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Finding Endogenously Formed Communities  [PDF]
Maria-Florina Balcan,Christian Borgs,Mark Braverman,Jennifer Chayes,Shang-Hua Teng
Computer Science , 2012,
Abstract: A central problem in e-commerce is determining overlapping communities among individuals or objects in the absence of external identification or tagging. We address this problem by introducing a framework that captures the notion of communities or clusters determined by the relative affinities among their members. To this end we define what we call an affinity system, which is a set of elements, each with a vector characterizing its preference for all other elements in the set. We define a natural notion of (potentially overlapping) communities in an affinity system, in which the members of a given community collectively prefer each other to anyone else outside the community. Thus these communities are endogenously formed in the affinity system and are "self-determined" or "self-certified" by its members. We provide a tight polynomial bound on the number of self-determined communities as a function of the robustness of the community. We present a polynomial-time algorithm for enumerating these communities. Moreover, we obtain a local algorithm with a strong stochastic performance guarantee that can find a community in time nearly linear in the of size the community. Social networks fit particularly naturally within the affinity system framework -- if we can appropriately extract the affinities from the relatively sparse yet rich information from social networks, our analysis then yields a set of efficient algorithms for enumerating self-determined communities in social networks. In the context of social networks we also connect our analysis with results about $(\alpha,\beta)$-clusters introduced by Mishra, Schreiber, Stanton, and Tarjan \cite{msst}. In contrast with the polynomial bound we prove on the number of communities in the affinity system model, we show that there exists a family of networks with superpolynomial number of $(\alpha,\beta)$-clusters.
Finding communities in sparse networks  [PDF]
Abhinav Singh,Mark Humphries
Computer Science , 2015, DOI: 10.1038/srep08828
Abstract: Spectral algorithms based on matrix representations of networks are often used to detect communities but classic spectral methods based on the adjacency matrix and its variants fail to detect communities in sparse networks. New spectral methods based on non-backtracking random walks have recently been introduced that successfully detect communities in many sparse networks. However, the spectrum of non-backtracking random walks ignores hanging trees in networks that can contain information about the community structure of networks. We introduce the reluctant backtracking operators that explicitly account for hanging trees as they admit a small probability of returning to the immediately previous node unlike the non-backtracking operators that forbid an immediate return. We show that the reluctant backtracking operators can detect communities in certain sparse networks where the non-backtracking operators cannot while performing comparably on benchmark stochastic block model networks and real world networks. We also show that the spectrum of the reluctant backtracking operator approximately optimises the standard modularity function similar to the flow matrix. Interestingly, for this family of non- and reluctant-backtracking operators the main determinant of performance on real-world networks is whether or not they are normalised to conserve probability at each node.
Finding flavor genes
Philippe Reymond
Genome Biology , 2000, DOI: 10.1186/gb-2000-1-2-reports0057
Abstract: Aharoni et al. randomly isolated 1,701 cDNA clones from a strawberry fruit cDNA library and 480 clones from petunia corolla (as control) and printed the PCR-amplified clones on chemically modified glass slides using a robotic device. They used these microarrays to monitor changes in gene expression at three fruit developmental stages (from green to red). Using a rigorous statistical analysis, the authors found that 401 clones were differentially expressed between all three stages, with 177 clones being upregulated between the green and red stages. Sequences of the latter group of genes revealed that more than 50% were related to primary and secondary metabolism. From the other sequences potentially involved in flavor formation, Aharoni et al. identified a novel gene (SAAT) for an alcohol acetyltransferase, an enzyme that catalyzes the final step in the synthesis of volatile esters. This gene shows 16-fold greater expression during the red stage than the green stage of fruit development. The authors expressed recombinant SAAT in Escherichia coli and confirmed that the enzyme has alcohol acetyltransferase activity. Analysis of a series of potential substrates suggests that SAAT is responsible for formation of the predominant esters found in ripe strawberries.Access to Arabidopsis cDNA microarrays is provided by the Arabidopsis Functional Genomics Consortium (AFGC). Links to information on plant microarrays can also be found via the Virtual library: plant-arrays.Large-scale cDNA microarrays are now used with model systems to investigate global patterns of gene expression at the level of the whole organism. The utility of microarrays that cover a restricted portion of the genome, like that described in this paper, will become increasingly recognized, however. This paper is a first example of the use of customized plant cDNA microarrays from a non-model system. It provides a good example of how a small selected array can be used to study a particular developmental proces
