Sparse Matrix Research Articles

Variational quantum algorithm for the Poisson equation based on the banded Toeplitz systems

Abstract For solving the Poisson equation it is usually possible to discretize it into solving the corresponding linear system $Ax=b$. Variational quantum algorithms (VQAs) for \textcolor{red}{the discreted} Poisson equation have been studied before. We give a VQA based on the banded Toeplitz systems for solving the Poisson equation with respect to the structural features of matrix $A$. In detail, we decompose the matrix $A$ and $A^2$ into a linear combination of the corresponding banded Toeplitz matrix and sparse matrices with only a few non-zero elements. For the one-dimensional Poisson equation with different boundary conditions and the $d$-dimensional Poisson equation with Dirichlet boundary conditions, \textcolor{red}{the number of decomposition terms is less than the work in [Phys. Rev. A108, 032418 (2023)]}. Based on the decomposition of the matrix, we design quantum circuits that \textcolor{red}{evaluate efficiently} the cost function. \textcolor{red}{Additionally, numerical simulation verifies the feasibility of the proposed algorithm. In the end,} the VQAs for linear systems of equations and matrix–vector multiplications with $K$-banded Teoplitz matrix $T_n^K$ \textcolor{red}{are} given, where $T_n^K\in R^{n\times n}$ and $K\in O(ploy\log n)$.

Matrix Factorization and Prediction for High-Dimensional Co-Occurrence Count Data via Shared Parameter Alternating Zero Inflated Gamma Model

High-dimensional sparse matrix data frequently arise in various applications. A notable example is the weighted word–word co-occurrence count data, which summarizes the weighted frequency of word pairs appearing within the same context window. This type of data typically contains highly skewed non-negative values with an abundance of zeros. Another example is the co-occurrence of item–item or user–item pairs in e-commerce, which also generates high-dimensional data. The objective is to utilize these data to predict the relevance between items or users. In this paper, we assume that items or users can be represented by unknown dense vectors. The model treats the co-occurrence counts as arising from zero-inflated Gamma random variables and employs cosine similarity between the unknown vectors to summarize item–item relevance. The unknown values are estimated using the shared parameter alternating zero-inflated Gamma regression models (SA-ZIG). Both canonical link and log link models are considered. Two parameter updating schemes are proposed, along with an algorithm to estimate the unknown parameters. Convergence analysis is presented analytically. Numerical studies demonstrate that the SA-ZIG using Fisher scoring without learning rate adjustment may fail to find the maximum likelihood estimate. However, the SA-ZIG with learning rate adjustment performs satisfactorily in our simulation studies.

Shrinkage estimation of gene interaction networks in single-cell RNA sequencing data

BackgroundGene interaction networks are graphs in which nodes represent genes and edges represent functional interactions between them. These interactions can be at multiple levels, for instance, gene regulation, protein-protein interaction, or metabolic pathways. To analyse gene interaction networks at a large scale, gene co-expression network analysis is often applied on high-throughput gene expression data such as RNA sequencing data. With the advance in sequencing technology, expression of genes can be measured in individual cells. Single-cell RNA sequencing (scRNAseq) provides insights of cellular development, differentiation and characteristics at the transcriptomic level. High sparsity and high-dimensional data structures pose challenges in scRNAseq data analysis.ResultsIn this study, a sparse inverse covariance matrix estimation framework for scRNAseq data is developed to capture direct functional interactions between genes. Comparative analyses highlight high performance and fast computation of Stein-type shrinkage in high-dimensional data using simulated scRNAseq data. Data transformation approaches also show improvement in performance of shrinkage methods in non-Gaussian distributed data. Zero-inflated modelling of scRNAseq data based on a negative binomial distribution enhances shrinkage performance in zero-inflated data without interference on non zero-inflated count data.ConclusionThe proposed framework broadens application of graphical model in scRNAseq analysis with flexibility in sparsity of count data resulting from dropout events, high performance, and fast computational time. Implementation of the framework is in a reproducible Snakemake workflow https://github.com/calathea24/ZINBGraphicalModel and R package ZINBStein https://github.com/calathea24/ZINBStein.

