Sparse Matrix Research Articles

Three-layered location recommendation algorithm using spectral clustering

Users utilize Location-Based Social Networks (LBSNs) to check into diverse venues and share their experiences through ratings and comments. However, these platforms typically feature a considerably larger number of locations than users, resulting in a challenge known as insufficient historical data or user-location matrix sparsity. This sparsity arises because not all users can check into all available locations on a given LBSN, such as Yelp. To address this challenge, this paper proposes combining Spectral Clustering with a three-layered location recommendation model to develop a recommender system named LSC, applied to Yelp datasets. LSC leverages various information, including users’ check-in data, demographics, location demographics, and users’ friendship network data, to train the recommender system and generate recommendations. Evaluation of LSC’s performance utilizes the Yelp dataset and several comparison metrics, such as accuracy, RMSE, and F1-score. The results demonstrate that our proposed algorithm delivers reliable and significant performance improvements across various evaluation metrics compared to competing algorithms.

Multiresolution kernel matrix algebra

AbstractWe propose a sparse algebra for samplet compressed kernel matrices to enable efficient scattered data analysis. We show that the compression of kernel matrices by means of samplets produces optimally sparse matrices in a certain S-format. The compression can be performed in cost and memory that scale essentially linearly with the number of data points for kernels of finite differentiability. The same holds true for the addition and multiplication of S-formatted matrices. We prove that the inverse of a kernel matrix, given that it exists, is compressible in the S-format as well. The use of selected inversion allows to directly compute the entries in the corresponding sparsity pattern. Moreover, S-formatted matrix operations enable the efficient, approximate computation of more complicated matrix functions such as $${\varvec{A}}^\alpha $$ A α or $$\exp ({\varvec{A}})$$ exp ( A ) of a matrix $${\varvec{A}}$$ A . The matrix algebra is justified mathematically by pseudo differential calculus. As an application, we consider Gaussian process learning algorithms for implicit surfaces. Numerical results are presented to illustrate and quantify our findings.

Application of optimized sparse encoding algorithm in data compression

Data transmission is crucial in the process of equipment monitoring. The compression algorithms are adopted to reduce the amount of data transmission. When sparse encoding algorithms are used for this purpose, despite extensive attempts to improve their performance, some problems still remain. The main issues pertain to: (1) Dictionary construction − As practical dictionary better matches the input signal, such a dictionary must be efficiently established; 2) The setting of sparsity value − It is difficult to determine the size of sparsity values when prior knowledge is insufficient (when the parameter settings are too large, the cost of data transmission increases considerably, while excessively small values can result in poor reconstruction accuracy); and (3) How to implement engineering applications of data compression based on sparse encoding. To address these issues, in this work, an optimized sparse encoding algorithm is proposed by combining the non-negative Online Dictionary Learning (ODL) with the optimized Orthogonal Matching Pursuit (OMP) algorithm. First, a non-negative ODL algorithm is adopted for dictionary learning based on the training dataset to obtain an effective dictionary. Next, the optimized OMP algorithm is used to obtain the sparsity and the sparse coefficient matrix. Further analyses confirm that the reconstructed signal has a small reconstruction error. Finally, A lossy compression framework is proposed for the compressing equipment condition monitoring data using sparse encoding algorithms. Compared with the compression algorithms based on compressive sensing and DCT, the average compression ratio can reach 42.7 when the reconstruction accuracy is similar. In terms of comprehensive compression performance, the quality score is also higher compared to other algorithms.

I❤MESH: A DSL for Mesh Processing

I❤MESH: A DSL for Mesh Processing

Dictionary-Based Multi-View Learning With Privileged Information

Multi-view learning can improve classification performance by combining information between different views. Due to the similarity in different views of the dataset, sometimes the features obtained are highly limited and redundant. At the same time, different views accumulate a large amount of noisy information, which will affect the classification performance of the model. To solve these problems, we embed privileged information in the model and introduce dictionary learning, and proposed a new dictionary-based multi-view learning method with privileged information (MVDL-PI). First, two sets of dictionaries (synthetic dictionary and analysis dictionary) and sparse representation matrices of different information domains are obtained for each view information and privilege information through dictionary learning. Then, we obtain consistency information from the regularization terms of the two different sets of synthetic dictionaries and construct a LUPI (Learning using privileged information) classifier by the sparse representation. In addition, we use alternating convex optimization and Lagrange multiplier methods to optimize the model and prove its convergence. In the experiment, we did a number of experiments comparing this method with similar recent methods. The experimental results show that the MVDL-PI method is superior to other methods in terms of stability and classification accuracy.

