p-rank: a comprehensive structural similarity measure over information networks
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P-Rank: A Comprehensive Structural Similarity Measure over Information Networks. Peixiang Zhao, Jiawei Han, Yizhou Sun University of Illinois at Urbana-Champaign. CIKM’ 09 November 3 rd , 2009, Hong Kong. Presented by Prof. Hong Cheng, CUHK. Outline. Introduction & Motivation P-Rank - PowerPoint PPT PresentationTRANSCRIPT
P-Rank: A Comprehensive Structural Similarity Measure
over Information Networks
CIKM’ 09 November 3rd, 2009, Hong Kong
Peixiang Zhao, Jiawei Han, Yizhou SunUniversity of Illinois at Urbana-Champaign
Presented by Prof. Hong Cheng, CUHK
Outline• Introduction & Motivation• P-Rank
– Formula– Derivatives– Computation
• Experimental Studies• Future direction & Conclusion
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Introduction• Information Networks (INs)
– Physical, conceptual, and human/societal entities– Interconnected relationships among different
entities• INs are ubiquitous and form a critical component of
modern information infrastructure– The Web– highway or urban transportation networks– research collaboration and publication networks– Biological networks– social networks
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Problem• Similarity computation on entities of INs
– How similar is webpage A with webpage B in the Web ?
– How similar is researcher A with researcher B in DBLP co-authorship network ?
• First of all, how to define “similarity” within a massive IN?– Textual proximity of entity labels/contents– Structural proximity conveyed through links!
• A good structural similarity measure in INs: SimRank (KDD’02)
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Why SimRank is not Enough?• Philosophy
– two entities are similar if they are referenced by similar entities
• Potential problems– Semantic incomplete
• Only partial structural information from in-link direction is considered during similarity computation
• Biased similarity results
• May fail in different IN settings !
– Inefficient in computation• Worst-case O(n4), can be improved to O(n3), where n
is the number of vertices in the information network
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Why SimRank is not Enough?
(a) A Heterogeneous IN and Structural Similarity Scores
(b) A Homogeneous IN and Structural Similarity Scores
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P(enetrating)-Rank• Philosophy: Two entities are similar, if
1. they are referenced by similar entities2. they reference similar entities
• Advantages– Semantic complete
• Structural information from both in-link and out-link directions are considered during similarity computation
• Robust in different IN settings
– A unified structural similarity framework• SimRank is just a special case
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P-Rank Formula• The structural similarity between vertex a and vertex
b (a ≠ b), s(a, b):– Recursive form
– Approximate iterative form
In-link similarity
Out-link similarity
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P-Rank Property• The iterative P-Rank has the following properties:
– Symmetry: sk(a, b) = sk(b, a)
– Monotonicity: 0 ≤ sk(a, b) ≤ sk+1(a, b) ≤ 1– Existence: The solution to the iterative P-Rank
formula always exists and converges to a fixed point, s(∗, ∗), which is the theoretical solution to the recursive P-Rank formula
– Uniqueness: the solution to the iterative P-Rank formula is unique when C ≠ 1
• The theoretical solution to P-Rank can be reached by a repetitive computation via the iterative form
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P-Rank Derivatives
• P-Rank proposes a unified structural similarity framework, upon which many structural similarity measures are just its special cases
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P-Rank Computation• An iterative algorithm is executed until it reaches the
fixed point– Space complexity: O(n2)– Time complexity: O(n4), can be improved to
O(n3) by amortization• Approximation algorithms on different IN scenarios
– Homogeneous IN• Radius based pruning: vertex-pairs beyond a radius of r are
no longer considered in similarity computation– Heterogeneous IN
• Category based pruning: vertex-pairs in different categories are no longer considered in similarity computation
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Experimental Studies• Data sets:
– Heterogeneous IN: DBLP (paper, author, conference, year)
– Homogeneous IN: DBLP (paper with citation), Synthetic data R-MAT
• Methods– P-Rank– SimRank
• Metrics– Compactness of clusters– Algorithmic nature– Ground truth
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Compactness of Clusters• P-Rank and SimRank are used as underlying similarity
measures, respectively, and K-Medoids are used to cluster different vertices– Compactness: intra-cluster distance/inter-
cluster distance
Heterogeneous IN Homogeneous IN
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Algorithmic Nature
• Iterative P-Rank converges fast to the fixed point
P-Rank v.s. the damping factor C
P-Rank v.s. lambda
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Ground Truth Ranking Result
• Top-10 ranking results for author vertices in DBLP by P-Rank
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Conclusion• The proliferation of information networks calls for
effective structural similarity measures in– Ranking– Clustering– Top-k Query Processing– ……
• Compared with SimRank, P-Rank is witnessed to be a more effective structural similarity measure in large information networks– Semantic complete, general, robust, and
flexible enough to be employed in different IN settings
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Thank you
CIKM’ 09 November 3rd, 2009, Hong Kong