Concentration of a Sparse Bayesian Model With Horseshoe Prior in Estimating High‐Dimensional Precision Matrix

ABSTRACTPrecision matrices are crucial in many fields such as social networks, neuroscience and economics, representing the edge structure of Gaussian graphical models (GGMs), where a zero in an off‐diagonal position of the precision matrix indicates conditional independence between nodes. In high‐dimensional settings where the dimension of the precision matrix exceeds the sample size and the matrix is sparse, methods like graphical Lasso, graphical SCAD and CLIME are popular for estimating GGMs. While frequentist methods are well‐studied, Bayesian approaches for (unstructured) sparse precision matrices are less explored. The graphical horseshoe estimate, applying the global‐local horseshoe prior, shows superior empirical performance, but theoretical work for sparse precision matrix estimations using shrinkage priors is limited. This paper addresses these gaps by providing concentration results for the tempered posterior with the fully specified horseshoe prior in high‐dimensional settings. Moreover, we also provide novel theoretical results for model misspecification, offering a general oracle inequality for the posterior. A concise set of simulations is performed to validate our theoretical findings.

Research on the fusion imaging method of sign coherence and time reversal for Lamb wave sparse array

Time-reversal imaging struggles to detect plate-like structures due to interference from Lamb wave mode conversion and the processing demands, leading to less effective outcomes. This paper proposes a sign coherence factor and time reversal fusion (SCF-TR) imaging method based on amplitude and phase estimation. This method removes the coherence of array signals during signal reversal and refocusing. It reintroduces the sign coherence component to reduce interference from non-target scattered waves and partially overcome the constraints imposed by the Rayleigh criterion. The method allows imaging at a resolution smaller than the wavelength of Lamb and enhances the quality of the resulting images. In addition, a sparse array design utilizing the White Shark Optimisation Algorithm (WSO) is proposed to streamline the SCF-TR calculation process. This design utilizes sparse full matrix data to improve imaging efficiency. The experimental results show that for single blind hole defects, the SCF-TR method improves the array performance metrics and signal-to-noise ratio by 22.46% and 42.50%, respectively, compared to the TR method. For multiple asymmetric blind hole defects, when the defect size exceeds the resolution threshold, SCF-TR accurately reflects the position and morphology of defects smaller than the wavelength. When the defect size is below the resolution threshold, SCF-TR achieves super-resolution imaging. The sparse array designed using the White Shark Optimization algorithm demonstrates good sidelobe characteristics, effectively reducing sidelobe noise without reducing the array aperture. Moreover, the SCF-TR imaging time is reduced by approximately half while maintaining imaging accuracy.

Gaussian Mixture Regression Model with Sparsity for Clustering of Territory Risk in Auto Insurance

Abstract Insurance rating territory design and accurate estimation of territory risk relativities are fundamental aspects of auto insurance rate regulation. It is crucial to develop methodologies that can facilitate the effective design of rating territories and their risk relativities estimate, as they directly impact the rate filing and the decision support of the rate change review process. This article proposes a Gaussian Mixture Regression model clustering approach for territory design. The proposed method incorporates a linear regression model, taking spatial location as model covariates, which helps estimate the cluster mean more accurately. Also, to further enhance the estimation of territory risk relativities, we impose sparsity through sparse matrix decomposition of the membership coefficient matrix obtained from the Gaussian Mixture Regression model. By transitioning from the current hard clustering method to a soft approach, our methodology could improve the evaluation of territory risk for rate-making purposes. Moreover, using non-negative sparse matrix approximation ensures that the estimation of risk relativities for basic rating units remains smooth, effectively eliminating data noise from the territory risk relativity estimate. Overall, our novel methodology aims to significantly enhance the accuracy and reliability of risk analysis in auto insurance. Furthermore, the proposed method exhibits potential for extension to various other domains that involve spatial clustering of data, thereby broadening its applicability and expanding its usefulness beyond auto insurance rate regulation.

Beamforming-integrated neural networks for ultrasound imaging

Sparse matrix beamforming (SMB) is a computationally efficient reformulation of delay-and-sum (DAS) beamforming as a single sparse matrix multiplication. This reformulation can potentially dovetail with machine learning platforms like TensorFlow and PyTorch that already support sparse matrix operations. In this work, using SMB principles, we present the development of beamforming-integrated neural networks (BINNs) that can rationally infer ultrasound images directly from pre-beamforming channel-domain radiofrequency (RF) datasets. To demonstrate feasibility, a toy BINN was first designed with two 2D-convolution layers that were respectively placed both before and after an SMB layer. This toy BINN correctly updated kernel weights in all convolution layers, demonstrating efficiency in both training (PyTorch – 133 ms, TensorFlow – 22 ms) and inference (PyTorch – 4 ms, TensorFlow – 5 ms). As an application demonstration, another BINN with two RF-domain convolution layers, an SMB layer, and three image-domain convolution layers was designed to infer high-quality B-mode images in vivo from single-shot plane-wave channel RF data. When trained using 31-angle compounded plane wave images (3000 frames from 22 human volunteers), this BINN showed mean-square logarithmic error improvements of 21.3 % and 431 % in the inferred B-mode image quality respectively comparing to an image-to-image convolutional neural network (CNN) and an RF-to-image CNN with the same number of layers and learnable parameters (3,777). Overall, by including an SMB layer to adopt prior knowledge of DAS beamforming, BINN shows potential as a new type of informed machine learning framework for ultrasound imaging.

