Identification Of Subgraphs Research Articles

FSM-BC-BSP: Frequent Subgraph Mining Algorithm Based on BC-BSP

As graph models become increasingly prevalent in the processing of scientific data, the exploration of effective methods for the mining of meaningful patterns from large-scale graphs has garnered significant research attention. This paper delves into the complexity of frequent subgraph mining and proposes a frequent subgraph mining (FSM) algorithm. This FSM algorithm is developed within a distributed graph iterative system, designed for the Big Cloud (BC) environment of the China Mobile Corp., and is based on the bulk synchronous parallel (BSP) model, named FSM-BC-BSP. Its aim is to address the challenge of mining frequent subgraphs within a single, large graph. This study advocates for the incorporation of a message sending and receiving mechanism to facilitate data sharing across various stages of the frequent subgraph mining algorithm. Additionally, it suggests employing a standard coded subgraph and sending it to the same node for global support calculation on the large graph. The adoption of the rightmost path expansion strategy in generating candidate subgraphs helps to mitigate the occurrence of redundant subgraphs. The use of standard coding ensures the unique identification of subgraphs, thus eliminating the need for isomorphism calculations. Support calculation is executed using the Minimum Image (MNI) measurement method, aligning with the downward closure attribute. The experimental results demonstrate the robust performance of the FSM-BC-BSP algorithm across diverse input datasets and parameter configurations. Notably, the algorithm exhibits exceptional efficacy, particularly in scenarios with low support requirements, showcasing its superior performance under such conditions.

Unextendible Sets of Mutually Unbiased Basis Obtained from Complete Subgraphs

We propose a method, based on the search and identification of complete subgraphs of a regular graph, to obtain sets of Pauli operators whose eigenstates form unextendible complete sets of mutually unbiased bases of n-qubit systems. With this method we can obtain results for complete and inextensible sets of mubs for 2, 3, 4 and 5 qubits.

Community-based network analyses reveal emerging connectivity patterns of protein-protein interactions in murine melanoma secretome

Protein-protein interaction networks (PPINs) are static representations of protein connections in which topological features such as subgraphs (communities) may contain proteins functionally related, revealing an additional layer of interactome complexity. We created two PPINs from the secretomes of a paired set of murine melanocytes (a normal melanocyte and its transformed phenotype). Community structures, identified by a graph clustering algorithm, resulted in the identification of subgraphs in both networks. Interestingly, the underlying structure of such communities revealed shared and exclusive proteins (core and exclusive nodes, respectively), in addition to proteins that changed their location within each community (rewired nodes). Functional enrichment analysis of core nodes revealed conserved biological functions in both networks whereas exclusive and rewired nodes in the tumoral phenotype network were enriched in cancer-related processes, including TGFβ signaling. We found a remarkable shift in the tumoral interactome, resulting in an emerging pattern which was driven by the presence of exclusive nodes and may represent functional network motifs. Our findings suggest that the rearrangement in the tumoral interactome may be correlated with the malignant transformation of melanocytes associated with substrate adhesion impediment. The interactions found in core and new/rewired nodes might potentially be targeted for therapeutic intervention in melanoma treatment. SignificanceMalignant transformation is a result of synergistic action of multiple molecular factors in which genetic alterations as well as protein expression play paramount roles. During oncogenesis, cellular crosstalk through the secretion of soluble mediators modulates the phenotype of transformed cells which ultimately enables them to successfully disrupt important signaling pathways, including those related to cell growth and proliferation. Therefore, in this work we profiled the secretomes of a paired set of normal and transformed phenotypes of a murine melanocyte. After assembling the two interactomes, clusters of functionally related proteins (network communities) were observed as well as emerging patterns of network rewiring which may represent an interactome signature of transformed cells. In summary, the significance of this study relies on the understanding of the repertoire of ‘normal’ and ‘tumoral’ secretomes and, more importantly, the set of interacting proteins (the interactome) in both of these conditions, which may reveal key components that might be potentially targeted for therapeutic intervention.

Genetic Algorithms for Finding Episodes in Temporal Networks

The evolution of networks is a fundamental topic in network analysis and mining. One of the approaches that has been recently considered in this field is the analysis of temporal networks, where relations between elements can change over time. A relevant problem in the analysis of temporal networks is the identification of cohesive or dense subgraphs since they are related to communities. In this contribution, we present a method based on genetic algorithms and on a greedy heuristic to identify dense subgraphs in a temporal network. We present experimental results considering both synthetic and real-networks, and we analyze the performance of the proposed method when varying the size of the population and the number of generations. The experimental results show that our heuristic generally performs better in terms of quality of the solutions than the state-of-art method for this problem. On the other hand, the state-of-art method is faster, although comparable with our method, when the size of the population and the number of generations are limited to small values.

