Multiple Types Of Edges Research Articles

Consistent community detection in multi-relational data through restricted multi-layer stochastic blockmodel

In recent years there has been an increased interest in statistical analysis of data with multiple types of relations among a set of entities. Such multi-relational data can be represented as multi-layer graphs where the set of vertices represents the entities and multiple types of edges represent the different relations among them. For community detection in multi-layer graphs, we consider two random graph models, the multi-layer stochastic blockmodel (MLSBM) and a model with a restricted parameter space, the restricted multi-layer stochastic blockmodel (RMLSBM). We derive consistency results for community assignments of the maximum likelihood estimators (MLEs) in both models where MLSBM is assumed to be the true model, and either the number of nodes or the number of types of edges or both grow. We compare MLEs in the two models with other baseline approaches, such as separate modeling of layers, aggregating the layers and majority voting. RMLSBM is shown to have advantage over MLSBM when either the growth rate of the number of communities is high or the growth rate of the average degree of the component graphs in the multi-graph is low. We also derive minimax rates of error and sharp thresholds for achieving consistency of community detection in both models, which are then used to compare the multi-layer models with a baseline model, the aggregate stochastic block model. The simulation studies and real data applications confirm the superior performance of the multi-layer approaches in comparison to the baseline procedures.

Minimized-cost cube query on heterogeneous information networks

Data cube is the foundation of on-line analytical processing (OLAP), which can provide users with data views from different perspectives and granularities. Heterogeneous information networks consist of multiple types of nodes and edges which represent different semantic relations. With the rapid development of social networks and knowledge graphs, heterogeneous information networks have become increasingly popular. In heterogeneous information networks, cube is the set of aggregate graphs and cube query is required for supporting OLAP. The existing research mainly studies aggregate graph query on homogeneous networks, but only considers the attributes of nodes. To overcome these challenges, this paper investigates cube query problem on heterogeneous information networks. (1) A novel cube model for heterogeneous information networks is proposed, which captures both the attribute and structure semantics. (2) Because the total number of aggregate graphs is huge, computing and storing them cost plenty of time and storage. The problem of partial cube materialization on heterogeneous information networks is investigated. Given a fixed size of memory space, select a subset of aggregate graphs in cube, to minimize the computing cost of the whole cube. This optimization problem is proved to be NP-complete and there is no $$n^{1-{\epsilon }}$$n1-∈ approximation algorithm unless P $$=$$= NP. (3) A greedy algorithm is proposed for partial cube materialization based on two interesting dependencies between aggregate graphs, attribute dependence and path dependence. (4) Experiments on real world data sets show the cube definition is meaningful, and the partial cube materialization algorithm is efficient.

Heterogeneous Network Edge Prediction: A Data Integration Approach to Prioritize Disease-Associated Genes.

The first decade of Genome Wide Association Studies (GWAS) has uncovered a wealth of disease-associated variants. Two important derivations will be the translation of this information into a multiscale understanding of pathogenic variants and leveraging existing data to increase the power of existing and future studies through prioritization. We explore edge prediction on heterogeneous networks—graphs with multiple node and edge types—for accomplishing both tasks. First we constructed a network with 18 node types—genes, diseases, tissues, pathophysiologies, and 14 MSigDB (molecular signatures database) collections—and 19 edge types from high-throughput publicly-available resources. From this network composed of 40,343 nodes and 1,608,168 edges, we extracted features that describe the topology between specific genes and diseases. Next, we trained a model from GWAS associations and predicted the probability of association between each protein-coding gene and each of 29 well-studied complex diseases. The model, which achieved 132-fold enrichment in precision at 10% recall, outperformed any individual domain, highlighting the benefit of integrative approaches. We identified pleiotropy, transcriptional signatures of perturbations, pathways, and protein interactions as influential mechanisms explaining pathogenesis. Our method successfully predicted the results (with AUROC = 0.79) from a withheld multiple sclerosis (MS) GWAS despite starting with only 13 previously associated genes. Finally, we combined our network predictions with statistical evidence of association to propose four novel MS genes, three of which (JAK2, REL, RUNX3) validated on the masked GWAS. Furthermore, our predictions provide biological support highlighting REL as the causal gene within its gene-rich locus. Users can browse all predictions online (http://het.io). Heterogeneous network edge prediction effectively prioritized genetic associations and provides a powerful new approach for data integration across multiple domains.

