Identification of cancer driver genes based on hierarchical weak consensus model

Cancer is a complex gene mutation disease that derives from the accumulation of mutations during somatic cell evolution. With the advent of high-throughput technology, a large amount of omics data has been generated, and how to find cancer-related driver genes from a large number of omics data is a challenge. In the early stage, the researchers developed many frequency-based driver genes identification methods, but they could not identify driver genes with low mutation rates well. Afterwards, researchers developed network-based methods by fusing multi-omics data, but they rarely considered the connection among features. In this paper, after analyzing a large number of methods for integrating multi-omics data, a hierarchical weak consensus model for fusing multiple features is proposed according to the connection among features. By analyzing the connection between PPI network and co-mutation hypergraph network, this paper firstly proposes a new topological feature, called co-mutation clustering coefficient (CMCC). Then, a hierarchical weak consensus model is used to integrate CMCC, mRNA and miRNA differential expression scores, and a new driver genes identification method HWC is proposed. In this paper, the HWC method and current 7 state-of-the-art methods are compared on three types of cancers. The comparison results show that HWC has the best identification performance in statistical evaluation index, functional consistency and the partial area under ROC curve.

Supplementary Information

The online version contains supplementary material available at 10.1007/s13755-024-00279-6.

Self-paced regularized adaptive multi-view unsupervised feature selection

Multi-view unsupervised feature selection (MUFS) is an efficient approach for dimensional reduction of heterogeneous data. However, existing MUFS approaches mostly assign the samples the same weight, thus the diversity of samples is not utilized efficiently. Additionally, due to the presence of various regularizations, the resulting MUFS problems are often non-convex, making it difficult to find the optimal solutions. To address this issue, a novel MUFS method named Self-paced Regularized Adaptive Multi-view Unsupervised Feature Selection (SPAMUFS) is proposed. Specifically, the proposed approach firstly trains the MUFS model with simple samples, and gradually learns complex samples by using self-paced regularizer. l2,p-norm (0 Collapse

Key Words

• Hypergraph
• Multi-view unsupervised feature selection
• Self-paced learning
• Sparse learning
• l(2,p)-norm

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MESH Headings

• Unsupervised Machine Learning
• Algorithms
• Humans
• Neural Networks, Computer

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Grants Collapse

Affiliation(s)

Xuanhao Yang College of Electronic and Information Engineering, Southwest University, Chongqing, 400715, China.
Hangjun Che College of Electronic and Information Engineering, Southwest University, Chongqing, 400715, China; Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, Chongqing, 400715, China.
Man-Fai Leung School of Computing and Information Science, Faculty of Science and Engineering, Anglia Ruskin University, Cambridge, UK.
Shiping Wen Faculty of Engineering and Information Technology, Australian Artificial Intelligence Institute, University of Technology Sydney, Sydney, NSW 2007, Australia.

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Multiview hyperedge-aware hypergraph embedding learning for multisite, multiatlas fMRI based functional connectivity network analysis

Recently, functional magnetic resonance imaging (fMRI) based functional connectivity network (FCN) analysis via graph convolutional networks (GCNs) has shown promise for automated diagnosis of brain diseases by regarding the FCNs as irregular graph-structured data. However, multiview information and site influences of the FCNs in a multisite, multiatlas fMRI scenario have been understudied. In this paper, we propose a Class-consistency and Site-independence Multiview Hyperedge-Aware HyperGraph Embedding Learning (CcSi-MHAHGEL) framework to integrate FCNs constructed on multiple brain atlases in a multisite fMRI study. Specifically, for each subject, we first model brain network as a hypergraph for every brain atlas to characterize high-order relations among multiple vertexes, and then introduce a multiview hyperedge-aware hypergraph convolutional network (HGCN) to extract a multiatlas-based FCN embedding where hyperedge weights are adaptively learned rather than employing the fixed weights precalculated in traditional HGCNs. In addition, we formulate two modules to jointly learn the multiatlas-based FCN embeddings by considering the between-subject associations across classes and sites, respectively, i.e., a class-consistency module to encourage both compactness within every class and separation between classes for promoting discrimination in the embedding space, and a site-independence module to minimize the site dependence of the embeddings for mitigating undesired site influences due to differences in scanning platforms and/or protocols at multiple sites. Finally, the multiatlas-based FCN embeddings are fed into a few fully connected layers followed by the soft-max classifier for diagnosis decision. Extensive experiments on the ABIDE demonstrate the effectiveness of our method for autism spectrum disorder (ASD) identification. Furthermore, our method is interpretable by revealing ASD-relevant brain regions that are biologically significant.