Eigenvector-based identification of bipartite subgraphs

We report our experiments on identifying large bipartite subgraphs of simple connected graphs which are based on the sign pattern of eigenvectors belonging to the extremal eigenvalues of different graph matrices: adjacency, signless Laplacian, Laplacian, and normalized Laplacian matrix. We compare these methods to a ‘local switching’ algorithm based on the proof of the Erdös’ bound that each graph contains a bipartite subgraph with at least half of its edges. Experiments with one scale-free and three random graph models, which cover a wide range of real-world networks, show that the methods based on the eigenvectors of the normalized Laplacian and the adjacency matrix, while yielding comparable results to the local switching algorithm, are still outperformed by it. We also formulate two edge bipartivity indices based on the former eigenvectors, and observe that the method of iterative removal of edges with maximum bipartivity index until one obtains a bipartite subgraph, also yields comparable results to the local switching algorithm.

A method for identification of highly conserved elements and evolutionary analysis of superphylum Alveolata.

BackgroundPerfectly or highly conserved DNA elements were found in vertebrates, invertebrates, and plants by various methods. However, little is known about such elements in protists. The evolutionary distance between apicomplexans can be very high, in particular, due to the positive selection pressure on them. This complicates the identification of highly conserved elements in alveolates, which is overcome by the proposed algorithm.ResultsA novel algorithm is developed to identify highly conserved DNA elements. It is based on the identification of dense subgraphs in a specially built multipartite graph (whose parts correspond to genomes). Specifically, the algorithm does not rely on genome alignments, nor pre-identified perfectly conserved elements; instead, it performs a fast search for pairs of words (in different genomes) of maximum length with the difference below the specified edit distance. Such pair defines an edge whose weight equals the maximum (or total) length of words assigned to its ends. The graph composed of these edges is then compacted by merging some of its edges and vertices. The dense subgraphs are identified by a cellular automaton-like algorithm; each subgraph defines a cluster composed of similar inextensible words from different genomes. Almost all clusters are considered as predicted highly conserved elements. The algorithm is applied to the nuclear genomes of the superphylum Alveolata, and the corresponding phylogenetic tree is built and discussed.ConclusionWe proposed an algorithm for the identification of highly conserved elements. The multitude of identified elements was used to infer the phylogeny of Alveolata.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-016-1257-5) contains supplementary material, which is available to authorized users.

Algorithmic aspects of graph reduction for hardware/software partitioning

The hardware/software (HW/SW) partitioning is a major concern in heterogeneous multi-processor system-on-a-chip design, where the large design space prohibits rapid identification of optimal HW/SW solutions to meet tight time-to-market constraints. In this paper, we propose graph reduction techniques to reduce the design space for HW/SW partitioning without sacrificing the partition quality. There are two major phases in the proposed approach: reducible sub-graph searching and sub-graph evaluation and reduction. In the former phase, we design a dynamic programming-based algorithm, named path flow algorithm (PFA), to identify reducible sub-graph candidates for directed acyclic graph (DAG) as most previous works use DAG as task graph model. We also propose algorithm DeLoop to transform an arbitrary directed graph into a DAG such that all reducible sub-graphs on the original graph can be detected by performing algorithm PFA on the DAG. Our approach overcomes the limitation of the existing approach by enabling the identification of candidate sub-graphs in arbitrary task graphs. In latter phase, we propose a reduction model which enables accurate estimation of task execution time on hardware and design a method to select candidate sub-graphs for reduction. Experimental results demonstrate that the proposed methods not only reduce the design space, but also notably improve the partitioning quality since hardware-parallel execution of tasks is taken into account in the proposed sub-graph reduction model.

A survey of frequent subgraph mining algorithms

AbstractGraph mining is an important research area within the domain of data mining. The field of study concentrates on the identification of frequent subgraphs within graph data sets. The research goals are directed at: (i) effective mechanisms for generating candidate subgraphs (without generating duplicates) and (ii) how best to process the generated candidate subgraphs so as to identify the desired frequent subgraphs in a way that is computationally efficient and procedurally effective. This paper presents a survey of current research in the field of frequent subgraph mining and proposes solutions to address the main research issues.

More power via graph-structured tests for differential expression of gene networks

We consider multivariate two-sample tests of means, where the location shift between the two populations is expected to be related to a known graph structure. An important application of such tests is the detection of differentially expressed genes between two patient populations, as shifts in expression levels are expected to be coherent with the structure of graphs reflecting gene properties such as biological process, molecular function, regulation or metabolism. For a fixed graph of interest, we demonstrate that accounting for graph structure can yield more powerful tests under the assumption of smooth distribution shift on the graph. We also investigate the identification of nonhomogeneous subgraphs of a given large graph, which poses both computational and multiple hypothesis testing problems. The relevance and benefits of the proposed approach are illustrated on synthetic data and on breast and bladder cancer gene expression data analyzed in the context of KEGG and NCI pathways.

