Regular Hypergraphs Research Articles

Layer-wise normalized deep incomplete multiview nonnegative matrix factorization

Deep (semi-)nonnegative matrix factorization based models have demonstrated promising performance in the multiview clustering tasks. However, they are all developed upon the assumption that the multiview datasets are complete in all views, and need to be pre-trained layer-by-layer to get reasonable results. Addressing these issues, an algorithm named layer-wise normalized deep incomplete multiview nonnegative matrix factorization (LWNdimNMF) is presented in this paper to tackle the multiview clustering problem with arbitrary missing views. Specifically, a novel layer-wise normalization strategy is developed to constrain the value distribution of the factor matrix in each layer to ensure the numerical stability of the model and make it robust to the initialization. Another benefit of this strategy is that it can effectively depress the objective function value and make the model fit data well. An instance selection alignment is adopted to fuse the incomplete multiple views by aligning the paired instances. To discover the high-order geometrical information in each incomplete view, a hypergraph regularization is incorporated into the proposed model. An effective iterative optimization algorithm based on the multiplicative updating rules is designed to solve the minimizing problem. Extensive experiments are conducted to evaluate the effectiveness of the proposed model by comparing with several state-of-the-art (SOTA) incomplete multiview clustering (IMC) methods on ten real-world multiview datasets. The source code is available at: https://github.com/GuoshengCui/LWNdimNMF.

SPLHRNMTF: robust orthogonal non-negative matrix tri-factorization with self-paced learning and dual hypergraph regularization for predicting miRNA-disease associations

MicroRNAs (miRNAs) have been demonstrated to be closely related to human diseases. Studying the potential associations between miRNAs and diseases contributes to our understanding of disease pathogenic mechanisms. As traditional biological experiments are costly and time-consuming, computational models can be considered as effective complementary tools. In this study, we propose a novel model of robust orthogonal non-negative matrix tri-factorization (NMTF) with self-paced learning and dual hypergraph regularization, named SPLHRNMTF, to predict miRNA-disease associations. More specifically, SPLHRNMTF first uses a non-linear fusion method to obtain miRNA and disease comprehensive similarity. Subsequently, the improved miRNA-disease association matrix is reformulated based on weighted k-nearest neighbor profiles to correct false-negative associations. In addition, we utilize L2,1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_{2,1}$$\\end{document} norm to replace Frobenius norm to calculate residual error, alleviating the impact of noise and outliers on prediction performance. Then, we integrate self-paced learning into NMTF to alleviate the model from falling into bad local optimal solutions by gradually including samples from easy to complex. Finally, hypergraph regularization is introduced to capture high-order complex relations from hypergraphs related to miRNAs and diseases. In 5-fold cross-validation five times experiments, SPLHRNMTF obtains higher average AUC values than other baseline models. Moreover, the case studies on breast neoplasms and lung neoplasms further demonstrate the accuracy of SPLHRNMTF. Meanwhile, the potential associations discovered are of biological significance.

Joint consensus kernel learning and adaptive hypergraph regularization for graph-based clustering

Recent advancements in multiple kernel learning-based graph clustering methods have demonstrated significant promise in effectively learning a consensus kernel matrix from various candidate kernel matrices. This approach enables the creation of a low-dimensional representation in the kernel space of high-dimensional data through self-expressiveness. However, a key challenge remains in capturing the latent geometric properties embedded within different kernel matrices to enhance data representation. In this paper, we propose a novel method called joint consensus kernel learning and adaptive hypergraph regularization for graph-based clustering (JKHR). Our approach integrates an innovative adaptive hypergraph Laplacian regularizer, which is characterized by the fusion of multiple nearest neighbor kernel graphs, into the multiple kernel learning-based graph clustering framework. JKHR jointly and adaptively optimizes both the consensus kernel matrix and the hypergraph Laplacian regularizer to achieve a low-dimensional representation that effectively preserves the intrinsic geometry of the data. Experimental results on both synthetic and real benchmark datasets demonstrate that JKHR outperforms state-of-the-art self-expressiveness-based graph clustering methods as well as traditional clustering techniques.

Prognosis and diagnosis of prostate cancer based on hypergraph regularization sparse least partial squares regression algorithm.