Partial multi-label feature selection via low-rank and sparse factorization with manifold learning

Feature selection is a commonly utilized methodology in multi-label learning (MLL) for tackling the challenge of high-dimensional data. Accurate annotation of relevant labels is crucial for successful multi-label feature selection (MFS). Nevertheless, multi-label datasets frequently consist of ground-truth and noisy labels in real-world applications, giving rise to the partial multi-label learning (PML) problem. The inclusion of noisy labels complicates the task of conventional MFS methods in accurately identifying the optimal features subset in such datasets. To tackle this issue, we propose a novel partial multi-label feature selection method with low-rank sparse factorization and manifold learning, called PMFS-LRS. Specifically, we first decompose the candidate label matrix into two distinct components: a low-rank matrix referring to ground-truth labels and a sparse matrix referring to noisy labels. This decomposition allows PMFS-LRS to effectively distinguish noise labels from ground-truth labels, thereby mitigating the impact of noisy data. Then, the local label correlations are explored using a manifold learning framework to improve the label disambiguation performance. Finally, a l2,1-norm regularization is integrated into the objective function to facilitate effective feature selection. Comprehensive experiments conducted on both real-world and synthetic PML datasets demonstrate that PMFS-LRS is superior to several existing state-of-the-art MFS methods.

Sparse graph cascade multi-kernel fusion contrastive learning for microbe–disease association prediction

Predicting microbe–disease associations (MDA) is crucial for proactively demystifying diseases causes and preventing them. Traditional prediction methods endure labor-intensive, time-consuming, and expensive. Therefore, this paper proposes CasMF-GCL, a novel Graph Contrastive Learning model based on sparse relation augmentation and a Cascaded Multi-kernel Fusion Network for MDA prediction. CasMF-GCL maximizes the use of sparse correlation information and eliminates data noise through an association augmentation technique based on low-rank sparse matrix completion. We employ diverse strategies to enhance the features of heterogeneous networks by exploring the similarity between microbes and diseases. Our model employs a new multi-layer graph convolutional network variant with a cascaded multi-kernel fusion mechanism, enabling weighted coding of local and global features for diseases and microbes. To further improve performance, we incorporate a self-supervised contrastive learning schema using multi-grain disease and microbe features and large-scale relation augmentations. Extensive experiments on two renowned datasets demonstrate that CasMF-GCL outperforms current state-of-the-art methods in seven indexes. The AUC values from 5-fold cross-validation are 0.997 and 0.989 for the two datasets, respectively. Ablation studies confirm the effectiveness of graph data augmentation, the power of the contrastive strategy, and the indispensability of the cascaded multi-kernel fusion network. Furthermore, case studies validate the prediction performance of CasMF-GCL.

FNIRS based study of brain network characteristics in children with cerebral palsy during bilateral lower limb movement.

