Tensor-based Method Research Articles

Dual-layer feature extraction based soft sensor methods and applications to industrial polyethylene processes

In chemical processes, products of different grades are often produced. Data measured in each grade have different latent features. Multiple data sets can be measured corresponding to different grades. To handle the modeling of multiple nonlinear data sets, multiple two-dimensional matrices of various grades are stacked into a three-dimensional tensor. Then a high-order tensor-based method, named high-order partial least squares (HOPLS), determines the common features among the multiple data sets. PLS is sequentially used to calculate the implied special features of each grade so that the grades can be distinguished from one another. A dual-layer feature extraction method is also proposed. To keep the prediction accuracy of HOPLS-PLS in nonlinear multi-grade processes, a just-in-time learning strategy, named JHOPLS-PLS, is used to establish local HOPLS-PLS models for each query sample. JHOPLS-PLS can extract both common and special features of multi-grade process data. The proposed JHOPLS-PLS has obvious advantages over existing methods.

Multimodal tensor-based method for integrative and continuous patient monitoring during postoperative cardiac care

Patients recovering from cardiovascular surgeries may develop life-threatening complications such as hemodynamic decompensation, making the monitoring of patients for such complications an essential component of postoperative care. However, this need has given rise to an inexorable increase in the number and modalities of data points collected, making it challenging to effectively analyze in real time. While many algorithms exist to assist in monitoring these patients, they often lack accuracy and specificity, leading to alarm fatigue among healthcare practitioners.In this study we propose a multimodal approach that incorporates salient physiological signals and EHR data to predict the onset of hemodynamic decompensation. A retrospective dataset of patients recovering from cardiac surgery was created and used to train predictive models. Advanced signal processing techniques were employed to extract complex features from physiological waveforms, while a novel tensor-based dimensionality reduction method was used to reduce the size of the feature space. These methods were evaluated for predicting the onset of decompensation at varying time intervals, ranging from a half-hour to 12 h prior to a decompensation event. The best performing models achieved AUCs of 0.87 and 0.80 for the half-hour and 12-h intervals respectively. These analyses evince that a multimodal approach can be used to develop clinical decision support systems that predict adverse events several hours in advance.

Nonnegative Tensor Factorization based on Low-Rank Subspace for Facial Expression Recognition

Important progresses have been made in the field of artificial intelligence in recent years, and facial expression recognition (FER), which could greatly facilitate the development of human-computer interaction, has been becoming a significant research hotspot. In this paper, a novel nonnegative tensor factorization method is proposed based on low-rank subspace (NTF−LRS) for FER. Firstly, in order to find the high order correlations underlying multi-dimensional data, a data tensor model is constructed, which could represent different dimensional features ingeniously. And then, the low-rank subspace model is adopted to reconstruct the original tensor model, reduce the redundancy of the learned new tensor, and improve the discriminant abilities of inter-class information. Finally, the reconstructed tensor is decomposed to get factor matrices by nonnegative tensor factorization, where all factor matrices are used to extract subspace features. To verify the effectiveness of our proposal, two well-known facial expression datasets named as “JAFFE” and “CK+” are utilized for evaluation, and the experimental results show that the tensor-based method preserves the original structure of whole samples, which avoids the case of dimension curse because of vectorization. In addition, this method uses Laplacian graph to impose regularization on low-rank subspace model, which keeps the local relationship between sample neighbors.

5G Positioning and Mapping With Diffuse Multipath

5G mmWave communication is useful for positioning due to the geometric connection between the propagation channel and the propagation environment. Channel estimation methods can exploit the resulting sparsity to estimate parameters (delay and angles) of each propagation path, which in turn can be exploited for positioning and mapping. When paths exhibit significant spread in either angle or delay, these methods break down or lead to significant biases. We present a novel tensor-based method for channel estimation that allows estimation of mmWave channel parameters in a non-parametric form. The method is able to accurately estimate the channel, even in the absence of a specular component. This in turn enables positioning and mapping using only diffuse multipath. Simulation results are provided to demonstrate the efficacy of the proposed approach.