Prostate cancer (PCa) is a malignant tumor of the male reproductive system, and its incidence has increased significantly in recent years. This study aimed to further identify candidate biomarkers with prognostic and diagnostic significance by integrating gene expression and DNA methylation data from PCa patients through association analysis. To this end, this paper proposes a sparse partial least squares regression algorithm based on hypergraph regularization (HR-SPLS) by integrating and clustering two kinds of data. Next, module 2, with the most significant weight, was selected for further analysis according to the weight of each module related to DNA methylation and mRNAs. Based on the DNA methylation sites in module 2, this paper uses multiple machine learning methods to construct a PCa diagnosis-related model of 10-DNA methylation sites. The results of Receiver Operating Characteristic (ROC) analysis showed that the DNA methylation-related diagnostic model we constructed could diagnose PCa patients with high accuracy. Subsequently, based on the mRNAs in module 2, we constructed a prognostic model for 7-mRNAs (MYH11, ACTG2, DDR2, CDC42EP3, MARCKSL1, LMOD1, and MYLK) using multivariate Cox regression analysis. The prognostic model could predict the disease free survival of PCa patients with moderate to high accuracy (area under the curve (AUC) =0.761). In addition, Gene Set EnrichmentAnalysis (GSEA) and immune analysis indicated that the prognosis of patients in the risk group might be related to immune cell infiltration. Our findings may provide new methods and insights for identifying disease-related biomarkers by integrating DNA methylation and gene expression data.

On the Chromatic Number of Random Regular Hypergraphs

On the Chromatic Number of Random Regular Hypergraphs

Diverse Deep Matrix Factorization with Hypergraph Regularization for Multi-View Data Representation

Diverse Deep Matrix Factorization with Hypergraph Regularization for Multi-View Data Representation

New bounds on the size of nearly perfect matchings in almost regular hypergraphs

AbstractLet be a ‐uniform ‐regular simple hypergraph on vertices. Based on an analysis of the Rödl nibble, in 1997, Alon, Kim and Spencer proved that if , then contains a matching covering all but at most vertices, and asked whether this bound is tight. In this paper we improve their bound by showing that for all , contains a matching covering all but at most vertices for some , when and are sufficiently large. Our approach consists of showing that the Rödl nibble process not only constructs a large matching but it also produces many well‐distributed ‘augmenting stars’ which can then be used to significantly improve the matching constructed by the Rödl nibble process. Based on this, we also improve the results of Kostochka and Rödl from 1998 and Vu from 2000 on the size of matchings in almost regular hypergraphs with small codegree. As a consequence, we improve the best known bounds on the size of large matchings in combinatorial designs with general parameters. Finally, we improve the bounds of Molloy and Reed from 2000 on the chromatic index of hypergraphs with small codegree (which can be applied to improve the best known bounds on the chromatic index of Steiner triple systems and more general designs).

Hypergraph-Regularized Lp Smooth Nonnegative Matrix Factorization for Data Representation

Nonnegative matrix factorization (NMF) has been shown to be a strong data representation technique, with applications in text mining, pattern recognition, image processing, clustering and other fields. In this paper, we propose a hypergraph-regularized Lp smooth nonnegative matrix factorization (HGSNMF) by incorporating the hypergraph regularization term and the Lp smoothing constraint term into the standard NMF model. The hypergraph regularization term can capture the intrinsic geometry structure of high dimension space data more comprehensively than simple graphs, and the Lp smoothing constraint term may yield a smooth and more accurate solution to the optimization problem. The updating rules are given using multiplicative update techniques, and the convergence of the proposed method is theoretically investigated. The experimental results on five different data sets show that the proposed method has a better clustering effect than the related state-of-the-art methods in the vast majority of cases.

Hypergraph regularity and random sampling

AbstractSuppose that a ‐uniform hypergraph satisfies a certain regularity instance (that is, there is a partition of given by the hypergraph regularity lemma into a bounded number of quasirandom subhypergraphs of prescribed densities). We prove that with high probability a large enough uniform random sample of the vertex set of also admits the same regularity instance. Here the crucial feature is that the error term measuring the quasirandomness of the subhypergraphs requires only an arbitrarily small additive correction. This has applications to combinatorial property testing. The graph case of the sampling result was proved by Alon, Fischer, Newman and Shapira.

MV-H-RKM: A Multiple View-Based Hypergraph Regularized Restricted Kernel Machine for Predicting DNA-Binding Proteins.