HSG-MGAF Net: Heterogeneous subgraph-guided multiscale graph attention fusion network for interpretable prediction of whole-slide image

BACKGROUND AND OBJECTIVE

Pathological whole slide image (WSI) prediction and region of interest (ROI) localization are important issues in computer-aided diagnosis and postoperative analysis in clinical applications. Existing computer-aided methods for predicting WSI are mainly based on multiple instance learning (MIL) and its variants. However, most of the methods are based on instance independence and identical distribution assumption and performed at a single scale, which not fully exploit the hierarchical multiscale heterogeneous information contained in WSI.

METHODS

Heterogeneous Subgraph-Guided Multiscale Graph Attention Fusion Network (HSG-MGAF Net) is proposed to build the topology of critical image patches at two scales for adaptive WSI prediction and lesion localization. The HSG-MGAF Net simulates the hierarchical heterogeneous information of WSI through graph and hypergraph at two scales, respectively. This framework not only fully exploits the low-order and potential high-order correlations of image patches at each scale, but also leverages the heterogeneous information of the two scales for adaptive WSI prediction.

RESULTS

We validate the superiority of the proposed method on the CAMELYON16 and the TCGA- NSCLC, and the results show that HSG-MGAF Net outperforms the state-of-the-art method on both datasets. The average ACC, AUC and F1 score of HSG-MGAF Net can reach 92.7 %/0.951/0.892 and 92.2 %/0.957/0.919, respectively. The obtained heatmaps can also localize the positive regions more accurately, which have great consistency with the pixel-level labels.

CONCLUSIONS

The results demonstrate that HSG-MGAF Net outperforms existing weakly supervised learning methods by introducing critical heterogeneous information between the two scales. This approach paves the way for further research on light weighted heterogeneous graph-based WSI prediction and ROI localization.

Identifying frequency-dependent imaging genetic associations via hypergraph-structured multi-task sparse canonical correlation analysis

Identifying complex associations between genetic variations and imaging phenotypes is a challenging task in the research of brain imaging genetics. The previous study has proved that neuronal oscillations within distinct frequency bands are derived from frequency-dependent genetic modulation. Thus it is meaningful to explore frequency-dependent imaging genetic associations, which may give important insights into the pathogenesis of brain disorders. In this work, the hypergraph-structured multi-task sparse canonical correlation analysis (HS-MTSCCA) was developed to explore the associations between multi-frequency imaging phenotypes and single-nucleotide polymorphisms (SNPs). Specifically, we first created a hypergraph for the imaging phenotypes of each frequency and the SNPs, respectively. Then, a new hypergraph-structured constraint was proposed to learn high-order relationships among features in each hypergraph, which can introduce biologically meaningful information into the model. The frequency-shared and frequency-specific imaging phenotypes and SNPs could be identified using the multi-task learning framework. We also proposed a useful strategy to tackle this algorithm and then demonstrated its convergence. The proposed method was evaluated on four simulation datasets and a real schizophrenia dataset. The experimental results on synthetic data showed that HS-MTSCCA outperforms the other competing methods according to canonical correlation coefficients, canonical weights, and cosine similarity. And the results on real data showed that HS-MTSCCA could obtain superior canonical coefficients and canonical weights. Furthermore, the identified frequency-shared and frequency-specific biomarkers could provide more interesting and meaningful information, demonstrating that HS-MTSCCA is a powerful method for brain imaging genetics.