Video SAR Imaging Based on Low-Rank Tensor Recovery

Due to its ability of forming continuous images for a ground scene of interest, the video synthetic aperture radar (SAR) has been studied in recent years. However, as video SAR needs to reconstruct many frames, the data are of enormous amount and the imaging process is of large computational cost, which limits its applications. In this article, we exploit the redundancy property of multiframe video SAR data, which can be modeled as low-rank tensor, and formulate the video SAR imaging process as a low-rank tensor recovery problem, which is solved by an efficient alternating minimization method. We empirically compare the proposed method with several state-of-the-art video SAR imaging algorithms, including the fast back-projection (FBP) method and the compressed sensing (CS)-based method. Experiments on both simulated and real data show that the proposed low-rank tensor-based method requires significantly less amount of data samples while achieving similar or better imaging performance.

A Feature Tensor-Based Epileptic Detection Model Based on Improved Edge Removal Approach for Directed Brain Networks.

Electroencephalograph (EEG) plays a significant role in the diagnostics process of epilepsy, but the detection rate is unsatisfactory when the length of interictal EEG signals is relatively short. Although the deliberate attacking theories for undirected brain network based on node removal method can extract potential network features, the node removal method fails to sufficiently consider the directionality of brain electrical activities. To solve the problems above, this study proposes a feature tensor-based epileptic detection method of directed brain networks. First, a directed functional brain network is constructed by calculating the transfer entropy of EEG signals between different electrodes. Second, the edge removal method is used to imitate the disruptions of brain connectivity, which may be related to the disorder of brain diseases, to obtain a sequence of residual networks. After that, topological features of these residual networks are extracted based on graph theory for constructing a five-way feature tensor. To exploit the inherent interactions among multiple modes of the feature tensor, this study uses the Tucker decomposition method to get a core tensor which is finally reshaped into a vector and input into the support vectors machine (SVM) classifier. Experiment results suggest that the proposed method has better epileptic screening performance for short-term interictal EEG data.

Automatic Tortuosity Estimation of Nerve Fibers and Retinal Vessels in Ophthalmic Images

The tortuosity changes of curvilinear anatomical organs such as nerve fibers or vessels have a close relationship with a number of diseases. Therefore, the automatic estimation and representation of the tortuosity is desired in medical image for such organs. In this paper, an automated framework for tortuosity estimation is proposed for corneal nerve and retinal vessel images. First, the weighted local phase tensor-based enhancement method is employed and the curvilinear structure is extracted from raw image. For each curvilinear structure with a different position and orientation, the curvature is measured by the exponential curvature estimation in the 3D space. Then, the tortuosity of an image is calculated as the weighted average of all the curvilinear structures. Our proposed framework has been evaluated on two corneal nerve fiber datasets and one retinal vessel dataset. Experiments on three curvilinear organ datasets demonstrate that our proposed tortuosity estimation method achieves a promising performance compared with other state-of-the-art methods in terms of accuracy and generality. In our nerve fiber dataset, the method achieved overall accuray of 0.820, and 0.734, 0.881 for sensitivity and specificity, respectively. The proposed method also achieved Spearman correlation scores 0.945 and 0.868 correlated with tortuosity grading ground truth for arteries and veins in the retinal vessel dataset. Furthermore, the manual labeled 403 corneal nerve fiber images with different levels of tortuosity, and all of them are also released for public access for further research.

Direction of arrival estimation in vector-sensor arrays using higher-order statistics

MUSIC algorithm is an effective method in solving the direction-finding problems. Due to the good performance of this algorithm, many variations of it including tesnor-MUSIC for verctor-sensor arrays, have been developed. However, these MUSIC-based methods have some limitations with respect to the number of sources, modeling errors and the noise power. It has been shown that using 2qth-order $$(q>1)$$ statistics in MUSIC algorithm is very effective to overcome these drawbacks. However, the existing 2q-order MUSIC-like methods are appropriate for scalar-sensor arrays, which only measure one parameter, and have a matrix of measurements. In vector-sensor arrays, each sensor measures multiple parameters, and to keep this multidimensional structure, we should use a tensor of measurements. The contribution of this paper is to develop a new tensor-based 2q-order MUSIC-like method for vector-sensor arrays. In this regard, we define a tensor of the cumulants which will be used in the proposed algorithm. The new method is called tensor-2q-MUSIC. Computer simulations have been used to compare the performance of the proposed method with a higher-order extension of the conventional MUSIC method for the vector-sensor arrays which is called matrix-2q-MUSIC. Moreover, we compare the performance of tensor-2q-MUSIC method with the existing second-order methods for the vector-sensor arrays. The simulation results show the better performance of the proposed method.

DTF: Deep Tensor Factorization for predicting anticancer drug synergy.

