete fractional random transform for simultaneous compression and encryption of video images

Existing image compression and encryption methods have several shortcomings: they have low reconstruction accuracy and are unsuitable for three-dimensional (3D) images. To overcome these limitations, this paper proposes a tensor-based approach adopting tensor compressive sensing and tensor discrete fractional random transform (TDFRT). The source video images are measured by three key-controlled sensing matrices. Subsequently, the resulting tensor image is further encrypted using 3D cat map and the proposed TDFRT, which is based on higher-order singular value decomposition. A multiway projection algorithm is designed to reconstruct the video images. The proposed algorithm can greatly reduce the data volume and improve the efficiency of the data transmission and key distribution. The simulation results validate the good compression performance, efficiency, and security of the proposed algorithm.

Tensor Decompositions for Identifying Directed Graph Topologies and Tracking Dynamic Networks

Directed networks are pervasive both in nature and engineered systems, often underlying the complex behavior observed in biological systems, microblogs and social interactions over the web, as well as global financial markets. Since their structures are often unobservable, in order to facilitate network analytics, one generally resorts to approaches capitalizing on measurable nodal processes to infer the unknown topology. Structural equation models (SEMs) are capable of incorporating exogenous inputs to resolve inherent directional ambiguities. However, conventional SEMs assume full knowledge of exogenous inputs, which may not be readily available in some practical settings. The present paper advocates a novel SEM-based topology inference approach that entails factorization of a three-way tensor, constructed from the observed nodal data, using the well-known parallel factor (PARAFAC) decomposition. It turns out that second-order piecewise stationary statistics of exogenous variables suffice to identify the hidden topology. Capitalizing on the uniqueness properties inherent to high-order tensor factorizations, it is shown that topology identification is possible under reasonably mild conditions. In addition, to facilitate real-time operation and inference of time-varying networks, an adaptive (PARAFAC) tensor decomposition scheme which tracks the topology-revealing tensor factors is developed. Extensive tests on simulated and real stock quote data demonstrate the merits of the novel tensor-based approach.

Anisotropic elastic-plastic deformation of paper: In-plane model

Laminated paperboard and paper is widely used in packaging products. It generally exhibits highly anisotropic and nonlinear mechanical behavior. The aim of this study is to describe the in-plane material behavior with an orthotropic elastic-plastic model based on the observed experimental behavior. A structural tensor-based approach was applied to model the elastic deformation, while a multi-surface based yield criterion was adopted to describe the yield behavior. The model incorporated nonlinear kinematic and isotropic hardening to capture the anisotropic hardening effect. In the experiment, the compressive yield stress was found to be insensitive to the previous tensile deformation. The proposed model could capture this compression yield stress preserving effect under reverse loading, which in turn reduced the required material parameters as expected. With the material parameters calibrated from a set of simple uniaxial tests in various directions, the model was shown to predict the stress-strain behavior for other orientations satisfactorily. The model was further validated with experiments under complex loading conditions and found to capture the highly anisotropic, elastic-plastic behavior accurately.

Towards developing a compact model for magnetization switching in straintronics magnetic random access memory devices