HCTMFS: A multi-modal feature selection framework with higher-order correlated topological manifold for ESRDaMCI

BACKGROUND AND OBJECTIVE

The diagnosis of end-stage renal disease associated with mild cognitive impairment (ESRDaMCI) mainly relies on objective cognitive assessment, clinical observation, and neuro-psychological evaluation, while only adopting clinical tools often limits the diagnosis accuracy.

METHODS

We proposed a multi-modal feature selection framework with higher-order correlated topological manifold (HCTMFS) to classify ESRDaMCI patients and identify the discriminative brain regions. It constructed brain structural and functional networks with diffuse kurtosis imaging (DKI) and functional magnetic resonance imaging (fMRI) data, and extracted node efficiency and clustering coefficient from the brain networks to construct multi-modal feature matrices. The topological relationship matrices were constructed to measure the lower-order topological correlation between features. Then the consensus matrices were learned to approximate the topological relationship matrices at different confidence levels and eliminate the noise influence of individual matrices.

RESULTS

The higher-order topological correlation between features was explored by the Laplacian matrix of the hypergraph, which was calculated through the consensus matrix. The new framework achieved an accuracy rate of 93.56 % for classifying ESRDaMCI patients, and outperformed the existing state-of-the-art methods in terms of sensitivity, specificity, and area under the curve.

CONCLUSIONS

This study contributes to effectively reflect the functional neural degradation of ESRDaMCI and provide a reference for the diagnosis of ESRDaMCI by selecting discriminative brain regions.

Warming during embryogenesis induces a lasting transcriptomic signature in fishes

Exposure to elevated temperatures during embryogenesis can influence the plasticity of tissues in later life. Despite these long-term changes in plasticity, few differentially expressed genes are ever identified, suggesting that the developmental programming of later life plasticity may occur through the modulation of other aspects of transcriptomic architecture, such as gene network organisation. Here, we use network modelling approaches to demonstrate that warm temperatures during embryonic development (developmental warming) have consistent effects in later life on the organisation of transcriptomic networks across four diverse species of fishes: Scyliorhinus canicula, Danio rerio, Dicentrarchus labrax, and Gasterosteus aculeatus. The transcriptomes of developmentally warmed fishes are characterised by an increased entropy of their pairwise gene interaction networks, implying a less structured, more 'random' set of gene interactions. We also show that, in zebrafish subject to developmental warming, the entropy of an individual gene within a network is associated with that gene's probability of expression change during temperature acclimation in later life. However, this association is absent in animals reared under 'control' conditions. Thus, the thermal environment experienced during embryogenesis can alter transcriptomic organisation in later life, and these changes may influence an individual's responsiveness to future temperature challenges.

Sctensor detects many-to-many cell-cell interactions from single cell RNA-sequencing data

BACKGROUND

Complex biological systems are described as a multitude of cell-cell interactions (CCIs). Recent single-cell RNA-sequencing studies focus on CCIs based on ligand-receptor (L-R) gene co-expression but the analytical methods are not appropriate to detect many-to-many CCIs.

RESULTS

In this work, we propose scTensor, a novel method for extracting representative triadic relationships (or hypergraphs), which include ligand-expression, receptor-expression, and related L-R pairs.

CONCLUSIONS

Through extensive studies with simulated and empirical datasets, we have shown that scTensor can detect some hypergraphs that cannot be detected using conventional CCI detection methods, especially when they include many-to-many relationships. scTensor is implemented as a freely available R/Bioconductor package.

The Wiener index, degree distance index and Gutman index of composite hypergraphs and sunflower hypergraphs

Topological invariants are numerical parameters of graphs or hypergraphs that indicate its topology and are known as graph or hypergraph invariants. In this paper, topological indices of hypergraphs such as Wiener index, degree distance index and Gutman index are considered. A g-composite hypergraphs is a hypergraphs that is obtained by the union of g hypergraphs with every hypergraph has exactly one vertex in common. In this article, results of above said indices for g-composite hypergraphs, where g ≥ 2 , are calculated. Further these results are used to find the Wiener index, degree distance index and Gutman index of sunflower hypergraphs and linear uniform hyper-paths.

