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The class of multi-relational graph convolutional networks (MRGCNs) is a recent extension of standard graph convolutional networks (GCNs) to handle heterogenous graphs with multiple types of relationships. MRGCNs have been shown to yield results superior than traditional GCNs in various machine learning tasks. The key idea is to introduce a new kind of convolution operated on tensors that can effectively exploit correlations exhibited in multiple relationships. The main objective of this paper is to analyze the algorithmic stability and generalization guarantees of MRGCNs to confirm the usefulness of MRGCNs. Our contributions are of three folds. First, we develop a matrix representation of various tensor operations underneath MRGCNs to simplify the analysis significantly. Next, we prove the uniform stability of MRGCNs and deduce the convergence of the generalization gap to support the usefulness of MRGCNs. The analysis sheds lights on the design of MRGCNs, for instance, how the data should be scaled to achieve the uniform stability of the learning process. Finally, we provide experimental results to demonstrate the stability results. [ABSTRACT FROM AUTHOR]

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Identification of patients with high-risk asymptomatic atherosclerotic plaques remains an elusive but essential step in preventing stroke. However, there is a lack of animal model that provides a reproducible method to predict where, when and what types of plaque formation, which fulfils the American Heart Association (AHA) histological classification of human plaques. We have developed a predictive mouse model that reflects different stages of human plaques in a single carotid artery by means of shear-stress modifying cuff. Validated with over 30000 histological sections, the model generates a specific pattern of plaques with different risk levels along the same artery depending on their position relative to the cuff. The further upstream of the cuff-implanted artery, the lower the magnitude of shear stress, the more unstable the plaques of higher grade according to AHA classification; with characteristics including greater degree of vascular remodeling, plaque size, plaque vulnerability and inflammation, resulting in higher risk plaques. By weeks 20 and 30, this model achieved 80% and near 100% accuracy respectively, in predicting precisely where, when and what stages/AHA types of plaques develop along the same carotid artery. This model can generate clinically-relevant plaques with varying phenotypes fulfilling AHA classification and risk levels, in specific locations of the single artery with near 100% accuracy of prediction. The model offers a promising tool for development of diagnostic tools to target high-risk plaques, increasing accuracy in predicting which individual patients may require surgical intervention to prevent stroke, paving the way for personalized management of carotid atherosclerotic disease. [ABSTRACT FROM AUTHOR]

• Making use of the nonnegativity and the support constraints as well as the dictionary learning approach. • Establishing a blind deconvolution model to determine the inverse filter and the deblurred image. • Using sparse and redundant representations of the objective deblurred image over learned dictionaries. • The objective image can be represented with more details by the dictionary basis. In this paper, we study a novel inverse filtering method by using a dictionary approach. The main idea is to combine a learned dictionary for the representation of the deconvoluted image and an inverse filter based on nonnegativity and support constraints, to deconvolute the observed image with an unknown point spread function. The advantage of this approach is that the target image can be represented with more details by learned basis in the dictionary. We also employ the alternating direction method of multipliers to solve the resulting optimization problem. Experimental results are presented to show that the performance of the proposed methods are better than other testing methods for several testing images. [ABSTRACT FROM AUTHOR]