Efficient Modeling of Spatial Extremes over Large Geographical Domains

Various natural phenomena exhibit spatial extremal dependence at short spatial distances. However, existing models proposed in the spatial extremes literature often assume that extremal dependence persists across the entire domain. This is a strong limitation when modeling extremes over large geographical domains, and yet it has been mostly overlooked in the literature. We here develop a more realistic Bayesian framework based on a novel Gaussian scale mixture model, with the Gaussian process component defined by a stochastic partial differential equation yielding a sparse precision matrix, and the random scale component modeled as a low-rank Pareto-tailed or Weibull-tailed spatial process determined by compactly-supported basis functions. We show that our proposed model is approximately tail-stationary and that it can capture a wide range of extremal dependence structures. Its inherently sparse structure allows fast Bayesian computations in high spatial dimensions based on a customized Markov chain Monte Carlo algorithm prioritizing calibration in the tail. We fit our model to analyze heavy monsoon rainfall data in Bangladesh. Our study shows that our model outperforms natural competitors and that it fits precipitation extremes well. We finally use the fitted model to draw inference on long-term return levels for marginal precipitation and spatial aggregates.

Development of high-efficient asphalt pavement modeling software for digital twin of road infrastructure

To develop digital twin (DT) of road infrastructure, one critical element is computation of pavement responses (strains, stresses, and deflections) under traffic and environmental loading. This study aims to develop high-efficient asphalt pavement modeling software based on semi-analytical finite element method (SAFEM) for DT application. The algorithms address important aspects in vehicle-tire-pavement interaction modeling, such as dynamic vehicular loading, three-dimensional (3-D) non-uniform tire contact stress, viscoelastic behavior of asphalt material, and interface bonding condition. The simulation accuracy is verified by comparison with full-scale test and field measurements, and the relative differences are around 5 % to 20 %. Techniques including optimized discrete Fourier transform, parallel computing, graphics processing unit (GPU) acceleration, and sparse matrices are implemented for computation efficiency. As compared to the traditional 3-D FEM, SAFEM shows significant savings in computation time and storage usage. The high efficiency and accuracy make the software full of potential to be applied for DT of roadway infrastructure.

Coastline target detection based on UAV hyperspectral remote sensing images

Timely and accurate monitoring of typical coastal targets using remote sensing technology is crucial for maintaining marine ecological stability. Hyperspectral target detection technology proves to be an effective tool in extracting various typical materials along the coastline. Traditional target detection methods using spectral domain information can effectively retain the intrinsic properties of the material. However, it is difficult to effectively recognize targets in homogeneous regions by using only spectral domain information, which may lead to insufficient utilization of spatial information. In this study, a detector based on signal-to-noise ratio fusion constrained energy minimization with low-rank sparse decomposition (SFLRSD) is proposed. This detector improves the separability of background and target by obtaining spatial domain information from hyperspectral images and fusing spectral domain information. First, total variation regularization and fractional Fourier transform are applied to process spatial and spectral domain information, respectively. The constrained energy minimization (CEM) detector is used to improve the separability between the target and background of the processed data. Then, the background and anomalies are represented as low-rank and sparse components, respectively, using low-rank sparse matrix factorization. This transforms the model solution into a covariance matrix problem, which is then solved using marginal distance difference (MDD) to isolate anomalous parts. Subsequently, the anomaly parts are fused with CEM detector results, weighted by their respective signal-to-noise ratios. This detection model leverages unified hyperspectral image features, enhancing spectral discreteness of anomalous targets and backgrounds. Finally, experiments on custom created hyperspectral dataset show that the proposed method outperforms other baseline methods in terms of visualization and quantitative performance. In this paper, we not only propose a new hyperspectral target detection method, but we also collect three typical marine litter of different materials by means of airborne hyperspectral remote sensing and construct four hyperspectral datasets in a real environment. All the simulation experiments in this paper are conducted in these four datasets.

