Detecting highly overlapping community structure by greedy clique expansion

In complex networks it is common for each node to belong to several communities, implying a highly overlapping community structure. Recent advances in benchmarking indicate that existing community assignment algorithms that are capable of detecting overlapping communities perform well only when the extent of community overlap is kept to modest levels. To overcome this limitation, we introduce a new community assignment algorithm called Greedy Clique Expansion (GCE). The algorithm identifies distinct cliques as seeds and expands these seeds by greedily optimizing a local fitness function. We perform extensive benchmarks on synthetic data to demonstrate that GCE's good performance is robust across diverse graph topologies. Significantly, GCE is the only algorithm to perform well on these synthetic graphs, in which every node belongs to multiple communities. Furthermore, when put to the task of identifying functional modules in protein interaction data, and college dorm assignments in Facebook friendship data, we find that GCE performs competitively.Comment: 10 pages, 7 Figures. Implementation source and binaries available at http://sites.google.com/site/greedycliqueexpansion

A Tutorial on Clique Problems in Communications and Signal Processing

Since its first use by Euler on the problem of the seven bridges of K\"onigsberg, graph theory has shown excellent abilities in solving and unveiling the properties of multiple discrete optimization problems. The study of the structure of some integer programs reveals equivalence with graph theory problems making a large body of the literature readily available for solving and characterizing the complexity of these problems. This tutorial presents a framework for utilizing a particular graph theory problem, known as the clique problem, for solving communications and signal processing problems. In particular, the paper aims to illustrate the structural properties of integer programs that can be formulated as clique problems through multiple examples in communications and signal processing. To that end, the first part of the tutorial provides various optimal and heuristic solutions for the maximum clique, maximum weight clique, and $k$-clique problems. The tutorial, further, illustrates the use of the clique formulation through numerous contemporary examples in communications and signal processing, mainly in maximum access for non-orthogonal multiple access networks, throughput maximization using index and instantly decodable network coding, collision-free radio frequency identification networks, and resource allocation in cloud-radio access networks. Finally, the tutorial sheds light on the recent advances of such applications, and provides technical insights on ways of dealing with mixed discrete-continuous optimization problems

Mining Novel Multivariate Relationships in Time Series Data Using Correlation Networks

In many domains, there is significant interest in capturing novel relationships between time series that represent activities recorded at different nodes of a highly complex system. In this paper, we introduce multipoles, a novel class of linear relationships between more than two time series. A multipole is a set of time series that have strong linear dependence among themselves, with the requirement that each time series makes a significant contribution to the linear dependence. We demonstrate that most interesting multipoles can be identified as cliques of negative correlations in a correlation network. Such cliques are typically rare in a real-world correlation network, which allows us to find almost all multipoles efficiently using a clique-enumeration approach. Using our proposed framework, we demonstrate the utility of multipoles in discovering new physical phenomena in two scientific domains: climate science and neuroscience. In particular, we discovered several multipole relationships that are reproducible in multiple other independent datasets and lead to novel domain insights.Comment: This is the accepted version of article submitted to IEEE Transactions on Knowledge and Data Engineering 201

JGraphT -- A Java library for graph data structures and algorithms

Mathematical software and graph-theoretical algorithmic packages to efficiently model, analyze and query graphs are crucial in an era where large-scale spatial, societal and economic network data are abundantly available. One such package is JGraphT, a programming library which contains very efficient and generic graph data-structures along with a large collection of state-of-the-art algorithms. The library is written in Java with stability, interoperability and performance in mind. A distinctive feature of this library is the ability to model vertices and edges as arbitrary objects, thereby permitting natural representations of many common networks including transportation, social and biological networks. Besides classic graph algorithms such as shortest-paths and spanning-tree algorithms, the library contains numerous advanced algorithms: graph and subgraph isomorphism; matching and flow problems; approximation algorithms for NP-hard problems such as independent set and TSP; and several more exotic algorithms such as Berge graph detection. Due to its versatility and generic design, JGraphT is currently used in large-scale commercial, non-commercial and academic research projects. In this work we describe in detail the design and underlying structure of the library, and discuss its most important features and algorithms. A computational study is conducted to evaluate the performance of JGraphT versus a number of similar libraries. Experiments on a large number of graphs over a variety of popular algorithms show that JGraphT is highly competitive with other established libraries such as NetworkX or the BGL.Comment: Major Revisio

Semantic Similarity of Spatial Scenes

The formalization of similarity in spatial information systems can unleash their functionality and contribute technology not only useful, but also desirable by broad groups of users. As a paradigm for information retrieval, similarity supersedes tedious querying techniques and unveils novel ways for user-system interaction by naturally supporting modalities such as speech and sketching. As a tool within the scope of a broader objective, it can facilitate such diverse tasks as data integration, landmark determination, and prediction making. This potential motivated the development of several similarity models within the geospatial and computer science communities. Despite the merit of these studies, their cognitive plausibility can be limited due to neglect of well-established psychological principles about properties and behaviors of similarity. Moreover, such approaches are typically guided by experience, intuition, and observation, thereby often relying on more narrow perspectives or restrictive assumptions that produce inflexible and incompatible measures. This thesis consolidates such fragmentary efforts and integrates them along with novel formalisms into a scalable, comprehensive, and cognitively-sensitive framework for similarity queries in spatial information systems. Three conceptually different similarity queries at the levels of attributes, objects, and scenes are distinguished. An analysis of the relationship between similarity and change provides a unifying basis for the approach and a theoretical foundation for measures satisfying important similarity properties such as asymmetry and context dependence. The classification of attributes into categories with common structural and cognitive characteristics drives the implementation of a small core of generic functions, able to perform any type of attribute value assessment. Appropriate techniques combine such atomic assessments to compute similarities at the object level and to handle more complex inquiries with multiple constraints. These techniques, along with a solid graph-theoretical methodology adapted to the particularities of the geospatial domain, provide the foundation for reasoning about scene similarity queries. Provisions are made so that all methods comply with major psychological findings about people’s perceptions of similarity. An experimental evaluation supplies the main result of this thesis, which separates psychological findings with a major impact on the results from those that can be safely incorporated into the framework through computationally simpler alternatives

Overlapping Community Discovery Methods: A Survey

The detection of overlapping communities is a challenging problem which is gaining increasing interest in recent years because of the natural attitude of individuals, observed in real-world networks, to participate in multiple groups at the same time. This review gives a description of the main proposals in the field. Besides the methods designed for static networks, some new approaches that deal with the detection of overlapping communities in networks that change over time, are described. Methods are classified with respect to the underlying principles guiding them to obtain a network division in groups sharing part of their nodes. For each of them we also report, when available, computational complexity and web site address from which it is possible to download the software implementing the method.Comment: 20 pages, Book Chapter, appears as Social networks: Analysis and Case Studies, A. Gunduz-Oguducu and A. S. Etaner-Uyar eds, Lecture Notes in Social Networks, pp. 105-125, Springer,201