Strain-mediated magnetization switching in a magnetic tunneling junction (MTJ) by exploiting a combination of piezoelectricity and magnetostriction has been proposed as an energy efficient alternative to spin transfer torque (STT) and field induced magnetization switching methods in MTJ-based magnetic random access memories (MRAM). Theoretical studies have shown the inherent advantages of strain-assisted switching, and the dynamic response of the magnetization has been modeled using the Landau-Lifshitz-Gilbert (LLG) equation. However, an attempt to use LLG for simulating dynamics of individual elements in large-scale simulations of multi-megabyte straintronics MRAM leads to extremely time-consuming calculations. Hence, a compact analytical solution, predicting the flipping delay of the magnetization vector in the nanomagnet under stress, combined with a liberal approximation of the LLG dynamics in the straintronics MTJ, can lead to a simplified model of the device suited for fast large-scale simulations of multi-megabyte straintronics MRAMs. In this work, a tensor-based approach is developed to study the dynamic behavior of the stressed nanomagnet. First, using the developed method, the effect of stress on the switching behavior of the magnetization is investigated to realize the margins between the underdamped and overdamped regimes. The latter helps the designer realize the oscillatory behavior of the magnetization when settling along the minor axis, and the dependency of oscillations on the stress level and the damping factor. Next, a theoretical model to predict the flipping delay of the magnetization vector is developed and tested against LLG-based numerical simulations to confirm the accuracy of findings. Lastly, the obtained delay is incorporated into the approximate solutions of the LLG dynamics, in order to create a compact model to liberally and quickly simulate the magnetization dynamics of the MTJ under stress. Using the developed delay equation, the efficiency of the straintronics switching over the STT method is highlighted by analytically investigating the energy-delay trade-off of both methodologies.

Trifocal Tensor-Based Adaptive Visual Trajectory Tracking Control of Mobile Robots.

In this paper, a trifocal tensor-based approach is proposed for the visual trajectory tracking task of a nonholonomic mobile robot equipped with a roughly installed monocular camera. The desired trajectory is expressed by a set of prerecorded images, and the robot is regulated to track the desired trajectory using visual feedback. Trifocal tensor is exploited to obtain the orientation and scaled position information used in the control system, and it works for general scenes owing to the generality of trifocal tensor. In the previous works, the start, current, and final images are required to share enough visual information to estimate the trifocal tensor. However, this requirement can be easily violated for perspective cameras with limited field of view. In this paper, key frame strategy is proposed to loosen this requirement, extending the workspace of the visual servo system. Considering the unknown depth and extrinsic parameters (installing position of the camera), an adaptive controller is developed based on Lyapunov methods. The proposed control strategy works for almost all practical circumstances, including both trajectory tracking and pose regulation tasks. Simulations are made based on the virtual experimentation platform (V-REP) to evaluate the effectiveness of the proposed approach.

Tensor-Based Channel Estimation Approach for One-Way Multi-Hop Relaying Communications

Tensor-Based Channel Estimation Approach for One-Way Multi-Hop Relaying Communications

A tensor-based dictionary learning approach to tomographic image reconstruction

We consider tomographic reconstruction using priors in the form of a dictionary learned from training images. The reconstruction has two stages: first we construct a tensor dictionary prior from our training data, and then we pose the reconstruction problem in terms of recovering the expansion coefficients in that dictionary. Our approach differs from past approaches in that (a) we use a third-order tensor representation for our images and (b) we recast the reconstruction problem using the tensor formulation. The dictionary learning problem is presented as a non-negative tensor factorization problem with sparsity constraints. The reconstruction problem is formulated in a convex optimization framework by looking for a solution with a sparse representation in the tensor dictionary. Numerical results show that our tensor formulation leads to very sparse representations of both the training images and the reconstructions due to the ability of representing repeated features compactly in the dictionary.

Tensor-Based Channel Estimation Approach for One-Way Multi-Hop Relaying Communications

Multi-hop relaying communications have great potentials in improving transmission performance by deploying relay nodes. The benefit is critically dependent on the accuracy of the channel state information (CSI) of all the transmitting links. However, the CSI has to be estimated. In this paper, we investigate the channel estimation problem in one-way multi-hop MIMO amplify-and-forward (AF) relay system, where both the two-hop and three-hop communication link exist. Traditional point-to-point MIMO channel estimation methods will result in error propagation in estimating relay links, and separately tackling the channel estimation issue of each link will lose the gain as part of channel matrices involved in multiple communication links. In order to exploit all the available gains, we develop a novel channel estimation model by structuring different communication links using the PARAFAC and PARATUCK2 tensor analysis. Furthermore, a two-stage fitting algorithm is derived to estimate all the channel matrices involved in the communication process. In particular, essential uniqueness is further discussed. Simulation results demonstrate the advantage and effectiveness of the proposed channel estimator.