Combination therapies have been widely used to treat cancers. However, it is cost and time consuming to experimentally screen synergistic drug pairs due to the enormous number of possible drug combinations. Thus, computational methods have become an important way to predict and prioritize synergistic drug pairs. We proposed a Deep Tensor Factorization (DTF) model, which integrated a tensor factorization method and a deep neural network (DNN), to predict drug synergy. The former extracts latent features from drug synergy information while the latter constructs a binary classifier to predict the drug synergy status. Compared to the tensor-based method, the DTF model performed better in predicting drug synergy. The area under precision-recall curve (PR AUC) was 0.58 for DTF and 0.24 for the tensor method. We also compared the DTF model with DeepSynergy and logistic regression models, and found that the DTF outperformed the logistic regression model and achieved similar performance as DeepSynergy using several performance metrics for classification task. Applying the DTF model to predict missing entries in our drug-cell-line tensor, we identified novel synergistic drug combinations for 10 cell lines from the 5 cancer types. A literature survey showed that some of these predicted drug synergies have been identified in vivo or in vitro. Thus, the DTF model could be a valuable in silico tool for prioritizing novel synergistic drug combinations. Source code and data are available at https://github.com/ZexuanSun/DTF-Drug-Synergy. Supplementary data are available at Bioinformatics online.

Global Sensitivity Analysis in Load Modeling via Low-Rank Tensor

Growing model complexities in load modeling have created high dimensionality in parameter estimations, and thereby substantially increasing associated computational costs. In this paper, a tensor-based method is proposed for identifying composite load modeling (CLM) parameters and for conducting a global sensitivity analysis. Tensor format and Fokker-Planck equations are used to estimate the power output response of CLM in the context of simultaneously varying parameters under their full parameter distribution ranges. The proposed tensor structured is shown as effective for tackling high-dimensional parameter estimation and for improving computational performances in load modeling through global sensitivity analysis.

Tensor-Based Light Field Compressed Sensing and Epipolar Plane Images Reconstruction via Deep Learning

Light field (LF) can capture the spatial and angular information of the light in one single exposure. And the LF images are widely used in various fields, especially in immersive media. The rich imaging information in the LF poses great challenges for transmission. However, LF images are sparse and redundant to some extent, which makes LF compression possible. Besides, the compressed sensing (CS) theory shows that images can be recovered from a small number of measurements when they are sparse. In this paper, we propose a Tensor-based Compressed Sensing method to compress images and Epipolar Plane Images for reconstruction (TCSEPI). This method divides the viewpoints of LF images into several regions and stacks the images in each region into a 4D tensor, which conduct CS together and yields measurements with common characteristics. Subsequently, the epipolar plane images are used to reconstruct the LF images and restore the geometric consistency information. To achieve better reconstruction results, we design two cascaded convolutional neural networks to implement the measurement matrix optimization and LF images reconstruction sequentially. Experimental results show the superior performance of TCSEPI, which achieves at least 3dB gain in PSNR and outperforms state-of-the-art in the reconstruction quality.

Semi-Blind Receivers for Multi-User Massive MIMO Relay Systems Based on Block Tucker2-PARAFAC Tensor Model

Massive multiple-input multiple-output (MIMO) relay can significantly improve the capacity and throughput of wireless networks, thus has been a sought-after technique for future communication systems. However, the development of massive MIMO relay systems faces several major challenges. For example, the knowledge of instantaneous channel state information (CSI) is needed to estimate signals and optimize systems. Traditional estimation schemes need to transmit pilot sequences, which occupy the spectrum resources. In this paper, we propose a tensor-based method for joint signal and channel estimation for multi-user massive MIMO relay systems without using pilot sequences, and develop two tensor-based semi-blind receivers. Through multidimensional signaling scheme, the signals received by each user are formulated as the block Tucker2-PARAFAC (TP) tensor model. Then, two semi-blind receivers are proposed to jointly estimate the information signals and channel matrices. One is based on the tensor-based closed-form receiver, the other is based on the tensor-based iterative receiver. The proposed closed-form approach can also be used to initialize the iterative receiver for improving the convergence speed. In particular, the proposed schemes are practicable for both time division duplexing (TDD) and frequency division duplexing (FDD) modes. Uniqueness, identifiability and complexity are analyzed for our receivers. Compared with existing receivers, our receivers offer superior bit error rate (BER) and normalized mean square error (NMSE) performance. Numerical examples are shown to demonstrate the effectiveness of the proposed tensor-based receivers.