Motor dysfunctions in children with cerebral palsy (CP) are caused by nonprogressive brain damage. Understanding the functional characteristics of the brain is important for rehabilitation. This paper aimed to study the brain networks of children with CP during bilateral lower limb movement using functional near-infrared spectroscopy (fNIRS) and to explore effective fNIRS indices for reflecting functional brain activity. Using fNIRS, cerebral oxygenation signals in the bilateral prefrontal cortex (LPFC/RPFC) and motor cortex (LMC/RMC) were recorded from fifteen children with spastic CP and seventeen children with typical development (CTDs) in the resting state and during bilateral lower limb movement. Functional connectivity matrices based on phase-locking values (PLVs) were calculated using Hilbert transformation, and binary networks were constructed at different sparsity levels. Network metrics such as the clustering coefficient, global efficiency, local efficiency, and transitivity were calculated. Furthermore, the time-varying curves of network metrics during movement were obtained by dividing the time window and using sparse inverse covariance matrices. Finally, conditional Granger causality (GC) was used to explore the causal relationships between different brain regions. Compared to CTDs, the connectivity between RMC-RPFC (p=0.017) and RMC-LMC (p=0.002) in the brain network was decreased in children with CP, and the clustering coefficient (p=0.003), global efficiency (p=0.034), local efficiency (p=0.015), and transitivity (p=0.009) were significantly lower. The standard deviation of the changes in global efficiency of children with CP during motion was also greater than that of CTDs. Using GC, it was found that there was a significant increase in causal strength from the RMC to the RPFC (p=0.04) and from the RMC to the LMC (p=0.042) in children with CP during motion. Additionally, there were significant negative correlations between the PLV of LMC-RMC (p=0.002) and the Gross Motor Function Classification System (GMFCS) and between the GMFCS and the clustering coefficient (p=0.01). During rehabilitation training of the lower limbs, there were significant differences in brain network indices between children with CP and CTDs. The indicators proposed in this paper are effective at evaluating motor function and the real-time impact of rehabilitation training on the brain network and have great potential for application in guiding clinical motor function assessment and planning rehabilitation strategies.

Compiling Recurrences over Dense and Sparse Arrays

We present a framework for compiling recurrence equations into native code. In our framework, users specify a system of recurrences, the types of data structures that store inputs and outputs, and scheduling commands for optimization. Our compiler then lowers these specifications into native code that respects the dependencies in the recurrence equations. Our compiler can generate code over both sparse and dense data structures, and determines if the recurrence system is solvable with the provided scheduling primitives. We evaluate the performance and correctness of the generated code on several recurrences, from domains as diverse as dense and sparse matrix solvers, dynamic programming, graph problems, and sparse tensor algebra. We demonstrate that the generated code has competitive performance to hand-optimized implementations in libraries. However, these handwritten libraries target specific recurrences, specific data structures, and specific optimizations. Our system, on the other hand, automatically generates implementations from recurrences, data formats, and schedules, giving our system more generality than library approaches.

An Adaptive Tracking Method for Moving Target in Fluctuating Reverberation Environment

In environments with a low signal-to-reverberation ratio (SRR) characterized by fluctuations in clutter number and distribution, particle filter-based tracking methods may experience significant fluctuations in the posterior probability of existence. This can lead to interruptions or even loss of the target trajectory. To address this issue, an adaptive PF-based tracking method (APF) with joint reverberation suppression is proposed. This method establishes the state space model under the Bayesian framework and implements it through particle filtering. To keep the weak target echoes, all the non-zero entries contained in the sparse matrix processed by the low-rank and sparsity decomposition (LRSD) are treated as the measurements. The prominent feature of this approach is introducing an adaptive measurement likelihood ratio (AMLR) into the posterior update step, which solves the problem of unstable tracking due to the strong fluctuation in the number of point measurements per frame. The proposed method is verified by four shallow water experimental datasets obtained by an active sonar with a uniform horizontal linear array. The results demonstrate that the tracking frame success ratio of the proposed method improved by over 14% compared with the conventional PF tracking method.

Distributed Consensus for Global Matrix Formation in the Principal Component Pursuit Scenario

The aim behind principal component pursuit is to recover a low-rank matrix and a sparse matrix from a noisy signal which is the sum of both matrices. This optimization problem is a priori and non-convex and is useful in signal processing, data compression, image processing, machine learning, fluid dynamics, and more. Here, a distributed scheme described by a static undirected graph, where each agent only observes part of the noisy or corrupted matrix, is applied to achieve a consensus; then, a robust approach that can also handle missing values is applied using alternating directions to solve the convex relaxation problem, which actually solves the non-convex problem under some weak assumptions. Some examples of image recovery are shown, where the network of agents achieves consensus exponentially fast.