Hypergraph and network flow-based quality function deployment

Quality function deployment (QFD) has been a widely-acknowledged tool for translating customer requirements into quality product characteristics based on which product development strategies and focus areas are identified. However, the QFD method considers the correlation and effect between development parameters, but it is not directly implemented in the importance ranking of development actions. Therefore, the cross-relationships between development parameters and their impact on customer requirement satisfaction are often neglected. The primary objective of this study is to make decision-making more reliable by improving QFD with methods that optimize the selection of development parameters even under capacity or cost constraints and directly implement cross-relationships between development parameters and support the identification of interactions visually. Therefore, QFD is accessed from two approaches that proved efficient in operations research. 1) QFD is formulated as a network flow problem with two objectives: maximizing the benefits of satisfying customer needs using linear optimization or minimizing the total cost of actions while still meeting customer requirements using assignment of minimum cost flow approach. 2) QFD is represented as a hypergraph, which allows efficient representation of the interactions of the relationship and correlation matrix and the determination of essential factors based on centrality metrics. The applicability of the methods is demonstrated through an application study in developing a sustainable design of customer electronic products and highlights the improvements' contribution to different development strategies, such as linear optimization performed the best in maximizing customer requirements' satisfaction, assignment as minimum cost flow approach minimized the total cost, while the hypergraph-based representation identified the indirect interactions of development parameters and customer requirements.

Counterfactual and Factual Reasoning over Hypergraphs for Interpretable Clinical Predictions on EHR

Electronic Health Record modeling is crucial for digital medicine. However, existing models ignore higher-order interactions among medical codes and their causal relations towards downstream clinical predictions. To address such limitations, we propose a novel framework CACHE, to provide effective and insightful clinical predictions based on hypergraph representation learning and counterfactual and factual reasoning techniques. Experiments on two real EHR datasets show the superior performance of CACHE. Case studies with a domain expert illustrate a preferred capability of CACHE in generating clinically meaningful interpretations towards the correct predictions.

HBRWRLDA: predicting potential lncRNA-disease associations based on hypergraph bi-random walk with restart

Accumulating evidence indicates that the regulation of long non-coding RNAs (lncRNAs) is closely related to a variety of diseases. Identifying meaningful lncRNA-disease associations will help to contribute to the understanding of the molecular mechanisms underlying these diseases. However, only a limited number of associations between lncRNAs and diseases have been inferred from traditional biological experiments due to the high cost and highly specialized. Therefore, computational methods are increasingly used to reduce time of biological experiments and complement biological research. In this paper, a computational method called HBRWRLDA is proposed to predict lncRNA-disease associations. First, HBRWRLDA models the relationships between multiple nodes using hypergraphs, which allows HBRWRLDA to integrate the expression similarity of lncRNAs and the semantic similarity of diseases to construct hypergraphs. Then, a bi-random walk on hypergraphs is used to predict potential lncRNA-disease associations. HBRWRLDA achieves a higher area under the curve value of 0.9551 and [Formula: see text], respectively, compared with the other five advanced methods under the framework of one-leave cross validation (LOOCV) and five-fold cross-validation (5-fold CV). In addition, the prediction effect of HBRWRLDA was confirmed case studies of three diseases: renal cell carcinoma, gastric cancer, and hepatocellular carcinoma. Case studies demonstrates the capacity of HBRWRLDA to identify potentially disease-associated lncRNAs. Overall, HBRWRLDA is excellent at predicting potential lncRNA-disease associations and could be useful in conducting further biological experiments by helping researchers identify candidates of lncRNA-disease association.