Baryons in the Cosmic Web of IllustrisTNG – II. The connection among galaxies, haloes, their formation time, and their location in the Cosmic Web

ABSTRACT The connections among galaxies, the dark matter haloes where they form and the properties of the large-scale Cosmic Web still need to be completely disentangled. We use the cosmological hydrodynamical simulation TNG100 of the IllustrisTNG suite to quantify the effects played by the large-scale density field and the Cosmic Web morphology on the relation between halo mass and galaxy stellar mass. We select objects with total dynamical mass in the range ${\ge}6.3\times 10^{10} \,h ^{-1}\, \mathrm{ M}_{\odot }$ up to a few $10^{14}\, h^{-1} \, \mathrm{ M}_{\odot }$ between redshift z = 4 and redshift z = 0. A Cosmic Web class (knot, filament, sheet, void) is assigned to each region of the volume using a density field deformation tensor-based method. We find that galaxy stellar mass strongly correlates with total dynamical mass and formation time, and more weakly with large-scale overdensity and Cosmic Web class. The latter two quantities correlate with each other, but are not entirely degenerate. Furthermore, we find that at fixed halo mass, galaxies with stellar mass lower than the median value are more likely to be found in voids and sheets, whereas galaxies with stellar mass higher than the median are more likely to be found in filaments and knots. Finally, we find that the dependence on environment is stronger for satellites than for centrals, and discuss the physical implications of these results.

A collection input based support tensor machine for lesion malignancy classification in digital breast tomosynthesis

Digital breast tomosynthesis (DBT) with improved lesion conspicuity and characterization has been adopted in screening practice. DBT-based diagnosis strongly depends on physicians’ experience, so an automatic lesion malignancy classification model using DBT could improve the consistency of diagnosis among different physicians. Tensor-based approaches that use the original imaging data as input have shown promising results for many classification tasks. However, DBT data are pseudo-3D volumetric imaging as the slice spacing of DBT is much coarser than that of the in-plane resolution. Thus, directly constructing DBT as the third-order tensor in a conventional tensor-based classifier with introducing additional information to the original DBT data along the slice-spacing dimension will lead to inconsistency across all three dimensions. To avoid such inconsistency, we introduce a collection input based support tensor machine (CISTM)-based classifier that uses the tensor collection as input for classifying lesion malignancy in DBT. In CISTM, instead of introducing the third dimension directly into the geometry construction, the third-dimension structural relationship is related by weight parameters in the decision function, which is dynamically and automatically constructed during the classifier training process and is more consistent with the pseudo-3D nature of DBT. We tested our method on a DBT dataset of 926 images among which 262 were malignant and 664 were benign. We compared our method with the latest tensor-based method, KSTM (kernelled support tensor machine), which does not consider the unique non-uniform resolution property of DBT. Experimental results illustrate that the CISTM-based classifier is effective for classifying breast lesion malignancy in DBT and that it outperforms the KSTM-based classifier.

QANet: Tensor Decomposition Approach for Query-Based Anomaly Detection in Heterogeneous Information Networks

Complex networks have now become integral parts of modern information infrastructures. This paper proposes a user-centric method for detecting anomalies in heterogeneous information networks, in which nodes and/or edges might be from different types. In the proposed anomaly detection method, users interact directly with the system and anomalous entities can be detected through queries. Our approach is based on tensor decomposition and clustering methods. We also propose a network generation model to construct synthetic heterogeneous information network to test the performance of the proposed method. The proposed anomaly detection method is compared with state-of-the-art methods in both synthetic and real-world networks. Experimental results show that the proposed tensor-based method considerably outperforms the existing anomaly detection methods.

Automated Iris Segmentation from Anterior Segment OCT Images with Occludable Angles via Local Phase Tensor.

Morphological changes in the iris are one of the major causes of angle-closure glaucoma, and an anteriorly-bowed iris may be further associated with greater risk of disease progression from primary angle-closure suspect (PACS) to chronic primary angle-closure glaucoma (CPCAG). In consequence, the automated detection of abnormalities in the iris region is of great importance in the management of glaucoma. In this paper, we present a new method for the extraction of the iris region by using a local phase tensor-based curvilinear structure enhancement method, and apply it to anterior segment optical coherence tomography (AS-OCT) imagery in the presence of occludable iridocorneal angle. The proposed method is evaluated across a dataset of 200 anterior chamber angle (ACA) images, and the experimental results show that the proposed method outperforms existing state-of-the-art method in applicability, effectiveness, and accuracy.