DNA-binding proteins (DBPs) have a significant impact on many life activities, so identification of DBPs is a crucial issue. And it is greatly helpful to understand the mechanism of protein-DNA interactions. In traditional experimental methods, it is significant time-consuming and labor-consuming to identify DBPs. In recent years, many researchers have proposed lots of different DBP identification methods based on machine learning algorithm to overcome shortcomings mentioned above. However, most existing methods cannot get satisfactory results. In this paper, we focus on developing a new predictor of DBPs, called Multi-View Hypergraph Restricted Kernel Machines (MV-H-RKM). In this method, we extract five features from the three views of the proteins. To fuse these features, we couple them by means of the shared hidden vector. Besides, we employ the hypergraph regularization to enforce the structure consistency between original features and the hidden vector. Experimental results show that the accuracy of MV-H-RKM is 84.09% and 85.48% on PDB1075 and PDB186 data set respectively, and demonstrate that our proposed method performs better than other state-of-the-art approaches. The code is publicly available at https://github.com/ShixuanGG/MV-H-RKM.

Neutrosophic Co-degree and Neutrosophic Degree alongside Chromatic Numbers in the Setting of Some Classes Related to Neutrosophic Hypergraphs

New setting is introduced to study types of coloring numbers, degree of vertices, degree of hyperedges, codegree of vertices, co-degree of hyperedges, neutrosophic degree of vertices, neutrosophic degree of hyperedges, neutrosophic co-degree of vertices, neutrosophic co-degree of hyperedges, neutrosophic number of vertices, neutrosophic number of hyperedges in neutrosophic hypergraphs. Different types of procedures including neutrosophic (r; n)-regular hypergraphs and neutrosophic complete r-partite hypergraphs are proposed in this way, some results are obtained. General classes of neutrosophic hypergraphs are used to obtain chromatic number, the representatives of the colors, degree of vertices, degree of hyperedges, co-degree of vertices, codegree of hyperedges, neutrosophic degree of vertices, neutrosophic degree of hyperedges, neutrosophic codegree of vertices, neutrosophic co-degree of hyperedges, neutrosophic number of vertices, neutrosophic number of hyperedges in neutrosophic hypergraphs. Using colors to assign to the vertices of neutrosophic hypergraphs and characterizing representatives of the colors are applied in neutrosophic (r; n)-regular hypergraphs and neutrosophic complete r-partite hypergraphs. Some questions and problems are posed concerning ways to do further studies on this topic. Using different ways of study on neutrosophic hypergraphs to get new results about number, degree and co-degree in the way that some number, degree and co-degree get understandable perspective. Neutrosophic (r; n)-regular hypergraphs and neutrosophic complete r-partite hypergraphs are studied to investigate about the notions, coloring, the representatives of the colors, degree of vertices, degree of hyperedges, co-degree of vertices, co-degree of hyperedges, neutrosophic degree of vertices, neutrosophic degree of hyperedges, neutrosophic co-degree of vertices, neutrosophic co-degree of hyperedges, neutrosophic number of vertices, neutrosophic number of hyperedges in neutrosophic (r; n)-regular hypergraphs and neutrosophic complete r-partite hypergraphs. In this way, sets of representatives of colors, degree of vertices, degree of hyperedges, co-degree of vertices, co-degree of hyperedges, neutrosophic degree of vertices, neutrosophic degree of hyperedges, neutrosophic co-degree of vertices, neutrosophic co-degree of hyperedges, neutrosophic number of vertices, neutrosophic number of hyperedges have key points to get new results but in some cases, there are usages of sets and numbers instead of optimal ones. Simultaneously, notions chromatic number, the representatives of the colors, degree of vertices, degree of hyperedges, co-degree of vertices, co-degree of hyperedges, neutrosophic degree of vertices, neutrosophic degree of hyperedges, neutrosophic co-degree of vertices, neutrosophic co-degree of hyperedges, neutrosophic number of vertices, neutrosophic number of hyperedges are applied into neutrosophic hypergraphs, especially, neutrosophic (r; n)-regular hypergraphs and neutrosophic complete r-partite hypergraphs to get sensible results about their structures. Basic familiarities with neutrosophic hypergraphs theory and hypergraph theory are proposed for this article.

Global eigenvalue fluctuations of random biregular bipartite graphs

We compute the eigenvalue fluctuations of uniformly distributed random biregular bipartite graphs with fixed and growing degrees for a large class of analytic functions. As a key step in the proof, we obtain a total variation distance bound for the Poisson approximation of the number of cycles and cyclically non-backtracking walks in random biregular bipartite graphs, which might be of independent interest. We also prove a semicircle law for random [Formula: see text]-biregular bipartite graphs when [Formula: see text]. As an application, we translate the results to adjacency matrices of uniformly distributed random regular hypergraphs.