• Previously we identified a causal association of Dupuytren's Disease (DD) with a non-synonymous SNP variant (rs1042704, p.D273N) of MT1-MMP. • We discovered that this SNP variant MT1-MMP (MT1-N 273) exhibits only 17% of cell surface collagenolytic activity compared to the ancestral form of MT1-MMP (MT1-D 273). • DD patients myofibroblasts with heterozygous (G/A) and homozygous (A/A) SNP genotypes exhibited around 30% of collagen degrading activities in comparison to cells with wild-type (G/G) genotype. • Low collagenolytic activity of the SNP would contribute to the fibrotic phenotype of DD. Dupuytren's Disease (DD) is a common fibroproliferative disease of the palmar fascia. We previously identified a causal association with a non-synonymous variant (rs1042704, p.D273N) in MMP14 (encoding MT1-MMP). In this study, we investigated the functional consequences of this variant, and demonstrated that the variant MT1-MMP (MT1-N 273) exhibits only 17% of cell surface collagenolytic activity compared to the ancestral enzyme (MT1-D 273). Cells expressing both MT1-D 273 and MT1-N 273 in a 1:1 ratio, mimicking the heterozygous state, possess 38% of the collagenolytic activity compared to the cells expressing MT1-D 273 , suggesting that MT1-N 273 acts in a dominant negative manner. Consistent with the above observation, patient-derived DD myofibroblasts with the alternate allele demonstrated around 30% of full collagenolytic activity detected in ancestral G/G genotype cells, regardless of the heterozygous (G/A) or homozygous (A/A) state. Small angle X-ray scattering analysis of purified soluble Fc-fusion enzymes allowed us to construct a 3D-molecular envelope of MT1-D 273 and MT1-N 273 , and demonstrate altered flexibility and conformation of the ectodomains due to D 273 to N substitution. Taking together, rs1042704 significantly reduces collagen catabolism in tissue, which tips the balance of homeostasis of collagen in tissue, contributing to the fibrotic phenotype of DD. Since around 30% of the worldwide population have at least one copy of the low collagenolytic alternate allele, further investigation of rs1042704 across multiple pathologies is needed. [ABSTRACT FROM AUTHOR]

In this paper, we study a discretization scheme and the corresponding fast solver for multi-dimensional time–space fractional diffusion equation with variable coefficients, in which L 1 formula and shifted Grünwald formula are employed to discretize the temporal and spatial derivatives, respectively. A divide-and-conquer strategy is applied to the large linear system assembling discrete equations of all time levels, which in turn requires to solve a series of multidimensional linear systems related to the spatial discretization. Preconditioned generalized minimal residual method is employed to solve the spatial linear systems resulting from the spatial discretization. The discretization is proven to be unconditionally stable and convergent in the sense of infinity norm for general nonnegative coefficients. Numerical results are reported to show the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Feature extraction is a prerequisite in many machine learning and data mining applications. As the advancement of data acquisition techniques, nowadays tensor objects are accumulated with respect to frequency or time information in a great number of fields. For instance color or hyperspectral faces in multichannel information, and human gait motion in time information are obtained. In this paper, we propose and develop a block principal component analysis (BPCA) to extract features for this kind of tensor objects. Our idea is to unfold tensor objects according to their spatial information and frequency/time information, and represent them in block matrix form. The corresponding covariance matrix for frequency/time information can be captured and used. The block eigen-decomposition of such covariance matrix is employed to seek for projection solution as features. Both reconstruction and classification problems can be solved via these projected features. Extensive experiments have been conducted on various face or gait databases to demonstrate the superiority of BPCA compared with existing methods such as PCA, (2D) 2 PCA, MPCA, and UMPCA in terms of effectiveness. Moreover, the proposed BPCA is competitively efficient compared to these existing methods. [ABSTRACT FROM AUTHOR]

Selective image segmentation is an important topic in medical imaging and real applications. In this paper, we propose a weighted variational selective image segmentation model which contains two steps. The first stage is to obtain a smooth approximation related to Mumford-Shah model to the target region in the input image. Using weighted function, the approximation provides a larger value for the target region and smaller values for other regions. In the second stage, we make use of this approximation and perform a thresholding procedure to obtain the object of interest. The approximation can be obtained by the alternating direction method of multipliers and the convergence analysis of the method can be established. Experimental results for medical image selective segmentation are given to demonstrate the usefulness of the proposed method. We also do some comparisons and show that the performance of the proposed method is more competitive than other testing methods. [ABSTRACT FROM AUTHOR]

In this paper, we study a fast algorithm for finding stationary joint probability distributions of sparse Markov chains or multilinear PageRank vectors which arise from data mining applications. In these applications, the main computational problem is to calculate and store solutions of many unknowns in joint probability distributions of sparse Markov chains. Our idea is to approximate large-scale solutions of such sparse Markov chains by two components: the sparsity component and the rank-one component. Here the non-zero locations in the sparsity component refer to important associations in the joint probability distribution and the rank-one component refers to a background value of the solution. We propose to determine solutions by formulating and solving sparse and rank-one optimization problems via closed form solutions. The convergence of the truncated power method is established. Numerical examples of multilinear PageRank vector calculation and second-order web-linkage analysis are presented to show the efficiency of the proposed method. It is shown that both computation and storage are significantly reduced by comparing with the traditional power method. [ABSTRACT FROM AUTHOR]

