77 research outputs found
Finding maximal bicliques in bipartite networks using node similarity
In real world complex networks, communities are usually both overlapping and hierarchical. A very important class of complex networks is the bipartite networks. Maximal bicliques are the strongest possible structural communities within them. Here we consider overlapping communities in bipartite networks and propose a method that detects an order-limited number of overlapping maximal bicliques covering the network. We formalise a measure of relative community strength by which communities can be categorised, compared and ranked. There are very few real bipartite datasets for which any external ground truth about overlapping communities is known. Here we test three such datasets. We categorise and rank the maximal biclique communities found by our algorithm according to our measure of strength. Deeper analysis of these bicliques shows they accord with ground truth and give useful additional insight. Based on this we suggest our algorithm can find true communities at the first level of a hierarchy. We add a heuristic merging stage to the maximal biclique algorithm to produce a second level hierarchy with fewer communities and obtain positive results when compared with other overlapping community detection algorithms for bipartite networks
Multipartite Graph Algorithms for the Analysis of Heterogeneous Data
The explosive growth in the rate of data generation in recent years threatens to outpace the growth in computer power, motivating the need for new, scalable algorithms and big data analytic techniques. No field may be more emblematic of this data deluge than the life sciences, where technologies such as high-throughput mRNA arrays and next generation genome sequencing are routinely used to generate datasets of extreme scale. Data from experiments in genomics, transcriptomics, metabolomics and proteomics are continuously being added to existing repositories. A goal of exploratory analysis of such omics data is to illuminate the functions and relationships of biomolecules within an organism. This dissertation describes the design, implementation and application of graph algorithms, with the goal of seeking dense structure in data derived from omics experiments in order to detect latent associations between often heterogeneous entities, such as genes, diseases and phenotypes. Exact combinatorial solutions are developed and implemented, rather than relying on approximations or heuristics, even when problems are exceedingly large and/or difficult. Datasets on which the algorithms are applied include time series transcriptomic data from an experiment on the developing mouse cerebellum, gene expression data measuring acute ethanol response in the prefrontal cortex, and the analysis of a predicted protein-protein interaction network. A bipartite graph model is used to integrate heterogeneous data types, such as genes with phenotypes and microbes with mouse strains. The techniques are then extended to a multipartite algorithm to enumerate dense substructure in multipartite graphs, constructed using data from three or more heterogeneous sources, with applications to functional genomics. Several new theoretical results are given regarding multipartite graphs and the multipartite enumeration algorithm. In all cases, practical implementations are demonstrated to expand the frontier of computational feasibility
A bitwise clique detection approach for accelerating power graph computation and clustering dense graphs
Graphs are at the essence of many data representations. The visual analytics over graphs is usually difficult due to their size, which makes their visual display challenging, and their fundamental algorithms, which are often classified as NP-hard problems. The Power Graph Analysis (PGA) is a method that simplifies networks using reduced representations for complete subgraphs (cliques) and complete bipartite subgraphs (bicliques), in both cases with edge reductions. The benefits of a power graph are the preservation of information and its capacity to show essential information about the original network. However, finding an optimal representation (maximum edges reduction) is also an NPhard problem. In this work, we propose BCD, a greedy algorithm that uses a Bitwise Clique Detection approach to finding power graphs. BCD is faster than competing strategies and allows the analysis of bigger graphs. For the display of larger power graphs, we propose an orthogonal layout to prevent overlapping of edges and vertices. Finally, we describe how the structure induced by the power graph is used for clustering analysis of dense graphs. We demonstrate with several datasets the results obtained by our proposal and compare against competing strategies.Os grafos são essenciais para muitas representações de dados. A análise visual de grafos é usualmente difícil devido ao tamanho, o que representa um desafio para sua visualização. Além de isso, seus algoritmos fundamentais são frequentemente classificados como NP-difícil. Análises dos grafos de potência (PGA em inglês) é um método que simplifica redes usando representações reduzidas para subgrafos completos chamados cliques e subgrafos bipartidos chamados bicliques, em ambos casos com una redução de arestas. Os benefícios da representação de grafo de potência são a preservação de informação e a capacidade de mostrar a informação essencial sobre a rede original. Entretanto, encontrar uma representação ótima (a máxima redução de arestas possível) é também um problema NP-difícil. Neste trabalho, propomos BCD, um algoritmo guloso que usa um abordagem de detecção de bicliques baseado em operações binarias para encontrar representações de grafos de potencia. O BCD é mas rápido que as estratégias atuais da literatura. Finalmente, descrevemos como a estrutura induzida pelo grafo de potência é utilizado para as análises dos grafos densos na detecção de agrupamentos de nodos
Cohesive subgraph identification in large graphs
Graph data is ubiquitous in real world applications, as the relationship among entities in the applications can be naturally captured by the graph model. Finding cohesive subgraphs is a fundamental problem in graph mining with diverse applications. Given the important roles of cohesive subgraphs, this thesis focuses on cohesive subgraph identification in large graphs.