On Laplacian Energy of r-Uniform Hypergraphs

The matrix representations of hypergraphs have been defined via hypermatrices initially. In recent studies, the Laplacian matrix of hypergraphs, a generalization of the Laplacian matrix, has been introduced. In this article, based on this definition, we derive bounds depending pair-degree, maximum degree, and the first Zagreb index for the greatest Laplacian eigenvalue and Laplacian energy of r-uniform hypergraphs and r-uniform regular hypergraphs. As a result of these bounds, Nordhaus–Gaddum type bounds are obtained for the Laplacian energy.

Robust capped norm dual hyper-graph regularized non-negative matrix tri-factorization.

Non-negative matrix factorization (NMF) has been widely used in machine learning and data mining fields. As an extension of NMF, non-negative matrix tri-factorization (NMTF) provides more degrees of freedom than NMF. However, standard NMTF algorithm utilizes Frobenius norm to calculate residual error, which can be dramatically affected by noise and outliers. Moreover, the hidden geometric information in feature manifold and sample manifold is rarely learned. Hence, a novel robust capped norm dual hyper-graph regularized non-negative matrix tri-factorization (RCHNMTF) is proposed. First, a robust capped norm is adopted to handle extreme outliers. Second, dual hyper-graph regularization is considered to exploit intrinsic geometric information in feature manifold and sample manifold. Third, orthogonality constraints are added to learn unique data presentation and improve clustering performance. The experiments on seven datasets testify the robustness and superiority of RCHNMTF.

An explainable autoencoder with multi-paradigm fMRI fusion for identifying differences in dynamic functional connectivity during brain development

Multi-paradigm deep learning models show great potential for dynamic functional connectivity (dFC) analysis by integrating complementary information. However, many of them cannot use information from different paradigms effectively and have poor explainability, that is, the ability to identify significant features that contribute to decision making. In this paper, we propose a multi-paradigm fusion-based explainable deep sparse autoencoder (MF-EDSAE) to address these issues. Considering explainability, the MF-EDSAE is constructed based on a deep sparse autoencoder (DSAE). For integrating information effectively, the MF-EDASE contains the nonlinear fusion layer and multi-paradigm hypergraph regularization. We apply the model to the Philadelphia Neurodevelopmental Cohort and demonstrate it achieves better performance in detecting dynamic FC (dFC) that differ significantly during brain development than the single-paradigm DSAE. The experimental results show that children have more dispersive dFC patterns than adults. The function of the brain transits from undifferentiated systems to specialized networks during brain development. Meanwhile, adults have stronger connectivities between task-related functional networks for a given task than children. As the brain develops, the patterns of the global dFC change more quickly when stimulated by a task.

Robust multi-view subspace enhanced representation based on collaborative constraints and HSIC induction

The design of effective multi-view subspace clustering (MSC) algorithms has recently garnered significant research attention. Herein, to effectively improve the recognition performance and anti-noise interference ability of an MSC model, we propose a novel MSC algorithm, termed as robust multi-view subspace enhancement representation, based on collaborative constraints and a Hilbert–Schmidt independence criterion (HSIC) induction method. To mine the complementary information between different views, we apply the HSIC as a diversity regularization term. Specifically, to enhance the diagonal block structure of a subspace representation, a new sparse constraint is introduced on the product of itself and the transpose of the subspace representation matrix in a multi-view subspace learning model. Furthermore, hypergraph regularization and a low-rank idea are considered to capture the local geometric structure and clean data. In addition, to optimize our model, we adopt an augmented Lagrangian multiplier method and discuss the convergence of the model. Extensive experiments on six challenging datasets reveal that the proposed method achieves a highly competent objective performance with and without noisy views, as compared with several state-of-the-art multi-view clustering methods.

Predicting multiple types of miRNA-disease associations using adaptive weighted nonnegative tensor factorization with self-paced learning and hypergraph regularization.