Ranking sets of morbidities using hypergraph centrality

Multi-morbidity, the health state of having two or more concurrent chronic conditions, is becoming more common as populations age, but is poorly understood. Identifying and understanding commonly occurring sets of diseases is important to inform clinical decisions to improve patient services and outcomes. Network analysis has been previously used to investigate multi-morbidity, but a classic application only allows for information on binary sets of diseases to contribute to the graph. We propose the use of hypergraphs, which allows for the incorporation of data on people with any number of conditions, and also allows us to obtain a quantitative understanding of the centrality, a measure of how well connected items in the network are to each other, of both single diseases and sets of conditions. Using this framework we illustrate its application with the set of conditions described in the Charlson morbidity index using data extracted from routinely collected population-scale, patient level electronic health records (EHR) for a cohort of adults in Wales, UK. Stroke and diabetes were found to be the most central single conditions. Sets of diseases featuring diabetes; diabetes with Chronic Pulmonary Disease, Renal Disease, Congestive Heart Failure and Cancer were the most central pairs of diseases. We investigated the differences between results obtained from the hypergraph and a classic binary graph and found that the centrality of diseases such as paraplegia, which are connected strongly to a single other disease is exaggerated in binary graphs compared to hypergraphs. The measure of centrality is derived from the weighting metrics calculated for disease sets and further investigation is needed to better understand the effect of the metric used in identifying the clinical significance and ranked centrality of grouped diseases. These initial results indicate that hypergraphs can be used as a valuable tool for analysing previously poorly understood relationships and information available in EHR data.

HTRPCA: Hypergraph Regularized Tensor Robust Principal Component Analysis for Sample Clustering in Tumor Omics Data

In recent years, clustering analysis of cancer genomics data has gained widespread attention. However, limited by the dimensions of the matrix, the traditional methods cannot fully mine the underlying geometric structure information in the data. Besides, noise and outliers inevitably exist in the data. To solve the above two problems, we come up with a new method which uses tensor to represent cancer omics data and applies hypergraph to save the geometric structure information in original data. This model is called hypergraph regularized tensor robust principal component analysis (HTRPCA). The data processed by HTRPCA becomes two parts, one of which is a low-rank component that contains pure underlying structure information between samples, and the other is some sparse interference points. So we can use the low-rank component for clustering. This model can retain complex geometric information between more sample points due to the addition of the hypergraph regularization. Through clustering, we can demonstrate the effectiveness of HTRPCA, and the experimental results on TCGA datasets demonstrate that HTRPCA precedes other advanced methods. This paper proposes a new method of using tensors to represent cancer omics data and introduces hypergraph items to save the geometric structure information of the original data. At the same time, the model decomposes the original tensor into low-order tensors and sparse tensors. The low-rank tensor was used to cluster cancer samples to verify the effectiveness of the method.

Hypergraph models of biological networks to identify genes critical to pathogenic viral response

Background

Representing biological networks as graphs is a powerful approach to reveal underlying patterns, signatures, and critical components from high-throughput biomolecular data. However, graphs do not natively capture the multi-way relationships present among genes and proteins in biological systems. Hypergraphs are generalizations of graphs that naturally model multi-way relationships and have shown promise in modeling systems such as protein complexes and metabolic reactions. In this paper we seek to understand how hypergraphs can more faithfully identify, and potentially predict, important genes based on complex relationships inferred from genomic expression data sets.

Results

We compiled a novel data set of transcriptional host response to pathogenic viral infections and formulated relationships between genes as a hypergraph where hyperedges represent significantly perturbed genes, and vertices represent individual biological samples with specific experimental conditions. We find that hypergraph betweenness centrality is a superior method for identification of genes important to viral response when compared with graph centrality.

Conclusions

Our results demonstrate the utility of using hypergraphs to represent complex biological systems and highlight central important responses in common to a variety of highly pathogenic viruses.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12859-021-04197-2.

Epidemic zone of COVID-19 from social media using hypergraph with weighting factor (HWF)