Cascades in multiplex financial networks with debts of different seniority.

The seniority of debt, which determines the order in which a bankrupt institution repays its debts, is an important and sometimes contentious feature of financial crises, yet its impact on systemwide stability is not well understood. We capture seniority of debt in a multiplex network, a graph of nodes connected by multiple types of edges. Here an edge between banks denotes a debt contract of a certain level of seniority. Next we study cascading default. There exist multiple kinds of bankruptcy, indexed by the highest level of seniority at which a bank cannot repay all its debts. Self-interested banks would prefer that all their loans be made at the most senior level. However, mixing debts of different seniority levels makes the system more stable in that it shrinks the set of network densities for which bankruptcies spread widely. We compute the optimal ratio of senior to junior debts, which we call the optimal seniority ratio, for two uncorrelated Erdős-Rényi networks. If institutions erode their buffer against insolvency, then this optimal seniority ratio rises; in other words, if default thresholds fall, then more loans should be senior. We generalize the analytical results to arbitrarily many levels of seniority and to heavy-tailed degree distributions.

A FRAMEWORK FOR COMMUNITY DETECTION IN HETEROGENEOUS MULTI-RELATIONAL NETWORKS

There has been a surge of interest in community detection in homogeneous single-relational networks which contain only one type of nodes and edges. However, many real-world systems are naturally described as heterogeneous multi-relational networks which contain multiple types of nodes and edges. In this paper, we propose a new method for detecting communities in such networks. Our method is based on optimizing the composite modularity, which is a new modularity proposed for evaluating partitions of a heterogeneous multi-relational network into communities. Our method is parameter-free, scalable, and suitable for various networks with general structure. We demonstrate that it outperforms the state-of-the-art techniques in detecting pre-planted communities in synthetic networks. Applied to a real-world Digg network, it successfully detects meaningful communities.

NovoHCD: de novo peptide sequencing from HCD spectra.

In recent years, de novo peptide sequencing from mass spectrometry data has developed as one of the major peptide identification methods with the emergence of new instruments and advanced computational methods. However, there are still limitations to this method; for example, the typically used spectrum graph model cannot represent all the information and relationships inherent in tandem mass spectra (MS/MS spectra). Here, we present a new method named NovoHCD which applies a spectrum graph model with multiple types of edges (called a multi-edge graph), and integrates into it amino acid combination (AAC) information and peptide tags. In addition, information on immonium ions observed particularly in higher-energy collisional dissociation (HCD) spectra is incorporated. Comparisons between NovoHCD and another successful de novo peptide sequencing method for HCD spectra, pNovo, were performed. Experiments were conducted on five HCD spectral datasets. Results show that NovoHCD outperforms pNovo in terms of full length peptide identification accuracy; specifically, the accuracy increases 13%-21% over the five datasets.

A fixed degree sequence model for the one-mode projection of multiplex bipartite graphs

A bipartite structure is a common property of many real-world network data sets such as agents which are affiliated with societies, customers who buy, rent, or rate products, and authors who write scientific papers. The one-mode projection of these networks onto either set of entities (e.g., societies, products, and articles) is a well-established approach for the analysis of such data and deduces relations between these entities. Some bipartite data sets of key importance contain several distinct types of relations between their entities. These networks require a projection method which accounts for multiple edge types. In this article, we present the multiplex extension of an existing projection algorithm for simplex bipartite networks, i.e., networks that contain a single type of relation. We use synthetic data to show the robustness of our method before applying it to a real-world network of user ratings for films, namely, the Netflix data set. Based on the assumption that co-ratings of films contain information about the films’ similarity, we analyse the multiplex projection as an approximation of the similarity landscape of the films. Besides comparing the projection to the coarse-grained classification of films into genres, we validate the resulting similarities based on ground truth data sets containing film series. Our analysis confirms the predictive power of the network of positive co-ratings. We furthermore explore the potential of additional, mixed co-rating patterns in improving the prediction of similarities and highlight necessary criteria for this approach.