Robust sparse concept factorization with graph regularization for subspace learning

Concept factorization (CF) is a powerful tool in subspace learning. Recently graph-based CF and local coordinate CF have been proposed to exploit the intrinsic geometrical structure of data, and have been shown quite successful in improving performance. However, these methods have limited robustness and might be sensitive to noises and disturbances in practical applications. In this paper, we propose a novel robust sparse CF framework (RSCF) for subspace learning. Specifically, we present a robust loss function to effectively eliminate the impact of the large outliers. The local coordinate constraint and the graph regularization term are incorporated into RSCF to simultaneously guarantee the sparsity of the coefficient matrix and maintain the local structure of the data. We prove that the local coordinate constraint implies the orthogonality of the coefficient matrix. By using the half-quadratic optimization technique, we transform the objective function of RSCF into a quadratic form and provide the iterative updating rules and the convergence analysis. Extensive experiments demonstrate the robustness and superiority of the proposed RSCF in comparison to state-of-the-art CF methods.

Algorithm xxx: Faster Randomized SVD with Dynamic Shifts

Aiming to provide a faster and convenient truncated SVD algorithm for large sparse matrices from real applications (i.e. for computing a few of largest singular values and the corresponding singular vectors), a dynamically shifted power iteration technique is applied to improve the accuracy of the randomized SVD method. This results in a d yn a mic sh ifts based randomized SVD (dashSVD) algorithm, which also collaborates with the skills for handling sparse matrices. An accuracy-control mechanism is included in the dashSVD algorithm to approximately monitor the per vector error bound of computed singular vectors with negligible overhead. Experiments on real-world data validate that the dashSVD algorithm largely improves the accuracy of randomized SVD algorithm or attains same accuracy with fewer passes over the matrix, and provides an efficient accuracy-control mechanism to the randomized SVD computation, while demonstrating the advantages on runtime and parallel efficiency. A bound of the approximation error of the randomized SVD with the shifted power iteration is also proved.

Leveraging index compression techniques to optimize the use of co-processors


 
 
 The significant presence that many-core devices like GPUs have these days, and their enormous computational power, motivates the study of sparse matrix operations in this hardware. The essential sparse kernels in scientific computing, such as the sparse matrix-vector multiplication (SpMV), usually have many different high-performance GPU implementations. Sparse matrix problems typically imply memory-bound operations, and this characteristic is particularly limiting in massively parallel processors. This work revisits the main ideas about reducing the volume of data required by sparse storage formats and advances in understanding some compression techniques. In particular, we study the use of index compression combined with sparse matrix reordering techniques in CSR and explore other approaches using a blocked format. The systematic experimental evaluation on a large set of real-world matrices confirms that this approach achieves meaningful data storage reductions. Additionally, we find promising results of the impact of the storage reduction on the execution time when using accelerators to perform the mathematical kernels.
 
 

Graph-based phishing detection: URLGBM model driven by machine learning

Phishing attacks are a form of social engineering that involves the transmission of deceptive communications imitating a trustworthy source to deceive users into revealing confidential information. Antiphishing systems have made significant strides in recent years, allowing internet users to secure confidential and private information against such attacks. In this study, we propose a URL graph representation based on a random walk algorithm, specifically PageRank, for weighting URL tokens. To create the graph, an imaginary walker visits the URL tokens one at a time and assigns a value to each token based on the probability of encountering the target URL during the walk. We studied different random walk (rw) variations and their effects on the URL string. The BM25 algorithm was employed to produce a sparse matrix for the classification task from the token scores obtained. Experiments conducted with logistic regression revealed that the proposed model achieved an accuracy of 98.98%, a false alarm rate of 1.72%, and a missing alarm rate of 0.302%. The model also attained a 97.17% accuracy on a benchmark dataset.

VerSA: Versatile Systolic Array Architecture for Sparse and Dense Matrix Multiplications

A key part of modern deep neural network (DNN) applications is matrix multiplication. As DNN applications are becoming more diverse, there is a need for both dense and sparse matrix multiplications to be accelerated by hardware. However, most hardware accelerators are designed to accelerate either dense or sparse matrix multiplication. In this paper, we propose VerSA, a versatile systolic array architecture for both dense and sparse matrix multiplications. VerSA employs intermediate paths and SRAM buffers between the rows of the systolic array (SA), thereby enabling an early termination in sparse matrix multiplication with a negligible performance overhead when running dense matrix multiplication. When running sparse matrix multiplication, 256 × 256 VerSA brings performance (i.e., an inverse of execution time) improvement and energy saving by 1.21×–1.60× and 7.5–30.2%, respectively, when compared to the conventional SA. When running dense matrix multiplication, VerSA results in only a 0.52% performance overhead compared to the conventional SA.