Speckle Noise Filtering in Side-Scan Sonar Images Based on the Tucker Tensor Decomposition.

Real signals are usually contaminated with various types of noise. This phenomenon has a negative impact on the operation of systems that rely on signals processing. In this paper, we propose a tensor-based method for speckle noise reduction in the side-scan sonar images. The method is based on the Tucker decomposition with automatically determined ranks of factoring tensors. As verified experimentally, the proposed method shows very good results, outperforming other types of speckle-noise filters.

A nested-PARAFAC based approach for target localization in bistatic MIMO radar systems

Bistatic MIMO radar systems gather several advantages such as increased resilience to electronic countermeasures, unknown receiver location, higher identifiability of targets and direct application of several high resolution adaptive techniques. In this paper, we propose a tensor-based method for joint direction of departure (DoD) and direction of arrival (DoA) estimation in bistatic MIMO radar systems. By assuming that the transmit array is divided into two maximally overlapping subarrays, we initially model the cross-covariance matrix of the matched filters outputs as a Nested-PARAFAC decomposition of a fourth-order covariance tensor. Then, exploiting the structure of this decomposition, we first propose a two stage algorithm for joint DoD and DoA estimation of multiple targets based on double alternating least squares (DALS). In addition, for scenarios in which the number of receive antennas exceeds the number of targets, we propose a closed-form solution to the second stage of the proposed method based on the least squares Khatri-Rao factorization (LS-KRF) concept. Simulation results show that the proposed method offers a highly-accurate localization of multiple targets in real-world scenarios where the antenna elements at the transmit and receive arrays have positioning errors as well as less complexity compared to competing state-of-the-art tensor-based solutions.

HSI-DeNet: Hyperspectral Image Restoration via Convolutional Neural Network

The spectral and the spatial information in hyperspectral images (HSIs) are the two sides of the same coin. How to jointly model them is the key issue for HSIs’ noise removal, including random noise, structural stripe noise, and dead pixels/lines. In this paper, we introduce the deep convolutional neural network (CNN) to achieve this goal. The learned filters can well extract the spatial information within their local receptive filed. Meanwhile, the spectral correlation can be depicted by the multiple channels of the learned 2-D filters, namely, the number of filters in each layer. The consequent advantages of our CNN-based HSI denoising method (HSI-DeNet) over previous methods are threefold. First, the proposed HSI-DeNet can be regarded as a tensor-based method by directly learning the filters in each layer without damaging the spectral-spatial structures. Second, the HSI-DeNet can simultaneously accommodate various kinds of noise in HSIs. Moreover, our method is flexible for both single image and multiple images by slightly modifying the channels of the filters in the first and last layers. Last but not least, our method is extremely fast in the testing phase, which makes it more practical for real application. The proposed HSI-DeNet is extensively evaluated on several HSIs, and outperforms the state-of-the-art HSI-DeNets in terms of both speed and performance.

A Tensor-Based Method for Completion of Missing Electromyography Data

This paper discusses the recovery of missing data in surface electromyography (sEMG) signals that arise during the acquisition process. Missing values in the EMG signals occur due to either the disconnection of electrodes, artifacts and muscle fatigue or the incapability of instruments to collect very low-amplitude signals. In many real-world EMG-related applications, algorithms need complete data to make accurate and correct predictions, or otherwise, the performance of prediction reduces sharply. We employ tensor factorization methods to recover unstructured and structured missing data from the EMG signals. In this paper, we use the first-order weighted optimization (WOPT) of the parallel factor analysis (PARAFAC) decomposition model to recover missing data. We tested our proposed framework against non-negative matrix factorization (NMF) and PARAFAC on simulated as well as on off-line EMG signals having unstructured missing values (randomly missing data ranging from 60% to 95%) and structured missing values. In the case of structured missing data having different channels, the percentage of missing data of a channel goes up to 50% for different movements. It has been observed empirically that our proposed framework recovers the missing data with relatively much-improved accuracy in terms of relative mean error (up to 50% and 30% for unstructured and structured missing data, respectively) compared with the matrix factorization methods even when the portion of unstructured and structured missing data reaches up to 95% and 50%, respectively.