Firstly, we study the size-bounded community search problem that aims to find a subgraph with the largest min-degree among all connected subgraphs that contain the query vertex q and have at least l and at most h vertices, where q, l, h are specified by the query. As the problem is NP-hard, we propose a branch-reduce-and-bound algorithm SC-BRB by developing nontrivial reducing techniques, upper bounding techniques, and branching techniques.
Secondly, we formulate the notion of similar-biclique in bipartite graphs which is a special kind of biclique where all vertices from a designated side are similar to each other, and aim to enumerate all maximal similar-bicliques. We propose a backtracking algorithm MSBE to directly enumerate maximal similar-bicliques, and power it by vertex reduction and optimization techniques. In addition, we design a novel index structure to speed up a time-critical operation of MSBE, as well as to speed up vertex reduction. Efficient index construction algorithms are developed.
Thirdly, we consider balanced cliques in signed graphs --- a clique is balanced if its vertex set can be partitioned into CL and CR such that all negative edges are between CL and CR --- and study the problem of maximum balanced clique computation. We propose techniques to transform the maximum balanced clique problem over G to a series of maximum dichromatic clique problems over small subgraphs of G. The transformation not only removes edge signs but also sparsifies the edge set
On finding bicliques in bipartite graphs: a novel algorithm and its application to the integration of diverse biological data types
BACKGROUND: Integrating and analyzing heterogeneous genome-scale data is a huge algorithmic challenge for modern systems biology. Bipartite graphs can be useful for representing relationships across pairs of disparate data types, with the interpretation of these relationships accomplished through an enumeration of maximal bicliques. Most previously-known techniques are generally ill-suited to this foundational task, because they are relatively inefficient and without effective scaling. In this paper, a powerful new algorithm is described that produces all maximal bicliques in a bipartite graph. Unlike most previous approaches, the new method neither places undue restrictions on its input nor inflates the problem size. Efficiency is achieved through an innovative exploitation of bipartite graph structure, and through computational reductions that rapidly eliminate non-maximal candidates from the search space. An iterative selection of vertices for consideration based on non-decreasing common neighborhood sizes boosts efficiency and leads to more balanced recursion trees.
RESULTS: The new technique is implemented and compared to previously published approaches from graph theory and data mining. Formal time and space bounds are derived. Experiments are performed on both random graphs and graphs constructed from functional genomics data. It is shown that the new method substantially outperforms the best previous alternatives.
CONCLUSIONS: The new method is streamlined, efficient, and particularly well-suited to the study of huge and diverse biological data. A robust implementation has been incorporated into GeneWeaver, an online tool for integrating and analyzing functional genomics experiments, available at http://geneweaver.org. The enormous increase in scalability it provides empowers users to study complex and previously unassailable gene-set associations between genes and their biological functions in a hierarchical fashion and on a genome-wide scale. This practical computational resource is adaptable to almost any applications environment in which bipartite graphs can be used to model relationships between pairs of heterogeneous entities. BMC Bioinformatics 2014; 15(1):110
Clustering and Classification of Multi-domain Proteins
Rapid development of next-generation sequencing technology has led to an unprecedented growth in protein sequence data repositories over the last decade. Majority of these proteins lack structural and functional characterization. This necessitates design and development of fast, efficient, and sensitive computational tools and algorithms that can classify these proteins into functionally coherent groups.
Domains are fundamental units of protein structure and function. Multi-domain proteins are extremely complex as opposed to proteins that have single or no domains. They exhibit network-like complex evolutionary events such as domain shuffling, domain loss, and domain gain. These events therefore, cannot be represented in the conventional protein clustering algorithms like phylogenetic reconstruction and Markov clustering. In this thesis, a multi-domain protein classification system is developed primarily based on the domain composition of protein sequences. Using the principle of co-clustering (biclustering), both proteins and domains are simultaneously clustered, where each bicluster contains a subset of proteins and domains forming a complete bipartite graph. These clusters are then converted into a network of biclusters based on the domains shared between the clusters, thereby classifying the proteins into similar protein families.
