CoSimRank: A Flexible and Efficient Graph-Theoretic Similarity Measure

Rothe, Sascha; Schütze, Hinrich

doi:10.3115/v1/p14-1131

Cited by 34 publications

(35 citation statements)

References 24 publications

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“…Conventional measures for comparing PPR vectors calculate the probability that a random walker meets a particular node after a specific number of iterations, which is potentially problematic (Rothe and Schütze, 2014). For example, consider the following connected nodes:…”

Section: Comparing Vectorsmentioning

confidence: 99%

See 1 more Smart Citation

A Graph-theoretic Summary Evaluation for ROUGE

ShafieiBavani¹,

Ebrahimi²,

Wong³

et al. 2018

Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing

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ROUGE is one of the first and most widely used evaluation metrics for text summarization. However, its assessment merely relies on surface similarities between peer and model summaries. Consequently, ROUGE is unable to fairly evaluate summaries including lexical variations and paraphrasing. We propose a graph-based approach adopted into ROUGE to evaluate summaries based on both lexical and semantic similarities. Experiment results over TAC AESOP datasets show that exploiting the lexico-semantic similarity of the words used in summaries would significantly help ROUGE correlate better with human judgments.

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Section: Comparing Vectorsmentioning

confidence: 99%

“…To prevent this type of false similarity, the random walker needs to take into account the walking path to reach a particular node (Rothe and Schütze, 2014). We formalize this by defining the semantic similarity of two sets of nodes I and J as:…”

Section: Comparing Vectorsmentioning

confidence: 99%

A Graph-theoretic Summary Evaluation for ROUGE

ShafieiBavani¹,

Ebrahimi²,

Wong³

et al. 2018

Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing

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“…Intuitively, the central theme behind SimRank is that "two nodes are considered as similar if their incoming neighbors are themselves similar". Based on this idea, there have emerged two widely-used SimRank models: (1) Li et al's model (e.g., [6,8,13,18,27]) and (2) Jeh and Widom's model (e.g., [4,9,11,16,20] Given a directed graph G = (V, E) with a node set V and an edge set E, let Q be its backward transition matrix (that is, the transpose of the column-normalized adjacency matrix), whose entry [Q] i,j = 1/in-degree(i) if there is an edge from j to i, and 0 otherwise. Then, Li et al's SimRank matrix, denoted by S, is defined as…”

Section: Simrank Backgroundmentioning

confidence: 99%

Dynamical SimRank search on time-varying networks

Lin

Zhang

et al. 2017

The VLDB Journal

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SimRank is an appealing pair-wise similarity measure based on graph structure. It iteratively follows the intuition that two nodes are assessed as similar if they are pointed to by similar nodes. Many real graphs are large, and links are constantly subject to minor changes. In this article, we study the efficient dynamical computation of all-pairs SimRanks on time-varying graphs. Existing methods for the dynamical SimRank computation [e.g., LTSF (Shao et al. in PVLDB 8(8):838-849, 2015) (1) We first consider edge update that does not accompany new node insertions. We show that the SimRank update S in response to every link update is expressible as a rankone Sylvester matrix equation. This provides an incremental method requiring O(K n 2 ) time and O(n 2 ) memory in the worst case to update n 2 pairs of similarities for K iterations.(2) To speed up the computation further, we propose a lossless pruning strategy that captures the "affected areas" of S to eliminate unnecessary retrieval. This reduces the time of the incremental SimRank to O(K (m + |AFF|)), where m is the number of edges in the old graph, and |AFF| (≤ n 2 ) is the size of "affected areas" in S, and in practice, |AFF| n 2 . (3) We also consider edge updates that accompany node insertions, and categorize them into three cases, according to which end of the inserted edge is a new node. For each case, we devise an efficient incremental algorithm that can support new node insertions and accurately update the affected SimRanks. (4) We next study batch updates for dynamical SimRank computation, and design an efficient batch incremental method that handles "similar sink edges" simultaneously and eliminates redundant edge updates. (5) To achieve linear memory, we devise a memory-efficient strategy that dynamically updates all pairs of SimRanks column by column in just O(K n + m) memory, without the need to store all (n 2 ) pairs of old SimRank scores. Experimental studies on various datasets demonstrate that our solution substantially outperforms the existing incremental SimRank methods and is faster and more memory-efficient than its competitors on million-scale graphs.

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“…Baselines. We compare our Co-Simmate with 1) Ite-Mat (Rothe and Schütze, 2014), a Co-Simrank method using the dot product of Pagerank vectors. 2) K-Sim (Kusumoto et al, 2014), a linearized method modified to Co-Simrank.…”

Section: Experimental Settingsmentioning

confidence: 99%

Co-Simmate: Quick Retrieving All Pairwise Co-Simrank Scores

Yu¹,

McCann

2015

Proceedings of the 53rd Annual Meeting of the Association for Computational Linguistics and the 7th International Joint Confere

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Co-Simrank is a useful Simrank-like measure of similarity based on graph structure. The existing method iteratively computes each pair of Co-Simrank score from a dot product of two Pagerank vectors, entailing O(log(1/ǫ)n 3 ) time to compute all pairs of Co-Simranks in a graph with n nodes, to attain a desired accuracy ǫ. In this study, we devise a model, Co-Simmate, to speed up the retrieval of all pairs of Co-Simranks to O(log 2 (log(1/ǫ))n 3 ) time. Moreover, we show the optimality of Co-Simmate among other hop-(u k ) variations, and integrate it with a matrix decomposition based method on singular graphs to attain higher efficiency. The viable experiments verify the superiority of Co-Simmate to others.

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CoSimRank: A Flexible and Efficient Graph-Theoretic Similarity Measure

Cited by 34 publications

References 24 publications

A Graph-theoretic Summary Evaluation for ROUGE

A Graph-theoretic Summary Evaluation for ROUGE

Dynamical SimRank search on time-varying networks

Co-Simmate: Quick Retrieving All Pairwise Co-Simrank Scores

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