LinkRank: Finding communities in directed networks  [PDF]
Youngdo Kim,Seung-Woo Son,Hawoong Jeong
Physics , 2009, DOI: 10.1103/PhysRevE.81.016103
Abstract: To identify communities in directed networks, we propose a generalized form of modularity in directed networks by introducing a new quantity LinkRank, which can be considered as the PageRank of links. This generalization is consistent with the original modularity in undirected networks and the modularity optimization methods developed for undirected networks can be directly applied to directed networks by optimizing our new modularity. Also, a model network, which can be used as a benchmark network in further community studies, is proposed to verify our method. Our method is supposed to find communities effectively in citation- or reference-based directed networks.
Finding compact communities in large graphs  [PDF]
J. Creusefond,T. Largillier,S. Peyronnet
Computer Science , 2014,
Abstract: This article presents an efficient hierarchical clustering algorithm that solves the problem of core community detection. It is a variant of the standard community detection problem in which we are particularly interested in the connected core of communities. To provide a solution to this problem, we question standard definitions on communities and provide alternatives. We also propose a function called compactness, designed to assess the quality of a solution to this problem. Our algorithm is based on a graph traversal algorithm, the LexDFS. The time complexity of our method is in $O(n\times log(n))$. Experiments show that our algorithm creates highly compact clusters.
Finding local communities in protein networks
Konstantin Voevodski, Shang-Hua Teng, Yu Xia
BMC Bioinformatics , 2009, DOI: 10.1186/1471-2105-10-297
Abstract: We develop a tool, named Local Protein Community Finder, which quickly finds a community close to a queried protein in any network available from BioGRID or specified by the user. Our tool uses two new local clustering algorithms Nibble and PageRank-Nibble, which look for a good cluster among the most popular destinations of a short random walk from the queried vertex. The quality of a cluster is determined by proportion of outgoing edges, known as conductance, which is a relative measure particularly useful in undersampled networks. We show that the two local clustering algorithms find communities that not only form excellent clusters, but are also likely to be biologically relevant functional components. We compare the performance of Nibble and PageRank-Nibble to other popular and effective graph partitioning algorithms, and show that they find better clusters in the graph. Moreover, Nibble and PageRank-Nibble find communities that are more functionally coherent.The Local Protein Community Finder, accessible at http://xialab.bu.edu/resources/lpcf webcite, allows the user to quickly find a high-quality community close to a queried protein in any network available from BioGRID or specified by the user. We show that the communities found by our tool form good clusters and are functionally coherent, making our application useful for biologists who wish to investigate functional modules that a particular protein is a part of.Using the link structure of a network to gain insight into the function of its nodes is a ubiquitous technique in biological, social, and computer networks [1-11]. For example, Kleinberg used the link structure of the Internet to give each node a hub and an authority index [9], and Brin and Page utilized the structure of the Web, rather than its content, to rank Web pages [10,11]. Of particular interest is the identification of network communities, also in the context of the Internet [6-8], and social and biological networks [1-5]. Communities are
Finding mesoscopic communities in sparse networks  [PDF]
I. Ispolatov,I. Mazo,A. Yuryev
Quantitative Biology , 2005, DOI: 10.1088/1742-5468/2006/09/P09014
Abstract: We suggest a fast method to find possibly overlapping network communities of a desired size and link density. Our method is a natural generalization of the finite-$T$ superparamegnetic Potts clustering introduced by Blatt, Wiseman, and Domany (Phys. Rev. Lett. v.76, 3251 (1996) and the recently suggested by Reichard and Bornholdt (Phys. Rev. Lett. v.93, 21870 (2004)) annealing of Potts model with global antiferromagnetic term. Similarly to both preceding works, the proposed generalization is based on ordering of ferromagnetic Potts model; the novelty of the proposed approach lies in the adjustable dependence of the antiferromagnetic term on the population of each Potts state, which interpolates between the two previously considered cases. This adjustability allows to empirically tune the algorithm to detect the maximum number of communities of the given size and link density. We illustrate the method by detecting protein complexes in high-throughput protein binding networks.