On Clustering on Graphs with Multiple Edge Types

We study clustering on graphs with multiple edge types. Our main motivation is that similarities between objects can be measured by many different metrics. For instance, similarity between two papers can be based on common authors, where they were published, keyword similarity, citations, etc. As such, graphs with multiple edges give a more accurate model to describe similarities between objects than models using single-edge graphs. Each edge/metric provides only partial information about the data; recovering full information requires aggregation of all the similarity metrics. Clustering becomes much more challenging in this context, since in addition to the difficulties of the traditional clustering problem, we have to deal with a space of clusterings. Reducing the multidimensional space into a single dimension poses significant challenges. At the same time, the multidimensional space can contain latent structures, and searching this multidimensional space can reveal important information about the graph...

Multi-Edge Gene Set Networks Reveal Novel Insights into Global Relationships between Biological Themes

Curated gene sets from databases such as KEGG Pathway and Gene Ontology are often used to systematically organize lists of genes or proteins derived from high-throughput data. However, the information content inherent to some relationships between the interrogated gene sets, such as pathway crosstalk, is often underutilized. A gene set network, where nodes representing individual gene sets such as KEGG pathways are connected to indicate a functional dependency, is well suited to visualize and analyze global gene set relationships. Here we introduce a novel gene set network construction algorithm that integrates gene lists derived from high-throughput experiments with curated gene sets to construct co-enrichment gene set networks. Along with previously described co-membership and linkage algorithms, we apply the co-enrichment algorithm to eight gene set collections to construct integrated multi-evidence gene set networks with multiple edge types connecting gene sets. We demonstrate the utility of approach through examples of novel gene set networks such as the chromosome map co-differential expression gene set network. A total of twenty-four gene set networks are exposed via a web tool called MetaNet, where context-specific multi-edge gene set networks are constructed from enriched gene sets within user-defined gene lists. MetaNet is freely available at http://blaispathways.dfci.harvard.edu/metanet/.

Biomine: predicting links between biological entities using network models of heterogeneous databases

BackgroundBiological databases contain large amounts of data concerning the functions and associations of genes and proteins. Integration of data from several such databases into a single repository can aid the discovery of previously unknown connections spanning multiple types of relationships and databases.ResultsBiomine is a system that integrates cross-references from several biological databases into a graph model with multiple types of edges, such as protein interactions, gene-disease associations and gene ontology annotations. Edges are weighted based on their type, reliability, and informativeness. We present Biomine and evaluate its performance in link prediction, where the goal is to predict pairs of nodes that will be connected in the future, based on current data. In particular, we formulate protein interaction prediction and disease gene prioritization tasks as instances of link prediction. The predictions are based on a proximity measure computed on the integrated graph. We consider and experiment with several such measures, and perform a parameter optimization procedure where different edge types are weighted to optimize link prediction accuracy. We also propose a novel method for disease-gene prioritization, defined as finding a subset of candidate genes that cluster together in the graph. We experimentally evaluate Biomine by predicting future annotations in the source databases and prioritizing lists of putative disease genes.ConclusionsThe experimental results show that Biomine has strong potential for predicting links when a set of selected candidate links is available. The predictions obtained using the entire Biomine dataset are shown to clearly outperform ones obtained using any single source of data alone, when different types of links are suitably weighted. In the gene prioritization task, an established reference set of disease-associated genes is useful, but the results show that under favorable conditions, Biomine can also perform well when no such information is available.The Biomine system is a proof of concept. Its current version contains 1.1 million entities and 8.1 million relations between them, with focus on human genetics. Some of its functionalities are available in a public query interface at http://biomine.cs.helsinki.fi, allowing searching for and visualizing connections between given biological entities.