Triangular Alignment (TAME): A Tensor-Based Approach for Higher-Order Network Alignment.

Network alignment has extensive applications in comparative interactomics. Traditional approaches aim to simultaneously maximize the number of conserved edges and the underlying similarity of aligned entities. We propose a novel formulation of the network alignment problem that extends topological similarity to higher-order structures and provides a new objective function that maximizes the number of aligned substructures. This objective function corresponds to an integer programming problem, which is NP-hard. Consequently, we identify a closely related surrogate function whose maximization results in a tensor eigenvector problem. Based on this formulation, we present an algorithm called Triangular AlignMEnt (TAME), which attempts to maximize the number of aligned triangles across networks. Using a case study on the NAPAbench dataset, we show that triangular alignment is capable of producing mappings with high node correctness. We further evaluate our method by aligning yeast and human interactomes. Our results indicate that TAME outperforms the state-of-art alignment methods in terms of conserved triangles. In addition, we show that the number of conserved triangles is more significantly correlated, compared to the conserved edge, with node correctness and co-expression of edges. Our formulation and resulting algorithms can be easily extended to arbitrary motifs.

Detecting Curvilinear Features Using Structure Tensors.

Few published articles on curvilinear structures exist compared with works on detecting lines or corners with high accuracy. In medical ultrasound imaging, the structures that need to be detected appear as a collection of microstructures correlated along a path. In this paper, we investigated techniques that extract meaningful low-level information for curvilinear structures, using techniques based on structure tensor. We proposed a novel structure tensor enhancement inspired by bilateral filtering. We compared the proposed approach with five state-of-the-art curvilinear structure detectors. We tested the algorithms against simulated images with known ground truth and real images from three different domains (medical ultrasound, scanning electron microscope, and astronomy). For the real images, we employed experts to delineate the ground truth for each domain. Techniques borrowed from machine learning robustly assessed the performance of the methods (area under curve and cross validation). As a practical application, we used the proposed method to label a set of 5000 ultrasound images. We conclude that the proposed tensor-based approach outperforms the state-of-the-art methods in providing magnitude and orientation information for curvilinear structures. The evaluation methodology ensures that the employed feature-detection method will yield reproducible performance on new, unseen images. We published all the implemented methods as open-source software.

Tensor-based real-valued subspace approach for angle estimation in bistatic MIMO radar with unknown mutual coupling

In this paper, a tensor-based real-valued subspace approach for joint direction of departure (DOD) and direction of arrival (DOA) estimation in bistatic MIMO radar with unknown mutual coupling is proposed. Exploiting the inherent multidimensional structure of received data after matched filtering, a third-order measurement tensor signal model is formulated. For eliminating the effect of the unknown mutual coupling, a sub-tensor can be extracted from the third-order measurement tensor by taking advantage of the banded symmetric Toeplitz structure of the mutual coupling matrix (MCM). Then the sub-tensor can be turned into a real-valued one by forward–backward averaging and unitary transformation, and a real-valued signal subspace is constructed to estimate the DOD and DOA by the higher-order singular value decomposition (HOSVD). Owing to utilize the multidimensional structure of received data and forward–backward averaging technique, the proposed method has better angle estimation performance than MUSIC-Like and ESPRIT-Like algorithms. Furthermore, the proposed method is suitable for coherent targets. Simulation results verify the effectiveness and advantage of the proposed method.