Online social network is one of the most prominent media that holds information about society's epidemic problem. Due to privacy reasons, most of the users will not disclose their location. Detecting the location of the tweet users is required to track the geographic location of the spreading diseases. This work aims to detect the spreading location of the COVID-19 disease from the Twitter users and content discussed in the tweet. COVID-19 is a disease caused by the "novel coronavirus." About 80% of confirmed cases recover from the disease. However, one out of every six people who get COVID-19 can become seriously ill, stated by the World health organization. Inferring the user location for identifying the spreading location for the disease is a very challenging task. This paper proposes a new technique based on a hypergraph model to detect the Twitter user's locations based on the spreading disease. This model uses hypergraph with weighting factor technique to infer the spreading disease's spatial location. The accuracy of prediction can be improved when a massive volume of streaming data is analyzed. The Helly property of the hypergraph was applied to discard less potential words from the text analysis, which claims this work of unique nature. A weighting factor was introduced to calculate the score of each location for a particular user. The location of each user is predicted based on the one that possesses the highest weighting factor. The proposed framework has been evaluated and tested for various measures like precision, recall and F-measure. The promising results obtained have substantiated the claim for this work compared to the state-of-the-art methodologies.

Counting frequent patterns in large labeled graphs: a hypergraph-based approach

In recent years, the popularity of graph databases has grown rapidly. This paper focuses on single-graph as an effective model to represent information and its related graph mining techniques. In frequent pattern mining in a single-graph setting, there are two main problems: support measure and search scheme. In this paper, we propose a novel framework for designing support measures that brings together existing minimum-image-based and overlap-graph-based support measures. Our framework is built on the concept of occurrence/instance hypergraphs. Based on such, we are able to design a series of new support measures: minimum instance (MI) measure, and minimum vertex cover (MVC) measure, that combine the advantages of existing measures. More importantly, we show that the existing minimum-image-based support measure is an upper bound of the MI measure, which is also linear-time computable and results in counts that are close to number of instances of a pattern. We show that not only most major existing support measures and new measures proposed in this paper can be mapped into the new framework, but also they occupy different locations of the frequency spectrum. By taking advantage of the new framework, we discover that MVC can be approximated to a constant factor (in terms of number of pattern nodes) in polynomial time. In contrast to common belief, we demonstrate that the state-of-the-art overlap-graph-based maximum independent set (MIS) measure also has constant approximation algorithms. We further show that using standard linear programming and semidefinite programming techniques, polynomial-time relaxations for both MVC and MIS measures can be developed and their counts stand between MVC and MIS. In addition, we point out that MVC, MIS, and their relaxations are bounded within constant factor. In summary, all major support measures are unified in the new hypergraph-based framework which helps reveal their bounding relations and hardness properties.

Structural conserved moiety splitting of a stoichiometric matrix

Characterising biochemical reaction network structure in mathematical terms enables the inference of functional biochemical consequences from network structure with existing mathematical techniques and spurs the development of new mathematics that exploits the peculiarities of biochemical network structure. The structure of a biochemical network may be specified by reaction stoichiometry, that is, the relative quantities of each molecule produced and consumed in each reaction of the network. A biochemical network may also be specified at a higher level of resolution in terms of the internal structure of each molecule and how molecular structures are transformed by each reaction in a network. The stoichiometry for a set of reactions can be compiled into a stoichiometric matrix N∈Z^m×n, where each row corresponds to a molecule and each column corresponds to a reaction. We demonstrate that a stoichiometric matrix may be split into the sum of m-rank(N) moiety transition matrices, each of which corresponds to a subnetwork accessible to a structurally identifiable conserved moiety. The existence of this moiety matrix splitting is a property that distinguishes a stoichiometric matrix from an arbitrary rectangular matrix.

HC-HDSD: A method of hypergraph construction and high-density subgraph detection for inferring high-order epistatic interactions

Detecting epistatic interactions, or nonlinear interactive effects of Single Nucleotide Polymorphisms (SNPs), has gained increasing attention in explaining the "missing heritability" of complex diseases. Though much work has been done in mapping SNPs underlying diseases, most of them constrain to 2-order epistatic interactions. In this paper, a method of hypergraph construction and high-density subgraph detection, named HC-HDSD, is proposed for detecting high-order epistatic interactions. The hypergraph is constructed by low-order epistatic interactions that identified using the normalized co-information measure and the exhaustive search. The hypergraph consists of two types of vertices: real ones representing main effects of SNPs and virtual ones denoting interactive effects of epistatic interactions. Then, both maximal clique centrality algorithm and near-clique mining algorithm are employed to detect high-density subgraphs from the constructed hypergraph. These high-density subgraphs are inferred as high-order epistatic interactions in the HC-HDSD. Experiments are performed on several simulation data sets, results of which show that HC-HDSD is promising in inferring high-order epistatic interactions while substantially reducing the computation cost. In addition, the application of HC-HDSD on a real Age-related Macular Degeneration (AMD) data set provides several new clues for the exploration of causative factors of AMD.