Wavelet-based spatiotemporal sparse quaternion dictionary learning for reconstruction of multi-channel vibration data

Accurate reconstruction of multi-source data information plays an essential role in remote intelligent operation, and prognostic and health maintenance (RIO-PHM) of industrial systems. However, traditional signal reconstruction methods such as compressed sensing fail to capture the spatio-temporal characteristics and coupling nature of the multi-source or multi-channel data. To alleviate this bottleneck, in this paper, a new wavelet-based spatiotemporal sparse quaternion dictionary learning (WSTS-QDL) algorithm is formulated for the reconstruction of multi-channel vibration data for the first time. Specifically, the wavelet-based spatiotemporal sparse low-rank matrix (SLRM) algorithm is elaborated and the sparse coefficient matrix of the multi-channel signals can be estimated using the split Bregman iteration (SBI) technique. Then, quaternion-based dictionary learning is introduced for multi-channel data reconstruction according to the updated sparse coefficient matrix during quaternion dictionary learning. Eventually, two equipmental scenarios including run-to-failure data of rolling bearing in bearing test bench and vibration signal of the failured bearing in corn thresher, are utilized for verification. The experimental results demonstrate that the highest recovery accuracy performance with scoring function and the lowest errors are achieved by the proposed method in contrast with the state-of-the-art benchmarks such as orthogonal matching pursuit (OMP) method and spatiotemporal sparse Bayesian learning (SSBL), and the waveform of phase space trajectory and points cloud distribution of the Poincare section in the original signal are similar/same to that obtained by the proposed method.

An exploratory Q-matrix estimation method based on sparse non-negative matrix factorization.

Cognitive diagnostic assessment (CDA) is widely used because it can provide refined diagnostic information. The Q-matrix is the basis of CDA, and can be specified by domain experts or by data-driven estimation methods based on observed response data. The data-driven Q-matrix estimation methods have become a research hotspot because of their objectivity, accuracy, and low calibration cost. However, most of the existing data-driven methods require known prior knowledge, such as initial Q-matrix, partial q-vector, or the number of attributes. Under the G-DINA model, we propose to estimate the number of attributes and Q-matrix elements simultaneously without any prior knowledge by the sparse non-negative matrix factorization (SNMF) method, which has the advantage of high scalability and universality. Simulation studies are carried out to investigate the performance of the SNMF. The results under a wide variety of simulation conditions indicate that the SNMF has good performance in the accuracy of attribute number and Q-matrix elements estimation. In addition, a set of real data is taken as an example to illustrate its application. Finally, we discuss the limitations of the current study and directions for future research.

Maxwell boundary condition for discrete velocity methods: macroscopic physical constraints and Lagrange multiplier-based implementation

In this paper, we propose an algorithm that imposes macroscopic physical constraints with Lagrange multiplier approach in implementing the Maxwell boundary condition within the framework of the discrete velocity method. For the simulation of rarefied gas flows in the presence of solid walls with complex geometry, the distribution function in the reflection region of the wall surface needs to be constructed in the discrete velocity space, to fulfill the specular reflection in the Maxwell boundary condition. The construction process should not consist of interpolation only, but include certain macroscopic physical constraints at the wall surface, so as to correctly account for gas-surface interaction on a macroscopic level. We demonstrate that for the specular reflection, keeping the symmetry of the first three moments of the distribution function between the incident and reflected region is sufficient for maintaining the conservation of mass, momentum, and energy at the wall surface. Furthermore, to strictly satisfy macroscopic physical constraints, a Lagrange multiplier method is introduced into the construction of the distribution function to correct the pure interpolation solution. In addition, the construction process requires the inversion of a large and sparse matrix (of dimension N × N, where N is the number of points in the velocity space). To improve the computational efficiency, the matrix inversion is converted into that of a much smaller matrix, i.e. (D+2) × (D+2) in the D-dimensional physical space. A series of numerical experiments are conducted to examine the performance of the proposed algorithm under different flow conditions. We demonstrate that the results obtained by the proposed algorithm are more accurate than the pure interpolation solution, comparing with the benchmark data. Moreover, after the validation of our results with previous studies, we find that the method significantly enhances the conservation of total mass and energy, especially for flows in an enclosed domain.