A Hierarchical Tensor-Based Approach to Compressing, Updating and Querying Geospatial Data

With the rapid development of data observation and model simulation in geoscience, spatial-temporal data have become increasingly multidimensional, massive and are consistently being updated. As a result, the integrated maintenance of these data is becoming a challenge. This paper presents a blocked hierarchical tensor representation within the split-and-merge paradigm for the compressed storage, continuously updating and data querying of multidimensional geospatial field data. The original multidimensional geospatial field data are split into small blocks according to their spatial-temporal references. These blocks are represented and compressed hierarchically, and then combined into a single hierarchical tree as the representation of original data. With a buffered binary tree data structure and corresponding optimized operation algorithms, the original multidimensional geospatial field data can be continuously compressed, appended, and queried. Data from the 20th Century Reanalysis Monthly Mean Composites are used to evaluate the performance of this approach. Compared to traditional methods, the new approach is shown to retain the quality of the original data with much lower storage costs and faster computational performance. The result suggests that the blocked hierarchical tensor representation provides an effective structure for integrated storage, presentation and computation of multidimensional geospatial field data.

Traffic speed data imputation method based on tensor completion.

Traffic speed data plays a key role in Intelligent Transportation Systems (ITS); however, missing traffic data would affect the performance of ITS as well as Advanced Traveler Information Systems (ATIS). In this paper, we handle this issue by a novel tensor-based imputation approach. Specifically, tensor pattern is adopted for modeling traffic speed data and then High accurate Low Rank Tensor Completion (HaLRTC), an efficient tensor completion method, is employed to estimate the missing traffic speed data. This proposed method is able to recover missing entries from given entries, which may be noisy, considering severe fluctuation of traffic speed data compared with traffic volume. The proposed method is evaluated on Performance Measurement System (PeMS) database, and the experimental results show the superiority of the proposed approach over state-of-the-art baseline approaches.

Multiple Morphological Profiles From Multicomponent-Base Images for Hyperspectral Image Classification

Morphological profiles (MPs) are a useful tool for remotely sensed image classification. These profiles are constructed on a base image that can be a single band of a multicomponent remote sensing image. Principal component analysis (PCA) has been used to provide other base images to construct MPs in high-dimensional remote sensing scenes such as hyperspectral images [e.g., by deriving the first principal components (PCs) and building the MPs on the first few components]. In this paper, we discuss several strategies for producing the base images for MPs, and further categorize the considered methods into four classes: linear, nonlinear, manifold learning-based, and multilinear transformation-based. It is found that the multilinear PCA (MPCA) is a powerful approach for base image extraction. That is because it is a tensor-based feature representation approach, which is able to simultaneously exploit the spectral-spatial correlation between neighboring pixels. We also show that independent component analysis (ICA) is more effective for constructing base images than PCA. Another important contribution of this paper is a new concept of multiple MPs (MMPs), aimed at synthesizing the spectral-spatial information extracted from the multicomponent base images, and further enhancing the classification accuracy of MPs. Moreover, we propose two different strategies to interpret the newly proposed MMPs by considering their hyperdimensional feature space: decision fusion and sparse classifier based on multinomial logistic regression (MLR). Experiments conducted on three well-known hyperspectral datasets are used to quantitatively assess the accuracy of different algorithms.

A nonlocal structure tensor-based approach for multicomponent image recovery problems.

Nonlocal total variation (NLTV) has emerged as a useful tool in variational methods for image recovery problems. In this paper, we extend the NLTV-based regularization to multicomponent images by taking advantage of the structure tensor (ST) resulting from the gradient of a multicomponent image. The proposed approach allows us to penalize the nonlocal variations, jointly for the different components, through various l(1, p)-matrix-norms with p ≥ 1. To facilitate the choice of the hyperparameters, we adopt a constrained convex optimization approach in which we minimize the data fidelity term subject to a constraint involving the ST-NLTV regularization. The resulting convex optimization problem is solved with a novel epigraphical projection method. This formulation can be efficiently implemented because of the flexibility offered by recent primal-dual proximal algorithms. Experiments are carried out for color, multispectral, and hyperspectral images. The results demonstrate the interest of introducing a nonlocal ST regularization and show that the proposed approach leads to significant improvements in terms of convergence speed over current state-of-the-art methods, such as the alternating direction method of multipliers.