An improved robust heteroscedastic probabilistic neural network based trust prediction approach for cloud service selection

Trustworthiness is a comprehensive quality metric which is used to assess the quality of the services in service-oriented environments. However, trust prediction of cloud services based on the multi-faceted Quality of Service (QoS) attributes is a challenging task due to the complicated and non-linear relationships between the QoS values and the corresponding trust result. Recent research works reveal the significance of Artificial Neural Network (ANN) and its variants in providing a reasonable degree of success in trust prediction problems. However, the challenges with respect to weight assignment, training time and kernel functions make ANN and its variants under continuous advancements. Hence, this work presents a novel multi-level Hypergraph Coarsening based Robust Heteroscedastic Probabilistic Neural Network (HC-RHRPNN) to predict trustworthiness of cloud services to build high-quality service applications. HC-RHRPNN employs hypergraph coarsening to identify the informative samples, which were then used to train HRPNN to improve its prediction accuracy and minimize the runtime. The performance of HC-RHRPNN was evaluated using Quality of Web Service (QWS) dataset, a public QoS dataset in terms of classifier accuracy, precision, recall, and F-Score.

An upper bound for the Z-spectral radius of adjacency tensors

Let [Formula: see text] be a k-uniform hypergraph on n vertices with degree sequence [Formula: see text]. In this paper, in terms of degree [Formula: see text], we give a new upper bound for the Z-spectral radius of the adjacency tensor of [Formula: see text]. Some examples are given to show the efficiency of the bound.

Finding the K best synthesis plans

In synthesis planning, the goal is to synthesize a target molecule from available starting materials, possibly optimizing costs such as price or environmental impact of the process. Current algorithmic approaches to synthesis planning are usually based on selecting a bond set and finding a single good plan among those induced by it. We demonstrate that synthesis planning can be phrased as a combinatorial optimization problem on hypergraphs by modeling individual synthesis plans as directed hyperpaths embedded in a hypergraph of reactions (HoR) representing the chemistry of interest. As a consequence, a polynomial time algorithm to find the K shortest hyperpaths can be used to compute the K best synthesis plans for a given target molecule. Having K good plans to choose from has many benefits: it makes the synthesis planning process much more robust when in later stages adding further chemical detail, it allows one to combine several notions of cost, and it provides a way to deal with imprecise yield estimates. A bond set gives rise to a HoR in a natural way. However, our modeling is not restricted to bond set based approaches—any set of known reactions and starting materials can be used to define a HoR. We also discuss classical quality measures for synthesis plans, such as overall yield and convergency, and demonstrate that convergency has a built-in inconsistency which could render its use in synthesis planning questionable. Decalin is used as an illustrative example of the use and implications of our results.

A Novel Hypergraph-Based Genetic Algorithm (HGGA) Built on Unimodular and Anti-homomorphism Properties for DNA Sequencing by Hybridization

The sequencing by hybridization (SBH) of determining the order in which nucleotides should occur on a DNA string is still under discussion for enhancements on computational intelligence although the next generation of DNA sequencing has come into existence. In the last decade, many works related to graph theory-based DNA sequencing have been carried out in the literature. This paper proposes a method for SBH by integrating hypergraph with genetic algorithm (HGGA) for designing a novel analytic technique to obtain DNA sequence from its spectrum. The paper represents elements of the spectrum and its relation as hypergraph and applies the unimodular property to ensure the compatibility of relations between l-mers. The hypergraph representation and unimodular property are bound with the genetic algorithm that has been customized with a novel selection and crossover operator reducing the computational complexity with accelerated convergence. Subsequently, upon determining the primary strand, an anti-homomorphism is invoked to find the reverse complement of the sequence. The proposed algorithm is implemented in the GenBank BioServer datasets, and the results are found to prove the efficiency of the algorithm. The HGGA is a non-classical algorithm with significant advantages and computationally attractive complexity reductions ranging to [Formula: see text] with improved accuracy that makes it prominent for applications other than DNA sequencing like image processing, task scheduling and big data processing.