Fractional partial differential equations (FPDEs) provide better modeling capabilities for challenging phenomena with long-range time memory and spatial interaction than integer-order PDEs do. A conventional numerical discretization of space–time FPDEs requires O ( N 2 + M N ) memory and O ( M N 3 + M 2 N ) computational work, where N is the number of spatial freedoms per time step and M is the number of time steps. We develop a fast finite difference method (FDM) for space–time FPDE: (i) We utilize the Toeplitz-like structure of the coefficient matrix to develop a matrix-free preconditioned fast Krylov subspace iterative solver to invert the coefficient matrix at each time step. (ii) We utilize a divide-and-conquer strategy, a recursive direct solver, to handle the temporal coupling of the numerical scheme. The fast method has an optimal memory requirement of O ( M N ) and an approximately linear computational complexity of O ( N M ( log N + log 2 M ) ) , without resorting to any lossy compression. Numerical experiments show the utility of the method. [ABSTRACT FROM AUTHOR]

Introduction Peripheral artery disease can lead to severe disability and limb loss. Therapeutic strategies focussing on macrovascular repair have shown benefit but have not significantly reduced amputation rates in progressive PAD. Proangiogenic small molecule therapies may substantially improve vascularisation in limb ischemia. The purpose of the current study was to assess the proangiogenic effects of simvastatin in a murine model of hind limb ischemia using longitudinal multimodal imaging. Methods Mice underwent surgical intervention to induce hind limb ischemia, and were treated with simvastatin orally for 28 days. Neovascularisation was assessed using 99m Tc-RGD SPECT imaging, and macrovascular volume was assessed by quantitative time of flight MRI. At each imaging time point, VEGF expression and capillary vessel density were quantified using immunohistochemical analysis. Results Simvastatin significantly increased 99m Tc-RGD retention in the ischemic hind limb by day 3 post-surgery, with maximal retention at day 8. Vascular volume was significantly increased in the ischemic hind limb of simvastatin treated animals, but only by day 22. Immunohistochemical analysis shows that simvastatin significantly augmented tissue VEGF expression from day 8 with increase in capillary density (CD31 + ) from day 14. Conclusions Early assessment of proangiogenic therapy efficacy can be identified using 99m Tc-RGD SPECT, which displays significant increases in retention before macrovascular volume changes are measureable with MRI. Advances in knowledge and implications for patient care Simvastatin offers an effective proangiogenic therapy as an adjunct for management of limb ischemia. Simvastatin induces integrin expression and vascular remodeling leading to neovascularisation and improved perfusion. [ABSTRACT FROM AUTHOR]

Multi-instance multi-label (MIML) learning is one of challenging research problems in machine learning. In the literature, there are several methods for solving MIML problems. However, they may take a long computational time and have a huge storage cost for large MIML data sets. The main aim of this paper is to propose and develop an efficient Markov Chain learning algorithm for MIML problems, especially for data represented by non-negative features. Our idea is to perform labels classification iteratively through two Markov chains constructed by using objects and features respectively. The classification of objects can be obtained by using labels propagation via training data in the iterative method. Moreover, we demonstrate that the proposed method can be formulated by considering normalized linear kernel. Because linear kernel function is explicit and separable, it is not necessary to compute and store a huge affinity matrix among objects/instances compared with the use of other kernel functions. Therefore, both the storage and computational time of the proposed algorithm are very efficient. Experimental results are presented to show that the classification performance of the proposed method using normalized linear kernel function is about the same as those using the other kernel functions, while the required computational time is much less, which together suggest that the linear kernel can be good enough for MIML problem. Also experimental results on some benchmark data sets are reported to illustrate the effectiveness of the proposed method in one-error, ranking loss, coverage and average precision, and show that it is competitive with the other MIML methods. [ABSTRACT FROM AUTHOR]

