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Register a new userCommunity detection, pattern recognition, and hypergraph-based learning: approaches using metric geometry and persistent homology
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Added by
Dong Quan Nguyen
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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Hypergraph data appear and are hidden in many places in the modern age. They are data structure that can be used to model many real data examples since their structures contain information about higher order relations among data points. One of the main contributions of our paper is to introduce a new topological structure to hypergraph data which bears a resemblance to a usual metric space structure. Using this new topological space structure of hypergraph data, we propose several approaches to study community detection problem, detecting persistent features arising from homological structure of hypergraph data. Also based on the topological space structure of hypergraph data introduced in our paper, we introduce a modified nearest neighbors methods which is a generalization of the classical nearest neighbors methods from machine learning. Our modified nearest neighbors methods have an advantage of being very flexible and applicable even for discrete structures as in hypergraphs. We then apply our modified nearest neighbors methods to study sign prediction problem in hypegraph data constructed using our method.
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In this work, we explore four common algorithms for community detection in networks, namely Agglomerative Hierarchical Clustering, Divisive Hierarchical Clustering (Girvan-Newman), Fastgreedy and the Louvain Method. We investigate their mechanics and compare their differences in terms of implementation and results of the clustering behavior on a standard dataset. We further propose some enhancements to these algorithms that show promising results in our evaluations, such as self-neighboring for Neighbor Matrix constructions, a deterministic slightly faster version of the Louvain Method that favors less bigger clusters and various implementation changes to the Fastgreedy algorithm.
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