Faint Space Target Information Extraction Based on Small Aperture Telescope in Complex Background

AbstractThere are many problems in space debris monitoring with ground‐based telescopes, such as too many stars in the same field of view, uneven background and optical distortion in the optical system. We propose a two‐stage weak debris detection algorithm. In the first stage, wavelet transform is used to extract different components of three frames of images, and the median of corresponding components of the images is taken respectively to eliminate the influence of stars. In the second stage, an improved version of the faint space target extraction based on principal component analysis. The algorithm uses a smooth‐detection idea to extract target information. Based on a 150 mm aperture telescope, we improved the existing method of faint space debris extraction based on principal component analysis by introducing the smooth‐detection idea, and transformed the target detection problem into the separation problem of sparse matrix and low‐rank matrix. We applied a certain preprocessing consisting of wavelet‐based star removal and median pre‐filtering to keep as little noise and other contaminants as possible. After experimental measurements by observers, the algorithm demonstrated advanced detection capabilities on multiple indicators.

Implicit EXP-RBF techniques for modeling unsaturated flow through soils with water uptake by plant roots

Modeling unsaturated flow through soils with water uptake by plan root has many applications in agriculture and water resources management. In this study, our aim is to develop efficient numerical techniques for solving the Richards equation with a sink term due to plant root water uptake. The Feddes model is used for water absorption by plant roots, and the van-Genuchten model is employed for capillary pressure. We introduce a numerical approach that combines the localized exponential radial basis function (EXP-RBF) method for space and the second-order backward differentiation formula (BDF2) for temporal discretization. The localized RBF methods eliminate the need for mesh generation and avoid ill-conditioning problems. This approach yields a sparse matrix for the global system, optimizing memory usage and computational time. The proposed implicit EXP-RBF techniques have advantages in terms of accuracy and computational efficiency thanks to the use of BDF2 and the localized RBF method. Modified Picards iteration method for the mixed form of the Richards equation is employed to linearize the system. Various numerical experiments are conducted to validate the proposed numerical model of infiltration with plant root water absorption. The obtained results conclusively demonstrate the effectiveness of the proposed numerical model in accurately predicting soil moisture dynamics under water uptake by plant roots. The proposed numerical techniques can be incorporated in the numerical models where unsaturated flows and water uptake by plant roots are involved such as in hydrology, agriculture, and water management.

Temperature rise of high-speed bearing in gearbox of 5 MW wind turbine based on Bayesian-LightGBM and improved PSO-SVM troubleshooting

5MW wind turbine gearbox high-speed bearing temperature rise failure is one of the important factors affecting the stable operation of the wind turbine, accurate prediction and timely diagnosis can effectively improve the efficiency of the wind turbine. In this paper, a combined modelling wind turbine gearbox high-speed bearing temperature rise prediction method based on Bayesian-LightGBM and improved PSO-SVM is proposed with a 5 MW wind turbine as the research object. Firstly, the initial dimensionality reduction of SCADA data is performed by sparse random projection matrix, which reduces the redundant data. Secondly, feature selection is performed on the remaining data using Bayesian-LightGBM to identify 13 key input feature parameters. Then, the hyperparameters of the PSO algorithm are optimised using Bayesian algorithm and further, the optimised PSO algorithm is applied to identify the SVM parameters. Finally, a simulation experiment platform is established based on MATLAB to verify the temperature rise of high-speed bearings in gearboxes of wind turbines by example calculation and comparative analysis. The results show that the model established in this paper is effective, the prediction results are accurate and the performance is stable, and then compared with the algorithms such as PSO-SVM, SVM, BP, etc, the coefficient of determination of the algorithm is greater than 0.994 in both the training set and the test set, and the average decision percentage error is around 1.88% in both.

Ground penetrating radar clutter suppression based on the weighted tensor Schatten p-paradigm minimization of tensor principal components

The issue of clutter suppression in ground-penetrating radar (GPR) detection has consistently been a prominent area of research. The existing tensor robust principal component analysis (TRPCA) approach encounters a challenge when handling different singular values, whereby all singular values are reduced to the same degree, leading to loss of information in the low-rank part. To address the aforementioned issues, this study developed a TRPCA method based on weighted tensor Schatten p-paradigm minimisation (p-TRPCA). This approach assigns distinct weights to each singular value by using a weighted tensor Schatten p-paradigm, facilitating the optimal decomposition of GPR data into low-rank clutter and sparse target components. The processing of target echoes is then completed by applying a threshold judgement to the results. The efficacy of the proposed method was validated through simulations and real-world testing. Its performance was benchmarked against established advanced clutter removal techniques in terms of peak signal-to-noise ratio (PSNR) and signal-to-clutter ratio. The findings demonstrated that the method effectively delineated the low-rank clutter matrix and sparse target matrix within the B-scan image and exhibited superior SNR compared to other methods.