This paper proposes a subspace clustering algorithm with automatic feature grouping for clustering high-dimensional data. In this algorithm, a new component is introduced into the objective function to capture the feature groups and a new iterative process is defined to optimize the objective function so that the features of high-dimensional data are grouped automatically. Experiments on both synthetic data and real data show that the new algorithm outperforms the FG- k -means algorithm in terms of accuracy and choice of parameters. [ABSTRACT FROM AUTHOR]

This paper proposes a subspace clustering algorithm by introducing attribute weights in the affinity propagation algorithm. A new step is introduced to the affinity propagation process to iteratively update the attribute weights based on the current partition of the data. The relative magnitude of the attribute weights can be used to identify the subspaces in which clusters are embedded. Experiments on both synthetic data and real data show that the new algorithm outperforms the affinity propagation algorithm in recovering clusters from data. [ABSTRACT FROM AUTHOR]

Deep neural networks have achieved great success in solving many machine learning and computer vision problems. In this paper, we propose a deep neural network called the Tucker network derived from the Tucker format and analyze its expressive power. The results demonstrate that the Tucker network has exponentially higher expressive power than the shallow network. In other words, a shallow network with an exponential width is required to realize the same score function as that computed by the Tucker network. Moreover, we discuss the expressive power between the hierarchical Tucker tensor network (HT network) and the proposed Tucker network. To generalize the Tucker network into a deep version, we combine the hierarchical Tucker format and Tucker format to propose a deep Tucker tensor decomposition. Its corresponding deep Tucker network is presented. Experiments are conducted on three datasets: MNIST, CIFAR-10 and CIFAR-100. The results experimentally validate the theoretical results and show that the Tucker network and deep Tucker network have better performance than the shallow network and HT network. [ABSTRACT FROM AUTHOR]

In many sparsity-based image processing problems, compared with the convex ℓ 1 norm approximation of the nonconvex ℓ 0 quasi-norm, one can often preserve the structures better by taking full advantage of the nonconvex ℓ p quasi-norm (0 ≤ p < 1). In this paper, we propose a nonconvex ℓ p quasi-norm approximation in the total generalized variation (TGV)-shearlet regularization for image reconstruction. By introducing some auxiliary variables, the nonconvex nonsmooth objective function can be solved by an efficient alternating direction method of multipliers with convergence analysis. Especially, we use a generalized iterated shrinkage operator to deal with the ℓ p quasi-norm subproblem, which is easy to implement. Extensive experimental results show clearly that the proposed nonconvex sparsity approximation outperforms some state-of-the-art algorithms in both the visual and quantitative measures for different sampling ratios and noise levels. [ABSTRACT FROM AUTHOR]

Paragangliomas are rare neoplasms arising from cells of the primitive neural crest. These tumours are often difficult to diagnose and treat. We report a case of a 42 year old female presenting with abdominal pain who had a retroperitoneal tumour situated at the aortic bifurcation. Serum catecholamine levels were normal. Complete resection of the tumour was performed. The histological examination and immunohistochemical analyses concluded the diagnosis of an organ of Zuckerkandl paraganglioma. [ABSTRACT FROM AUTHOR]

This paper describes a new algorithm for computing Nonnegative Low Rank Matrix (NLRM) approximation for nonnegative matrices. Our approach is completely different from classical nonnegative matrix factorization (NMF) which has been studied for more than twenty five years. For a given nonnegative matrix, the usual NMF approach is to determine two nonnegative low rank matrices such that the distance between their product and the given nonnegative matrix is as small as possible. However, the proposed NLRM approach is to determine a nonnegative low rank matrix such that the distance between such matrix and the given nonnegative matrix is as small as possible. There are two advantages. (i) The minimized distance by the proposed NLRM method can be smaller than that by the NMF method, and it implies that the proposed NLRM method can obtain a better low rank matrix approximation. (ii) Our low rank matrix admits a matrix singular value decomposition automatically which provides a significant index based on singular values that can be used to identify important singular basis vectors, while this information cannot be obtained in the classical NMF. The proposed NLRM approximation algorithm was derived using the alternating projection on the low rank matrix manifold and the non-negativity property. Experimental results are presented to demonstrate the above mentioned advantages of the proposed NLRM method compared the NMF method. [ABSTRACT FROM AUTHOR]