Bounding bubbles: The vertex representation of 3d group field theory and the suppression of pseudomanifolds

Based on recent work on simplicial diffeomorphisms in colored group field theories, we develop a representation of the colored Boulatov model, in which the group field theory (GFT) fields depend on variables associated to vertices of the associated simplicial complex, as opposed to edges. On top of simplifying the action of diffeomorphisms, the main advantage of this representation is that the GFT Feynman graphs have a different stranded structure, which allows a direct identification of subgraphs associated to bubbles, and their evaluation is simplified drastically. As a first important application of this formulation, we derive new scaling bounds for the regularized amplitudes, organized in terms of the genera of the bubbles, and show how the pseudomanifold configurations appearing in the perturbative expansion are suppressed as compared to manifolds. Moreover, these bounds are proved to be optimal.

Predicting protein complexes by data integration of different types of interactions

The explosion of high throughput interaction data from proteomics studies gives us the opportunity to integrate Protein-Protein Interactions (PPI) from different type of interactions. These methods rely on the assumption that proteins within a complex have more interactions across the different data sets which translate into the identification of dense subgraphs. However, the relative importance of the types of interaction are not equivalent in their reliability and accuracy consequently they should be analysed separately. Here we propose a method that use graph theory and mathematical modelling to solve this problem. Our approach has four steps that: i) score independently each type of interaction; ii) build an interaction specific networks for each type; iii) weight the specific networks; and iv) combine and normalise the scores. Using this approach to the BRCA1 Associated genome Surveillance Complex (BASC), we correctly identified the known core components of the complex and subcomplexes that have solved structures as well as predicted new interactions and core complexes. The method presented in this study is of general use. It is flexible enough to allow the development of any scoring system and can be applied to any protein complex to provide the latest knowledge in its interactions and structure.

A dependency graph approach for the analysis of differential gene expression profiles

A central aim of differential gene expression profile analysis is to provide an interpretation of given data at the level of biological processes and pathways. However, traversing descriptive data into context is not straightforward. We present a gene-centric dependency graph approach supporting an interpretation of omics profiles at the level of affected networks. The core of our dependency graph comprises data objects encoding the functional categorization of a particular gene, its tissue-specific reference gene expression, as well as known interactions and subcellular location of assigned proteins. On the basis of these genome, transcriptome, and proteome data we compute pair-wise object (gene) dependencies and interpret them as weighted edges in a dependency graph. Mapping of omics profiles on this graph can be used to identify connectors linking features of the omics list, in turn providing the basis for identification of subgraphs and motifs characterizing the cellular state under analysis. We exemplify this approach by analyzing differential gene expression data characterizing B-cell lymphoma and demonstrate the identification of B-cell lymphoma associated subgraphs.

Graph-Based Molecular Alignment (GMA)

We describe a combined 2D/3D approach for the superposition of flexible chemical structures, which is based on recent progress in the efficient identification of common subgraphs and a gradient-based torsion space optimization algorithm. The simplicity of the approach is reflected in its generality and computational efficiency: the suggested approach neither requires precalculated statistics on the conformations of the molecules nor does it make simplifying assumptions on the topology of the molecules being compared. Furthermore, graph-based molecular alignment produces alignments that are consistent with the chemistry of the molecules as well as their general structure, as it depends on both the local connectivities between atoms and the overall topology of the molecules. We validate this approach on benchmark sets taken from the literature and show that it leads to good results compared to computationally and algorithmically more involved methods. The results suggest that, for most practical purposes, graph-based molecular alignment is a viable alternative to molecular field alignment with respect to structural superposition and leads to structures of comparable quality in a fraction of the time.

Maximum diversity/similarity models with extension to part grouping

AbstractMaximum diversity/similarity models involve selecting a subset of desired size from a given pool of objects such that some measure of diversity or similarity among the selected objects is maximized. Such models have found application, among other places, in the formation of various groups, the location of obnoxious facilities and the identification of dense subgraphs. We present a mild generalization, which yields a stronger and more practical formulation and is seen to be solved effectively. As an extension, we consider the part‐grouping problem as encountered in manufacturing cell formation. We show how the enhanced diversity/similarity model can be used to form part families in a way that is both flexible and competitive with existing approaches. We provide an illustrative example and limited computational results.

Lagrangian solution of maximum dispersion problems

We address the so-called maximum dispersion problems where the objective is to maximize thesumor theminimumof interelement distances amongst a subset chosen from a given set. The problems arise in a variety of contexts including the location of obnoxious facilities, the selection of diverse groups, and the identification of dense subgraphs. They are known to be computationally difficult. In this paper, we propose a Lagrangian approach toward their solution and report the results of an extensive computational experimentation. Our results show that our Lagrangian approach is reasonably fast, that it yields heuristic solutions which provide good lower bounds on the optimum solution values for both the sum and the minimum problems, and further that it produces decent upper bounds in the case of the sum problem. For the sum problem, the results also show that the Lagrangian heuristic compares favorably against several existing heuristics. c 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 97{114, 2000