CINOEDV: a co-information based method for detecting and visualizing n-order epistatic interactions

BACKGROUND

Detecting and visualizing nonlinear interaction effects of single nucleotide polymorphisms (SNPs) or epistatic interactions are important topics in bioinformatics since they play an important role in unraveling the mystery of "missing heritability". However, related studies are almost limited to pairwise epistatic interactions due to their methodological and computational challenges.

RESULTS

We develop CINOEDV (Co-Information based N-Order Epistasis Detector and Visualizer) for the detection and visualization of epistatic interactions of their orders from 1 to n (n ≥ 2). CINOEDV is composed of two stages, namely, detecting stage and visualizing stage. In detecting stage, co-information based measures are employed to quantify association effects of n-order SNP combinations to the phenotype, and two types of search strategies are introduced to identify n-order epistatic interactions: an exhaustive search and a particle swarm optimization based search. In visualizing stage, all detected n-order epistatic interactions are used to construct a hypergraph, where a real vertex represents the main effect of a SNP and a virtual vertex denotes the interaction effect of an n-order epistatic interaction. By deeply analyzing the constructed hypergraph, some hidden clues for better understanding the underlying genetic architecture of complex diseases could be revealed.

CONCLUSIONS

Experiments of CINOEDV and its comparison with existing state-of-the-art methods are performed on both simulation data sets and a real data set of age-related macular degeneration. Results demonstrate that CINOEDV is promising in detecting and visualizing n-order epistatic interactions. CINOEDV is implemented in R and is freely available from R CRAN: http://cran.r-project.org and https://sourceforge.net/projects/cinoedv/files/ .

SIS Epidemic Propagation on Hypergraphs

Mathematical modelling of epidemic propagation on networks is extended to hypergraphs in order to account for both the community structure and the nonlinear dependence of the infection pressure on the number of infected neighbours. The exact master equations of the propagation process are derived for an arbitrary hypergraph given by its incidence matrix. Based on these, moment closure approximation and mean-field models are introduced and compared to individual-based stochastic simulations. The simulation algorithm, developed for networks, is extended to hypergraphs. The effects of hypergraph structure and the model parameters are investigated via individual-based simulation results.

A mathematical approach to emergent properties of metabolic networks: partial coupling relations, hyperarcs and flux ratios

Emergent properties in systems biology are those which arise only when the biological system passes a certain level of complexity. In this study, we introduce some of the emergent properties which appear in the constraint-based analysis of metabolic networks. These properties generally appear as a result of existence of hfdeyperarcs and irreversible reactions in networks. Here, we present examples of metabolic networks in which there exist at least two reactions whose fluxes cannot be written as products and/or ratios of the stoichiometric coefficients of the network. We show that any such network contains at least one hyperarc. Additionally, we prove that partial coupling cannot appear in consistent metabolic networks with less than four reactions, or with less than three irreversible reactions, or without hyperarc(s).

Hypergraph coloring complexes

The aim of this paper is to generalize the notion of the coloring complex of a graph to hypergraphs. We present three different interpretations of those complexes-a purely combinatorial one and two geometric ones. It is shown, that most of the properties, which are known to be true for coloring complexes of graphs, break down in this more general setting, e.g., Cohen-Macaulayness and partitionability. Nevertheless, we are able to provide bounds for the [Formula: see text]- and [Formula: see text]-vectors of those complexes which yield new bounds on chromatic polynomials of hypergraphs. Moreover, though it is proven that the coloring complex of a hypergraph has a wedge decomposition, we provide an example showing that in general this decomposition is not homotopy equivalent to a wedge of spheres. In addition, we can completely characterize those hypergraphs whose coloring complex is connected.