• A patched-tubes unitary transform method for robust tensor completion is developed, which is to extract similar patched-tubes to form a third-order sub-tensor, and then a transformed t-SVD is employed to recover such incomplete and/or corrupted sub-tensor. • The perturbation results of the transformed t-SVD for patched-tubes tensor completion are established. • Extensive numerical experiments are presented to demonstrate the superior performance of the proposed patched-tubes unitary transform method over testing state-of-the-art robust tensor completion methods. The aim of the robust tensor completion problem for third-order tensors is to recover a low-rank tensor from incomplete and/or corrupted observations. In this paper, we develop a patched-tubes unitary transform method for robust tensor completion. The proposed method is to extract similar patched-tubes to form a third-order sub-tensor, and then a transformed tensor singular value decomposition is employed to recover such low-rank incomplete and/or corrupted sub-tensor. Here the unitary transform matrix for transformed tensor singular value decomposition is constructed by using left singular vectors of the unfolding matrix arising from such sub-tensor. Moreover, we establish the perturbation results of the transformed tensor singular value decomposition for patched-tubes tensor completion. Extensive numerical experiments on hyperspectral, video and face data sets are presented to demonstrate the superior performance of the proposed patched-tubes unitary transform method over testing state-of-the-art robust tensor completion methods. [ABSTRACT FROM AUTHOR]

Pure quaternion matrix has been widely employed to represent data in real-world applications, such as colour images. Additionally, the imaginary part of quaternion matrix is usually nonnegative due to the natural nonnegativity of real-world data. In this paper, we propose an alternating projection-based algorithm for low rank nonnegative pure quaternion matrix approximation, which can exactly calculate the optimal fixed rank approximation while preserve the pure and nonnegative properties from the given data. More concretely, the proposed algorithm alternatively projects the given quaternion matrix onto the fixed rank quaternion matrix set and nonnegative pure quaternion matrix set in an iterative fashion. Moreover, we establish the theoretical convergence guarantee of the proposed algorithm. To extend the proposed algorithm to large-scaled data, we further propose a randomized algorithm with significant lower computational complexity and comparable accuracy. Numerical experiments on colour images show that our algorithms outperform the other state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

• SVTV regularization term is applied to model the target color image in HSV color space. • The fidelity term is well-adapted to multiplicative noise. • The existence and uniqueness of the minimizer of the proposed minimization problem is shown. • The convergence of an implicit scheme of the associated evolution problem is given. In this paper, we propose and develop a novel Saturation-Value Total Variation (SVTV) model for multiplicative noise and blur removal of color images. In the proposed model, SVTV regularization term is applied to model the target color image in HSV color space instead of RGB color space, and the fidelity term is well-adapted to multiplicative noise. We investigate into the existence and uniqueness of the minimizer of the proposed minimization problem. We study and show the convergence of an implicit scheme of the associated evolution problem for the numerical solution of the proposed SVTV model. Numerical examples are presented to demonstrate the performance of the proposed SVTV model is significantly better than that of other testing methods in terms of some criteria such as PSNR, SSIM and S-CIELAB color error. [ABSTRACT FROM AUTHOR]

In this paper, we make use of the fact that the matrix u is (approximately) low-rank in image inpainting, and the corresponding gradient transform matrices D x u , D y u are sparse in image reconstruction and restoration. Therefore we consider that these gradient matrices D x u , D y u also are (approximately) low-rank, and also verify it by numerical test and theoretical analysis. We propose a model called compressive total variation (CTV) to characterize the sparsity and low-rank prior knowledge of an image. In order to solve the proposed model, we design a concrete algorithm with provably convergence, which is based on inertial proximal ADMM. The performance of the proposed model is tested for magnetic resonance imaging (MRI) reconstruction, image denoising and image deblurring. The proposed method not only recovers edges of the image but also preserves fine details of the image. And our model is much better than the existing regularization models based on the TGV, Shearlet-TGV, ℓ 1 − α ℓ 2 TV and BM3D in test for images with piecewise constant regions. And it visibly improves the performances of TV, ℓ 1 − α ℓ 2 TV and TGV, and is comparable to Shearlet-TGV in test for natural images. [ABSTRACT FROM AUTHOR]

