InOvIn: A fuzzy-rough approach for detecting overlapping communities with intrinsic structures in evolving networks
Introduction
Rapid changes are occurring among the entities in any complex system due to the change in subjects of interest and relationship. As a outcome, the networks based on those entities are also evolving. Genetic networks, brain networks, protein interaction networks, and social networks are some of the striking examples of evolving networks. Like other networks, social network is also mapped as a graph, where objects (users) are represented as a set of vertices and the interaction between objects are represented as edges. Nodes with similar characteristics or functions usually brought together to single unit (sub-graph), termed as network communities or modules. Nodes in a community usually exhibit high intra-community connectivity and less inter-community connectivity.
In an evolving network, a community may pass through several phases of transformation over time. Due to frequent changes in the associations or choice of interests, an actor or a user (client) may develop an affinity towards different interest groups. It may leads to shared participation of a user in more than one group, simultaneously. Communities that share common members across different communities are frequently termed as overlapping communities. The spontaneous growth of the network and relationships among the nodes may create a trend of forming more compact sub-community within a community, which we termed it as intrinsic communities (also termed as embedded communities). The intrinsic community may exhibit varying intra-community connectivity (high or low) differing from the parent community it belongs to. Formation of intrinsic communities is more common in genetic networks [1], protein–protein interactions [2], [3], [4] and metabolic networks [5], [6], [7]. The being of such communities is also reported even in social networks [8], [9].
For the last few decades, efforts are on for effective community detection in both static and dynamic networks. Most of the study concentrates on finding disjoint (or non-overlapping) communities with an assumption that a node may exclusively be the member of one community only and networks are not altered over time. Very few attempts have been made in detecting overlapping [10], [11] and intrinsic communities [12], [13] in dynamic or evolving networks [14], [15]. However, they do not direct all three issues simultaneously. There is a need for a community detection method that can offer an integrated solution for the detection of overlapping as well as intrinsic communities in evolving networks. Traditional approaches are not effective in overlapping community detection when relationships are imprecise. Soft computing paradigm is an effective option to handle imprecise and uncertain scenarios. In this study, we address the issue of detecting overlapping communities in evolving networks with the help of fuzzy-rough clustering approach. The concept of community density variation has been applied to detect any possible existence of intrinsic communities. The contributions of our work are listed below.
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We propose an integrated overlapping and intrinsic community detection method in evolving networks. A fuzzy membership function is proposed to handle the imprecise affinity of a node towards a community which varies over time.
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Concept of rough boundaries, derived from the rough set is applied to identify the non-overlapping and overlapping nodes within multiple communities.
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Node degree density variations within a community are considered to detect the formation of intrinsic communities over time.
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Due to unavailability of appropriate benchmark networks with overlapping and intrinsic communities, we synthetically generate networks with both overlapping and intrinsic structures.
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The superiority of InOvIn over contemporary community detection methods is established using ten (10) different statistical assessment parameters for twelve (12) real-world benchmark social networks and six (6) synthetically generated networks.
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Proposed method able to detect the existence of intrinsic communities in PolBooks and Word Adjacencies networks for the first time.
The rest of the paper is organized as follow. In Sections 2 Background, 3 Prior research, we formally introduce the background of the problem and present different prior attempts on handling overlapping and intrinsic communities in evolving networks. In Section 4, proposed method has been discussed. Performance evaluation of the proposed method is reported in Section 5. Eventually, in Section 6 the paper is summarized with concluding remarks.
Section snippets
Background
Graph-theoretic formalism is the most common way of representing a social network. A network community is a cluster [16] or cohesive subgraph with significant intra-community connectivity among the nodes of a community than nodes of other communities in the network. Formally, it may be defined as follows.
Definition 2.1 Network Community Assume network , where and represent a set of nodes and edges respectively. A community
( and ) can be defined as a sub-graph of , where membership score (based
Prior research
Most of the prior work given attention more on detecting overlapping and non-overlapping communities. Some of them even handle dynamic network scenarios. We discuss here different community detection methods based on their working principles and the type of communities they detect.
