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DELTACON: A Principled MassiveGraph Similarity Function
"... How much did a network change since yesterday? How different is the wiring between Bob’s brain (a lefthanded male) and Alice’s brain (a righthanded female)? Graph similarity with known node correspondence, i.e. the detection of changes in the connectivity of graphs, arises in numerous settings. In ..."
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How much did a network change since yesterday? How different is the wiring between Bob’s brain (a lefthanded male) and Alice’s brain (a righthanded female)? Graph similarity with known node correspondence, i.e. the detection of changes in the connectivity of graphs, arises in numerous settings. In this work, we formally state the axioms and desired properties of the graph similarity functions, and evaluate when stateoftheart methods fail to detect crucial connectivity changes in graphs. We propose DELTACON, a principled, intuitive, and scalable algorithm that assesses the similarity between two graphs on the same nodes (e.g. employees of a company, customers of a mobile carrier). Experiments on various synthetic and real graphs showcase the advantages of our method over existing similarity measures. Finally, we employ DELTACON to real applications: (a) we classify people to groups of high and low creativity based on their brain connectivity graphs, and (b) do temporal anomaly detection in the whoemailswhom Enron graph. 1
A Boosting Approach to Learning Graph Representations ∗
"... Learning the right graph representation from noisy, multisource data has garnered significant interest in recent years. A central tenet of this problem is relational learning. Here the objective is to incorporate the partial information each data source gives us in a way that captures the true unde ..."
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Learning the right graph representation from noisy, multisource data has garnered significant interest in recent years. A central tenet of this problem is relational learning. Here the objective is to incorporate the partial information each data source gives us in a way that captures the true underlying relationships. To address this challenge, we present a general, boostinginspired framework for combining weak evidence of entity associations into a robust similarity metric. We explore the extent to which different quality measurements yield graph representations that are suitable for community detection. We then present empirical results on both synthetic and real datasets demonstrating the utility of this framework. Our framework leads to suitable global graph representations from quality measurements local to each edge. Finally, we discuss future extensions and theoretical considerations of learning useful graph representations from weak feedback in general application settings. 1
ASCOS++: An Asymmetric Similarity Measure for Weighted Networks to Address the Problem of SimRank
"... In this article, we explore the relationships among digital objects in terms of their similarity based on vertex similarity measures. We argue that SimRank—a famous similarity measure—and its families, such as PRank and SimRank++, fail to capture similar node pairs in certain conditions, especially ..."
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In this article, we explore the relationships among digital objects in terms of their similarity based on vertex similarity measures. We argue that SimRank—a famous similarity measure—and its families, such as PRank and SimRank++, fail to capture similar node pairs in certain conditions, especially when two nodes can only reach each other through paths of odd lengths. We present new similarity measures ASCOS and ASCOS++ to address the problem. ASCOS outputs a more complete similarity score than SimRank and SimRank’s families. ASCOS++ enriches ASCOS to include edge weight into the measure, giving all edges and network weights an opportunity to make their contribution. We show that both ASCOS++ and ASCOS can be reformulated and applied on a distributed environment for parallel contribution. Experimental results show that ASCOS++ reports a better score than SimRank and several famous similarity measures. Finally, we reexamine previous use cases of SimRank, and explain appropriate and inappropriate use cases. We suggest future SimRank users following the rules proposed here before naı̈vely applying it. We also discuss the relationship between ASCOS++ and PageRank.
Locally Boosted Graph Aggregation for Community Detection ∗
"... Learning the right graph representation from noisy, multisource data has garnered significant interest in recent years. A central tenet of this problem is relational learning. Here the objective is to incorporate the partial information each data source gives us in a way that captures the true unde ..."
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Learning the right graph representation from noisy, multisource data has garnered significant interest in recent years. A central tenet of this problem is relational learning. Here the objective is to incorporate the partial information each data source gives us in a way that captures the true underlying relationships. To address this challenge, we present a general, boostinginspired framework for combining weak evidence of entity associations into a robust similarity metric. Building on previous work, we explore the extent to which different local quality measurements yield graph representations that are suitable for community detection. We present empirical results on a variety of datasets demonstrating the utility of this framework, especially with respect to real datasets where noise and scale present serious challenges. Finally, we prove a convergence theorem in an ideal setting and outline future research into other application domains. 1
Edge Union of Networks on the Same Vertex Set.
"... Abstract. Random networks generators like ErdősRényi, WattsStrogatz and BarabásiAlbert models are used as models to study realworld networks. Let G1(V,E1) and G 2(V,E2) be two such networks on the same vertex set V. This paper studies the degree distribution and clustering coefficient of the ..."
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Abstract. Random networks generators like ErdősRényi, WattsStrogatz and BarabásiAlbert models are used as models to study realworld networks. Let G1(V,E1) and G 2(V,E2) be two such networks on the same vertex set V. This paper studies the degree distribution and clustering coefficient of the resultant networks, G(V,E1 ∪ E2). ar