• Propose to construct analysis by using forecast gradients instead of forecast values in 3DVar data assimilation. • The second-order finite difference matrix is used to replace background covariance matrix required for estimation. • The existence and uniqueness of the analysis solution of proposed objective function are established. • The solution can be calculated by using the conjugate gradient method iteratively. • CMAQ and WRF simulations are presented to demonstrate the performance of the proposed method is good. In this paper, we propose an optimization approach for data assimilation by the use of forecast gradients. The proposed objective function consists of two data-fitting terms. The first term is based on the difference between the gradients of the forecast and the analysis, and the second term is based on the difference between the observations and the analysis in observation space. The motivation for using forecast gradients is that the forecast values provide an estimation of the system state, but they may not be accurate enough. We therefore propose to construct analysis gradients driven by the forecast gradients, instead of the forecast values. The associated data-fitting term can be interpreted by using the second-order finite difference matrix as the inverse of the background error covariance matrix in the 3DVar setting. In the proposed approach, it is not necessary to estimate the background covariance matrix and to deal with its inverse in the 3DVar algorithm. The existence and uniqueness of the analysis solution of the proposed objective function are established in this paper. The solution can be calculated by using the conjugate gradient method iteratively. Experimental results based on Community Multiscale Air Quality (CMAQ) and Weather Research and Forecasting (WRF) simulations are presented. We show in our air quality data assimilation experiment that the performance of the proposed method is better than that of the 3DVar method and the En3DVar method. The average improvements over the CMAQ simulation results for single-species NO 2 , O 3 , SO 2 , NO, and CO are 18.9%, 34.0%, 22.2%, 4.3%, and 91.9%, respectively; and for the multiple-species PM2.5 and PM10, the improvements are 61.2% and 70.1%, respectively. In addition, the performance of the proposed method in temperature data assimilation is improved by 45.1% compared with the 3DVar method. [ABSTRACT FROM AUTHOR]

Abstract Color transfer methods usually suffer from spatial color coherency problem. In order to address this problem, this paper develops a fused color transfer method for image colorization. Our idea is to design a local student's t-test to screen the incoherent colors in the preliminary colorization results obtained by a simple color transfer method with DFT and variance features. Furthermore, we propose a variational fusion model to inpaint these incoherent colors and fuse the other useful colors together. We also present an efficient algorithm for solving the fusion model numerically, and show the convergence of the algorithm. Finally, experimental results are reported to demonstrate the effectiveness of the proposed method, and its performance is competitive with those of the other testing methods. [ABSTRACT FROM AUTHOR]

Detection of flowering and quantification of flowering phenology are key to monitoring the reproduction of tropical trees and their response to global change. However, effective monitoring of flowering over various scales from individuals to forest ecosystem levels is lacking due to the relatively small sizes of flowers, diverse flowering strategies across species, and the short duration of flowering, making accurate flower detection difficult. Drone-based surveys require less time and human resources than traditional ground-based flower surveys and thus may be able to help address this in a cost-effective manner but remain underexplored in species-rich tropical forest ecosystems. Here, we developed a method that integrated the Residual Networks 50 (ResNet50) deep learning algorithm with high resolution imagery (c. 0.05 m) from monthly drone surveys done in a 50-ha tropical forest plot on Barro Colorado Island (BCI), Panamá, over 2018–2020 to detect a diversity of flowering species in this tree community and to track the timing of flowering throughout the year. We built a comprehensive training library of canopy components (flower, leaf, branch, and shade) from this forest plot throughout the study period, trained a single deep learning model across all drone imagery, and validated it using five-fold cross validation at the pixel scale. We further generated image- and tree-crown-specific supervised classifications to evaluate the deep learning model at the tree-crown scale. Our deep learning method accurately classified flowers (User's accuracy = 95.3 %, Producer's accuracy = 85.8 %) while maintaining high predictive power for the other three classes (Overall accuracy = 98.4 %). Our results also demonstrated high consistency against tree-crown-specific supervised classifications for flower (r2 = 0.85), leaf (r2 = 0.84), and branch (r2 = 0.92) components, with lower agreement observed for the shade component (r2 = 0.59). These results demonstrate the effectiveness of our method in advancing fine-scale flower monitoring in the tropics, with potential to be extended to other regions or other remote sensing platforms with frequent high-resolution monitoring. The method will allow us to better monitor flowering in tropical forests and improve our understanding of how phenology and reproductive success may be affected by climate change. [ABSTRACT FROM AUTHOR]