Multiplexity-facilitated cascades in networks

Elements of networks interact in many ways, so modeling them with graphs requires multiple types of edges (or network layers). Here we show that such multiplex networks are generically more vulnerable to global cascades than simplex networks. We generalize the threshold cascade model [Watts, Proc. Natl. Acad. Sci. USA 99, 5766 (2002)] to multiplex networks, in which a node activates if a sufficiently large fraction of neighbors in any layer are active. We show that both combining layers (i.e., realizing other interactions play a role) and splitting a network into layers (i.e., recognizing distinct kinds of interactions) facilitate cascades. Notably, layers unsusceptible to global cascades can cooperatively achieve them if coupled. On one hand, this suggests fundamental limitations on predicting cascades without full knowledge of a system's multiplexity; on the other hand, it offers feasible means to control cascades by introducing or removing sparse layers in an existing network.

Hierarchical graphs for rule-based modeling of biochemical systems

BackgroundIn rule-based modeling, graphs are used to represent molecules: a colored vertex represents a component of a molecule, a vertex attribute represents the internal state of a component, and an edge represents a bond between components. Components of a molecule share the same color. Furthermore, graph-rewriting rules are used to represent molecular interactions. A rule that specifies addition (removal) of an edge represents a class of association (dissociation) reactions, and a rule that specifies a change of a vertex attribute represents a class of reactions that affect the internal state of a molecular component. A set of rules comprises an executable model that can be used to determine, through various means, the system-level dynamics of molecular interactions in a biochemical system.ResultsFor purposes of model annotation, we propose the use of hierarchical graphs to represent structural relationships among components and subcomponents of molecules. We illustrate how hierarchical graphs can be used to naturally document the structural organization of the functional components and subcomponents of two proteins: the protein tyrosine kinase Lck and the T cell receptor (TCR) complex. We also show that computational methods developed for regular graphs can be applied to hierarchical graphs. In particular, we describe a generalization of Nauty, a graph isomorphism and canonical labeling algorithm. The generalized version of the Nauty procedure, which we call HNauty, can be used to assign canonical labels to hierarchical graphs or more generally to graphs with multiple edge types. The difference between the Nauty and HNauty procedures is minor, but for completeness, we provide an explanation of the entire HNauty algorithm.ConclusionsHierarchical graphs provide more intuitive formal representations of proteins and other structured molecules with multiple functional components than do the regular graphs of current languages for specifying rule-based models, such as the BioNetGen language (BNGL). Thus, the proposed use of hierarchical graphs should promote clarity and better understanding of rule-based models.

Butterfly edge effects are predicted by a simple model in a complex landscape

Edge responses have been studied for decades and form a critical component of our understanding of how organisms respond to landscape structure and habitat fragmentation. Until recently, however, the lack of a general, conceptual framework has made it difficult to make sense of the patterns and variability reported in the edge literature. We present a test of an edge effects model which predicts that organisms should avoid edges with less-preferred habitat, show increased abundance near edges with preferred habitat or habitat containing complementary resources, and show no response to edges with similar-quality habitat that offers only supplementary resources. We tested the predictions of this model against observations of the edge responses of 15 butterfly species at 12 different edge types within a complex, desert riparian landscape. Observations matched model predictions more than would be expected by chance for the 211 species/edge combinations tested over 3 years of study. In cases where positive or negative edge responses were predicted, observed responses matched those predictions 70% of the time. While the model tends to underpredict neutral results, it was rare that an observed edge response contradicted that predicted by the model. This study also supported the two primary ecological mechanisms underlying the model, although not equally. We detected a positive relationship between habitat preferences and the slope of the observed edge response, suggesting that this basic life history trait underlies edge effects and influences their magnitude. Empirical evidence also suggested the presence of complementary resources underlies positive edge responses, but only when completely confined to the adjacent habitat. This multi-species test of a general edge effects model at multiple edge types shows that resource-based mechanisms can explain many edge responses and that a modest knowledge of life history attributes and resource availability is sufficient for predicting and understanding many edge responses in complex landscapes.