More and more evidence indicates that the dysregulations of microRNAs (miRNAs) lead to diseases through various kinds of underlying mechanisms. Identifying the multiple types of disease-related miRNAs plays an important role in studying the molecular mechanism of miRNAs in diseases. Moreover, compared with traditional biological experiments, computational models are time-saving and cost-minimized. However, most tensor-based computational models still face three main challenges: (i) easy to fall into bad local minima; (ii) preservation of high-order relations; (iii) false-negative samples. To this end, we propose a novel tensor completion framework integrating self-paced learning, hypergraph regularization and adaptive weight tensor into nonnegative tensor factorization, called SPLDHyperAWNTF, for the discovery of potential multiple types of miRNA-disease associations. We first combine self-paced learning with nonnegative tensor factorization to effectively alleviate the model from falling into bad local minima. Then, hypergraphs for miRNAs and diseases are constructed, and hypergraph regularization is used to preserve the high-order complex relations of these hypergraphs. Finally, we innovatively introduce adaptive weight tensor, which can effectively alleviate the impact of false-negative samples on the prediction performance. The average results of 5-fold and 10-fold cross-validation on four datasets show that SPLDHyperAWNTF can achieve better prediction performance than baseline models in terms of Top-1 precision, Top-1 recall and Top-1 F1. Furthermore, we implement case studies to further evaluate the accuracy of SPLDHyperAWNTF. As a result, 98 (MDAv2.0) and 98 (MDAv2.0-2) of top-100 are confirmed by HMDDv3.2 dataset. Moreover, the results of enrichment analysis illustrate that unconfirmed potential associations have biological significance.

Identification of Vesicle Transport Proteins via Hypergraph Regularized K-Local Hyperplane Distance Nearest Neighbour Model.

The prediction of protein function is a common topic in the field of bioinformatics. In recent years, advances in machine learning have inspired a growing number of algorithms for predicting protein function. A large number of parameters and fairly complex neural networks are often used to improve the prediction performance, an approach that is time-consuming and costly. In this study, we leveraged traditional features and machine learning classifiers to boost the performance of vesicle transport protein identification and make the prediction process faster. We adopt the pseudo position-specific scoring matrix (PsePSSM) feature and our proposed new classifier hypergraph regularized k-local hyperplane distance nearest neighbour (HG-HKNN) to classify vesicular transport proteins. We address dataset imbalances with random undersampling. The results show that our strategy has an area under the receiver operating characteristic curve (AUC) of 0.870 and a Matthews correlation coefficient (MCC) of 0.53 on the benchmark dataset, outperforming all state-of-the-art methods on the same dataset, and other metrics of our model are also comparable to existing methods.

Generalized matrix factorization based on weighted hypergraph learning for microbe-drug association prediction

The complex and diverse microbial communities are closely related to human health, and the research of microbial communities plays an increasingly critical role in drug development and precision medicine. Identifying potential microbe-drug associations not only benefits drug discovery and clinical therapy, but also contributes to a better understanding of the mechanisms of action of microbes. Compared with the complexity and high cost of biological experiments, computational methods can quickly and efficiently predict potential microbe-drug associations, which could be a useful complement to experimental methods. In this study, we propose a generalized matrix factorization based on weighted hypergraph learning, WHGMF, to predict potential microbial-drug associations. First, we integrate multi-omics data to compute multiple features of microbes and drugs, including functional and semantic similarity of microbes, structural similarity of drugs, and microbe-drug association information. Second, the hypergraph is constructed by using strong neighborhood information, and to improve the performance of the hypergraph, the simple volume is adopted to calculate the hyperedge weight. Finally, hypergraph regularization is introduced for the generalized matrix factorization model, and high-order structural information is used to improve the representation ability of low-dimensional features. Results from multiple experiments demonstrate that WHGMF not only accurately predicts potential microbe-drug associations, but also has considerable adaptability to class-imbalanced datasets. In addition, WHGMF is also suitable for the prediction of new drugs and new microbes. A case study further demonstrates the effectiveness of our method. The code and data in this study are freely available at https://github.com/Mayingjun20179/WHGMF.

On the spectrum and linear programming bound for hypergraphs

The spectrum of a graph is closely related to many graph parameters. In particular, the spectral gap of a regular graph which is the difference between its valency and second eigenvalue, is widely seen as an algebraic measure of connectivity and plays a key role in the theory of expander graphs. In this paper, we extend previous work done for graphs and bipartite graphs and present a linear programming method for obtaining an upper bound on the order of a regular uniform hypergraph with prescribed distinct eigenvalues. Furthermore, we obtain a general upper bound on the order of a regular uniform hypergraph whose second eigenvalue is bounded by a given value. Our results improve and extend previous work done by Feng and Li (1996) on Alon–Boppana theorems for regular hypergraphs and by Dinitz et al. (2020) on the Moore or degree-diameter problem. We also determine the largest order of an r-regular u-uniform hypergraph with second eigenvalue at most θ for several parameters (r,u,θ). In particular, orthogonal arrays give the structure of the largest hypergraphs with second eigenvalue at most 1 for every sufficiently large r. Moreover, we show that a generalized Moore geometry has the largest spectral gap among all hypergraphs of that order and degree.