Drug–target interaction (DTI) prediction is a challenging step in further drug repositioning, drug discovery and drug design. The advent of high-throughput technologies brings convenience to the development of DTI prediction methods. With the generation of a high number of data sets, many mathematical models and computational algorithms have been developed to identify the potential drug–target pairs. However, most existing methods are proposed based on the single view data. By integrating the drug and target data from different views, we aim to get more stable and accurate prediction results. In this paper, a multiview DTI prediction method based on clustering is proposed. We first introduce a model for single view drug–target data. The model is formulated as an optimization problem, which aims to identify the clusters in both drug similarity network and target protein similarity network, and at the same time make the clusters with more known DTIs be connected together. Then the model is extended to multiview network data by maximizing the consistency of the clusters in each view. An approximation method is proposed to solve the optimization problem. We apply the proposed algorithms to two views of data. Comparisons with some existing algorithms show that the multiview DTI prediction algorithm can produce more accurate predictions. For the considered data set, we finally predict 54 possible DTIs. From the similarity analysis of the drugs/targets, enrichment analysis of DTIs and genes in each cluster, it is shown that the predicted DTIs have a high possibility to be true. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to generalize matrix numerical ranges to the tensor case based on tensor norms. We show that the basic properties of matrix numerical ranges such as compactness and convexity are valid for tensor numerical ranges. We make use of convexity property to propose an algorithm for approximating tensor numerical ranges in which tensor eigenvalues are contained. Also we consider tensor numerical ranges based on inner products, however, they may not be convex in general. [ABSTRACT FROM AUTHOR]

Node classification is a popular and challenging task in graph neural networks, and existing approaches are mainly developed for a single network. With the advances in domain adaptation, researchers tend to leverage knowledge extracted from a fully-labeled source network to further improve the node classification performance in an unlabeled target network. This learning paradigm refers to cross-network node classification, which is the topic we studied in this paper. Specifically, we propose a novel model named Transferable Graph Auto-Encoders (TGAE), which first encodes the initial network data into latent representations and then decodes the learned features to preserve graph information. In the encoding phase, TGAE adopts the attentional mechanism to fuse the local and global information of nodes to discover latent node representations. To obtain transferable features between the source and target networks, TGAE aligns their distributions based on the learned representations by reducing marginal and conditional distribution differences. In the decoding phase, the latent representations are subjected to pairwise and reconstruction constraints, thus preserving structural proximity and graph topology information to learn discriminative features. Besides, a node classifier is trained to enhance the discriminant of the node representations further. Experimental results on several real-world datasets demonstrate that the proposed model achieves state-of-the-art performance in cross-network node classification tasks compared with existing methods. • TGAE is proposed to handle cross-network node classification problem. • TGAE encodes local and global information and preserves structural graph information. • Experimental results demonstrate the superior performance of the proposed model. [ABSTRACT FROM AUTHOR]

Primitivity is an important concept in the spectral theory of nonnegative matrices and tensors. It is well-known that an irreducible matrix is primitive if and only if the greatest common divisor of all the cycles in the associated directed graph is equal to 1. The main aim of this paper is to establish a similar result, i.e., we show that a nonnegative tensor is primitive if and only if the greatest common divisor of all the cycles in the associated directed hypergraph is equal to 1. [ABSTRACT FROM AUTHOR]