Finding Statistically Significant Communities in Networks  [PDF]
Andrea Lancichinetti,Filippo Radicchi,José J. Ramasco,Santo Fortunato
PLOS ONE , 2012, DOI: 10.1371/journal.pone.0018961
Abstract: Community structure is one of the main structural features of networks, revealing both their internal organization and the similarity of their elementary units. Despite the large variety of methods proposed to detect communities in graphs, there is a big need for multi-purpose techniques, able to handle different types of datasets and the subtleties of community structure. In this paper we present OSLOM (Order Statistics Local Optimization Method), the first method capable to detect clusters in networks accounting for edge directions, edge weights, overlapping communities, hierarchies and community dynamics. It is based on the local optimization of a fitness function expressing the statistical significance of clusters with respect to random fluctuations, which is estimated with tools of Extreme and Order Statistics. OSLOM can be used alone or as a refinement procedure of partitions/covers delivered by other techniques. We have also implemented sequential algorithms combining OSLOM with other fast techniques, so that the community structure of very large networks can be uncovered. Our method has a comparable performance as the best existing algorithms on artificial benchmark graphs. Several applications on real networks are shown as well. OSLOM is implemented in a freely available software (http://www.oslom.org), and we believe it will be a valuable tool in the analysis of networks.
Finding overlapping communities in networks by label propagation  [PDF]
Steve Gregory
Computer Science , 2009, DOI: 10.1088/1367-2630/12/10/103018
Abstract: We propose an algorithm for finding overlapping community structure in very large networks. The algorithm is based on the label propagation technique of Raghavan, Albert, and Kumara, but is able to detect communities that overlap. Like the original algorithm, vertices have labels that propagate between neighbouring vertices so that members of a community reach a consensus on their community membership. Our main contribution is to extend the label and propagation step to include information about more than one community: each vertex can now belong to up to v communities, where v is the parameter of the algorithm. Our algorithm can also handle weighted and bipartite networks. Tests on an independently designed set of benchmarks, and on real networks, show the algorithm to be highly effective in recovering overlapping communities. It is also very fast and can process very large and dense networks in a short time.
Finding and Testing Network Communities by Lumped Markov Chains  [PDF]
Carlo Piccardi
PLOS ONE , 2011, DOI: 10.1371/journal.pone.0027028
Abstract: Identifying communities (or clusters), namely groups of nodes with comparatively strong internal connectivity, is a fundamental task for deeply understanding the structure and function of a network. Yet, there is a lack of formal criteria for defining communities and for testing their significance. We propose a sharp definition that is based on a quality threshold. By means of a lumped Markov chain model of a random walker, a quality measure called “persistence probability” is associated to a cluster, which is then defined as an “-community” if such a probability is not smaller than . Consistently, a partition composed of -communities is an “-partition.” These definitions turn out to be very effective for finding and testing communities. If a set of candidate partitions is available, setting the desired -level allows one to immediately select the -partition with the finest decomposition. Simultaneously, the persistence probabilities quantify the quality of each single community. Given its ability in individually assessing each single cluster, this approach can also disclose single well-defined communities even in networks that overall do not possess a definite clusterized structure.
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