Determination of a Configuration for Sparse Matrix Phased Array Using Simulated Annealing for Imaging in Ultrasonic NDT

Determination of a Configuration for Sparse Matrix Phased Array Using Simulated Annealing for Imaging in Ultrasonic NDT

Saliency-Guided Sparse Low-Rank Tensor Approximation for Unsupervised Anomaly Detection of Hyperspectral Remote Sensing Images

Hyperspectral anomaly detection can separate sparse anomalies from the low-rank background component under an unsupervised behavior due to sufficient spectral information. Therefore, hyperspectral image anomaly detection technology has great application potential and value in public security and national defense. Currently, most existing models attempt to detect anomalous targets with a sparsity prior, without further considering the visual saliency of the targets themselves. To tackle this issue, this paper proposes a saliency-guided sparse low-rank tensor approximation model, called SSLR, to detect anomalous targets from hyperspectral remote sensing images in an unsupervised manner. Specifically, we first explore the saliency information of each pixel for regularizing the sparse anomaly matrix. We then suggest a three-directional tensor nuclear norm to obtain a low-rank background to characterize the background component. We solve the SSLR optimization problem by an efficient alternating direction method of multipliers framework. Experiments conducted on benchmark hyperspectral datasets demonstrate that the proposed SSLR outperforms some state-of-the-art anomaly detection methods.

SHORYUKEN: An open-source software package for calculating nonlocal exchange interactions in nanowires

We present the open-source software package, SHORYUKEN (Streamlined High-level Operations in Real-space to Yield, Understand, and Keep Exchange in Nanowires), for calculating nonlocal exchange interactions in nanowires with arbitrary geometries, sizes, doping densities, and compositions. In addition to enabling new calculations of nonlocal exchange, the SHORYUKEN software package is a significant enhancement of our previous HADOKEN code and includes new algorithmic improvements as well as an improved treatment of surface states for nanowires with intrinsic polarization. Our calculations show that the inclusion of nonlocal exchange can have significant effects on the eigenenergy spectrum, number of occupied states, and distribution of electrons within these nanosystems. The SHORYUKEN software package is the first open-source code for calculating nonlocal exchange to predict electron gas formation in nanowire systems with arbitrary cross-sectional geometries. Program summaryProgram Title: SHORYUKENCPC Library link to program files:https://doi.org/10.17632/f77p84pbcv.1Licensing provisions: GNU General Public License 3Programming language: MATLABNature of problem: The SHORYUKEN code calculates nonlocal exchange interactions of electrons in nanowires by solving modified nonlocal exchange and Poisson-like equations self-consistently on a finite element grid. The software package is capable of performing calculations for core-multishell nanowires with arbitrary cross-sectional shapes.Solution method: iterative solution of the Schrödinger-Poisson equations with nonlocal exchange using finite element methods and sparse matrix linear algebra

Low-complexity GFDM transmission scheme for low earth orbit satellite communications

As a promising multi-carrier modulation scheme, Generalized Frequency Division Multiplexing (GFDM) has certain advantages in low earth orbit satellite communications. However, the cost of GFDM to obtain these advantages is the self-interference caused by non-orthogonality and the increase of computational complexity. This paper proposes two low-complexity transceiver schemes for GFDM based on matrix sparsity. Firstly, the paper summarizes two GFDM modulation structures, referred to as structure types I and II, based on modulation data. Next, the modulation matrix in both structures is divided into sub-matrices, and the modulation sub-matrix is made sparse by leveraging the properties of the Fourier transform, so as to reduce the complexity of the transmitter. Similarly, by performing sparse processing on the received matrix and converting it into a block diagonal matrix form, the complexity of the receiver can be effectively reduced. The computational costs of our proposed schemes are analyzed in detail and compared with the existing solutions that are known to have the lowest complexity. The simulation results demonstrate that the two proposed schemes can provide satisfactory low-complexity performance depending on the time–frequency structure.