We applied our biclustering network approach on a multi-domain protein family, Regulator of G-protein Signalling (RGS) proteins, where heterogeneous domain composition exists among subfamilies. Our approach showed mostly consistent clustering with the existing RGS subfamilies. The average maximum Jaccard Index scores for the clusters obtained by Markov Clustering and phylogenetic clustering methods against the biclusters were 0.64 and 0.60, respectively. Compared to other clustering methods, our approach uses auxiliary domain information of each protein, and therefore, generates more functionally coherent protein clusters and differentiates each protein subfamily from each other. Biclustered networks on complete nine proteomes showed that the number of multi-domain proteins included in connected biclusters rapidly increased with genome complexity, 48.5% in bacteria to 80% in eukaryotes.
Protein clustering and classification, incorporating such wealth of additonal domain information on protein networks has wide applications and would impact functional analysis and characterization of novel proteins.
Advisers: Stephen D. Scott and Etsuko N. Moriyam
Complex information networks – detecting community structure in bipartite networks
The last decade has witnessed great expansion in research and study of complex networks. A complex network is a large-scale network that reflects the interactions between objects or components of complicated systems. These components, known as clusters, communities or modules, perform together in order to provide one or more functions of the system. A vast number of systems, from the brain to ecosystems, power grids and the Internet, criminal relationships and financial transactions, can all be described as large complex networks. For most complex networks, the complexity arises from the fact that the structure is highly irregular, complex and dynamically evolving in time; and that the observed patterns of interactions highly influence the behaviour of the entire system. One of the topological properties that can expose the hierarchical structure of complex networks is community structure. Community detection is a common problem in complex networks that consists in general of finding groups of densely connected nodes with few connections to nodes outside of a group. The lack of consensus on a definition for a community leads to extensive studies on community structure of complex networks in order to provide improved community detection methods. Community structure is a common and important topological characteristic of many real world complex networks. In particular, identifying communities in bipartite networks is an important task in many scientific domains. In a bipartite network, the node set consists of two disjoint sets of nodes, primary set (P) and secondary set (S), such that links between nodes may occur only if the nodes belong to different sets. There are really two approaches to identifying clusters in a bipartite network: the first, and more common, is when our real interest is in community structure within the primary node set P; and the second is when our real interest is in bipartite communities within the whole network. Thus, in this research we investigate and study the state-of-the-art of community detection algorithms, in particular, those to identify the communities in bipartite networks in order to provide us with a more complete understanding of the relationship between communities. The practical aim is to derive a coarse-grain description of the network topology that will aid understanding of its hierarchical structure. The research of the thesis consists of four main phases. First, one of the best algorithms for community detection in classical networks, Infomap, has not been adapted to the big and important class of bipartite networks. This research gap is one focus of the thesis. We integrate the weighted projection method for bipartite networks based on common neighbors similarity into Infomap, to acquire a weighted one mode network that can be clustered by this random walks technique. We apply this method to a number of real world bipartite networks, to detect significant community structure. We measure the performance of our approach based on the ground truth. This requires deep knowledge of the formation of relations within and between clusters in these real world networks. Although such investigation is excessively time consuming, and impractical or impossible in large networks, the result is much more accurate and more meaningful and gives us confidence that this method can be usefully applied to large networks where ground truth is not known. Second, several possible edge additions are conducted to test how random walks based algorithm, Infomap, performs when the minimal modification is made to convert a bipartite network to a nearly bipartite (but unipartite) network. The experiments on small bipartite networks obtain encouraging results. Third, we shift focus from community detection based on random walks to community detection based on the strongest communities possible in a bipartite network, which are bicliques. We develop a novel algorithm to identify overlapping communities at the base level of hierarchy in bipartite networks. We combine existing techniques (bicliques, cliques, structural equivalence) into a novel method to solve this new research problem. We classify the output communities into 5 categories based on community strength. From this base level, we apply the Jaccard index as a threshold in order to reduce the redundancy of overlapping communities, to obtain higher levels of the hierarchy. We compare results from our overlapping approach with other concurrent approaches not only directly to the ground truth, but also using a widely accepted scale for evaluating the quality of partitions, Normalized Mutual Information (NMI). In the last phase of the thesis, a large financial bipartite network collected during 6 months fieldwork is analysed and tested in order to reveal its hierarchical structure. We apply all methods presented in Chapter 3, Chapter 4 and Chapter 5. The main contribution of this thesis is an improved method to detect the hierarchical and overlapping community structure in bipartite complex networks based on structural equivalence of nodes. More generally, it aims to derive a coarse-grain depiction of real large-scale networks through structural properties of their identified communities as well as their performance with respect to the known ground truth
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