An integrated model for effective community detection
We develop a community detection model, considering the evolving scenario of a network, using the well-known fuzzy-rough clustering concept. Rough set [37] is good in effective decision making in a situation of uncertainty. It utilizes the concept of lower (strong) and upper (weak) approximation in an approximation space. Lower approximation probabilistic helps to discover the community shape. Objects that belong to a lower approximation of a community are indiscernible and exclusively belong
Performance evaluation
We implement InOvIn, in R and the executable code is available at.5 We use six (06) synthetic and twelve (12) real-world networks for evaluation of our model. We compare the performance of InOvIn with nine (09) contemporary community detection methods, namely COPRA [25], EAGLE [13], SLPAD [11], AFOCS [28], OSLOM [30], Infomap [17], DyPerm [14], TILES [29] and HAM [18]. We appraise the performance of candidate methods based on ten (10) different assessment
Conclusion
We introduced an incremental approach InOvIn for detecting overlapping and intrinsic community in evolving networks. A rough-fuzzy concept is used to cluster communities with varying connectedness density. InOvIn used two different concepts. First, a fuzzy membership for measuring dynamic membership of an object towards a community and second, a density variation detection technique to detect embedded communities. We used both synthetic and real-world networks to access and compare the
CRediT authorship contribution statement
Keshab Nath: Data curation, Investigation, Methodology, Software, Validation, Visualization, Writing - original draft. Swarup Roy: Conceptualization, Formal analysis, Methodology, Project administration, Supervision, Writing - original draft, Writing - review & editing. Sukumar Nandi: Conceptualization, Writing - review & editing.
Declaration of Competing Interest
No author associated with this paper has disclosed any potential or pertinent conflicts which may be perceived to have impending conflict with this work. For full disclosure statements refer to https://doi.org/10.1016/j.asoc.2020.106096.
References (54)
- et al.
Intrinsic-overlapping co-expression module detection with application to Alzheimer’s Disease
Comput. Biol. Chem.
(2018) - et al.
Detect overlapping and hierarchical community structure in networks
Physica A
(2009) - et al.
Fuzzy-rough community in social networks
Pattern Recognit. Lett.
(2015) - et al.
Overlapping community detection via preferential learning model
Physica A
(2019) - et al.
EADP: An extended adaptive density peaks clustering for overlapping community detection in social networks
Neurocomputing
(2019) - et al.
Detecting intrinsic communities in evolving networks
Soc. Netw. Anal. Min.
(2019) Fuzzy sets
Inf. Control
(1965)- et al.
Scale-free characteristics of random networks: the topology of the world-wide web
Physica A
(2000) Silhouettes: a graphical aid to the interpretation and validation of cluster analysis
J. Comput. Appl. Math.
(1987)- et al.
Global landscape of protein complexes in the yeast Saccharomyces cerevisiae
Nature
(2006)
Proteome survey reveals modularity of the yeast cell machinery
Nature
High-quality binary protein interaction map of the yeast interactome network
Science
Hierarchical organization of modularity in metabolic networks
Science
Functional cartography of complex metabolic networks
Nature
A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information
Mol. Syst. Biol.
Quantifying social group evolution
Nature
Understanding individual human mobility patterns
nature
Detection of overlapping communities in dynamical social networks
Overlapping community detection in dynamic networks
J. Softw. Eng. Appl.
Link communities reveal multiscale complexity in networks
Nature
DyPerm: Maximizing permanence for dynamic community detection
Slpa: Uncovering overlapping communities in social networks via a speaker-listener interaction dynamic process
Data Mining: Concepts and Techniques
Maps of random walks on complex networks reveal community structure
Proc. Natl. Acad. Sci.
A community detection algorithm using network topologies and rule-based hierarchical arc-merging strategies
PLoS One
Incremental density-based link clustering algorithm for community detection in dynamic networks
Math. Probl. Eng.
Fast unfolding of communities in large networks
J. Stat. Mech. Theory Exp.
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