Efficient SpMM Accelerator for Deep Learning: Sparkle and Its Automated Generator

Deep learning (DL) technology has made breakthroughs in a wide range of intelligent tasks, such as vision, language, recommendation systems, and so on. Sparse matrix multiplication (SpMM) is the key computation kernel of most sparse models. Conventional computing platforms, such as CPUs, GPUs, and AI chips with regular processing units, are unable to effectively support sparse computation due to their fixed structure and instruction sets. This work extends Sparkle, an accelerator architecture, which is developed specifically for processing SpMM in DL. During the balanced data loading process, some modifications are implemented to enhance the flexibility of the Sparkle architecture. Additionally, a Sparkle generator is proposed to accommodate diverse resource constraints and facilitate adaptable deployment. Leveraging Sparkle’s structural parameters and template-based design methods, the generator enables automatic Sparkle circuit generation under varying parameters. An instantiated Sparkle accelerator is implemented on the Xilinx xqvu11p FPGA platform with a specific configuration. Compared to the state-of-the-art SpMM accelerator SIGMA, the Sparkle accelerator instance improves the sparse computing efficiency by about 10 to 20 \(\%\) . Furthermore, the Sparkle instance achieved 7.76 \(\times\) higher performance over the Nvidia Orin NX GPU. More instances of accelerators with different parameters were evaluated, demonstrating that the Sparkle architecture can effectively accelerate SpMM.

A congenital periocular leiomyosarcoma in a dairy calf.

A mass was removed surgically from the right orbit of a 1-d-old Holstein calf. Grossly, the mass filled the rostral part of an enlarged orbit and compressed the globe toward the caudal pole of the orbit. The brown, 6-cm tumor had central yellow and brown areas, and a smooth, glistening cut surface. Microscopically, the neoplasm was highly cellular and composed of spindle cells arranged in irregular, broad, interlacing streams and bundles, forming a herringbone pattern and supported by a sparse collagenous matrix. Neoplastic cells infiltrated surrounding soft tissues and compressed the globe. The neoplastic cells had positive immunolabeling for α-smooth muscle actin, desmin, and vimentin, and negative immunolabeling for factor VIII, myoglobin, cytokeratin, and skeletal muscle actin. Histopathology and immunohistochemistry results confirmed a diagnosis of leiomyosarcoma. To our knowledge, congenital periocular leiomyosarcoma has not been reported in cattle previously. This rare tumor could be included as a differential diagnosis in newborn calves with periocular masses.

Sparse large-scale high-order fuzzy cognitive maps guided by spearman correlation coefficient

Time series prediction is one of the most important applications of Fuzzy Cognitive Maps (FCMs). In general, the state of FCMs in forecasting depends only on the state of the previous moment, but in fact it is also affected by the past state. Hence Higher-Order Fuzzy Cognitive Maps (HFCMs) are proposed based on FCMs considering historical information and have been widely used for time series forecasting. However, using HFCMs to deal with sparse and large-scale multivariate time series are still a challenge, while large-scale data makes it difficult to determine the causal relationship between nodes because of the increased number of nodes, so it is necessary to explore the relationship between nodes to guide large-scale HFCMs learning. Therefore, a sparse large-scale HFCMs learning algorithm guided by Spearman correlation coefficient, called SG-HFCM, is proposed in the paper. The SG-HFCM model is specified as follows: First, the solving of HFCMs model is transform into a regression model and an adaptive loss function is utilized to enhance the robustness of the model. Second, l1-norm is used to improve the sparsity of the weight matrix. Third, in order to more accurately characterize the correlation relationship between variables, the Spearman correlation coefficients is added as a regular term to guide the learning of weight matrices. When calculating the Spearman correlation coefficient, through splitting domain interval method, we can better understand the characteristics of the data, and get better correlation in different small intervals, and more accurately characterize the relationship between the variables in order to guide the weight matrix. In addition, the Alternating Direction Multiplication Method and quadratic programming method are used to solve the algorithms to get better solutions for the SG-HFCM, where the quadratic programming can well ensure that the range of the weights and obtaining the optimal solution. Finally, by comparing with five algorithms, the SG-HFCM model showed an average improvement of 11.93% in prediction accuracy for GRNs, indicating that our proposed model has good predictive performance.