An Axiomatic Role Similarity Measure Based on Graph Topology

Yu, Weiren; Iranmanesh, Sima; Haldar, Aparajita; Zhang, Maoyin; Ferhatosmanoğlu, Hakan

doi:10.1007/978-3-030-61133-0_3

Cited by 3 publications

(2 citation statements)

References 32 publications

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“…Acknowledgements A preliminary version of this work has been published in [33]. We summarise the main changes to [33] as follows: 1) For techniques and methods, we add three new sections on top of [33]: Section 4 (threshold-based RoleSim*), Section 5 (scaling single-source RoleSim* search on large graphs), and Section 6 (top-K efficient RoleSim* search using triangle inequality and partitioning). 2) Experiments (Section 8.2).…”

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RoleSim*: Scaling axiomatic role-based similarity ranking on large graphs

Iranmanesh

Haldar

et al. 2021

World Wide Web

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RoleSim and SimRank are among the popular graph-theoretic similarity measures with many applications in, e.g., web search, collaborative filtering, and sociometry. While RoleSim addresses the automorphic (role) equivalence of pairwise similarity which SimRank lacks, it ignores the neighboring similarity information out of the automorphically equivalent set. Consequently, two pairs of nodes, which are not automorphically equivalent by nature, cannot be well distinguished by RoleSim if the averages of their neighboring similarities over the automorphically equivalent set are the same. To alleviate this problem: 1) We propose a novel similarity model, namely RoleSim*, which accurately evaluates pairwise role similarities in a more comprehensive manner. RoleSim* not only guarantees the automorphic equivalence that SimRank lacks, but also takes into account the neighboring similarity information outside the automorphically equivalent sets that are overlooked by RoleSim. 2) We prove the existence and uniqueness of the RoleSim* solution, and show its three axiomatic properties (i.e., symmetry, boundedness, and non-increasing monotonicity). 3) We provide a concise bound for iteratively computing RoleSim* formula, and estimate the number of iterations required to attain a desired accuracy. 4) We induce a distance metric based on RoleSim* similarity, and show that the RoleSim* metric fulfills the triangular inequality, which implies the sum-transitivity of its similarity scores. 5) We present a threshold-based RoleSim* model that reduces the computational time further with provable accuracy guarantee. 6) We propose a single-source RoleSim* model, which scales well for sizable graphs. 7) We also devise methods to scale RoleSim* based search by incorporating its triangular inequality property with partitioning techniques. Our experimental results on real datasets demonstrate that RoleSim* achieves higher accuracy than its competitors while scaling well on sizable graphs with billions of edges.

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RoleSim*: Scaling axiomatic role-based similarity ranking on large graphs

Iranmanesh

Haldar

et al. 2021

World Wide Web

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“…Due to the vast applications of node similarity, many measures have been proposed to estimate the similarity between vertices [15][16][17]32]. Among these works, role similarity [5,17,18,24,40,49] stands out because of satisfying several axiomatic properties, including automorphism confirmation, which ensures that the similarity score between two nodes that are automorphically equivalent is 1 (the maximum similarity score). Thus, role similarity measures have the good merit of indicating automorphism, which keeps these measures from assigning counterintuitive similarity scores.…”

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Role Similarity Metric Based on Spanning Rooted Forest

Bao,

Zhang

2021

Preprint

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As a fundamental issue in network analysis, structural node similarity has received much attention in academia and is adopted in a wide range of applications. Among these proposed structural node similarity measures, role similarity stands out because of satisfying several axiomatic properties including automorphism conformation. Existing role similarity metrics cannot handle top-k queries on large real-world networks due to the high time and space cost. In this paper, we propose a new role similarity metric, namely ForestSim. We prove that ForestSim is an admissible role similarity metric and devise the corresponding top-k similarity search algorithm, namely ForestSimSearch, which is able to process a topk query in ( ) time once the precomputation is finished. Moreover, we speed up the precomputation by using a fast approximate algorithm to compute the diagonal entries of the forest matrix, which reduces the time and space complexity of the precomputation to ( −2 log 5 log 1 ) and ( log 3 ), respectively. Finally, we conduct extensive experiments on 26 real-world networks. The results show that ForestSim works efficiently on million-scale networks and achieves comparable performance to the state-of-art methods. CCS CONCEPTS• Information systems → Data mining.

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