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k-Nearest Neighbors in Uncertain Graphs

k-Nearest Neighbors in Uncertain Graphs. VLDB10. Lin Yincheng 2011-02-28. Outline . Background Motivation Problem Definition Query Answering Approach Experimental Results. Background. k-Nearest Neighbors. Uncertain Graphs. 15. 5. 15. 5. 5.

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k-Nearest Neighbors in Uncertain Graphs

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  1. k-Nearest Neighbors in Uncertain Graphs VLDB10 Lin Yincheng 2011-02-28

  2. Outline • Background • Motivation • Problem Definition • Query Answering Approach • Experimental Results

  3. Background k-Nearest Neighbors Uncertain Graphs 15 5 15 5 5 Find out 2-nearest neighbors for vertex B

  4. Motivation • Define meaningful distance functions which is more useful to identify true neighbors • Introduce a novel pruning algorithm to process knn queries in uncertain graphs. 15(0.2) 15(0.6) 5(0.4) 5(0.3) 5(0.7) most-probable-path-distance

  5. Problem Definition • Assumption: Independence among edges • Probabilistic Graph ModelG(V, E, P, W) • V and E denote the set of nodes and edges respectively; • P denotes the probabilities associated with each edge; • W assigns each edge with a weight • k-NN Query

  6. Distances • Median-Distance(s, t) • Majority-Distance(s, t) • Expected-Reliable-Distance(s, t)

  7. Challenges • For computation of median-distance and majority-distance, we need to obtain their distributions over all possible worlds. • For computation of expected-reliable-distance, it has been proved as a #P hard problem.

  8. Sampling

  9. Sample Size for Median-D

  10. Sample Size for E-R-D

  11. Qualitative Analysis • Classification Experiment • Testing data: two classes, one is a triplet set of the form <A, B0, B1> and the other is a triplet set of the form<A, B1, B0> • A classifier: it tries to identify the true neighbors. • Measure: <False positive rate, True positive rate> • Data sets: Protein-protein interaction network DBLP Co-authorship network

  12. Results

  13. ObservationMedian-D • Considering a new probability distribution • The below lemma could be achieved D is a distance value

  14. Core Pruning Scheme • Query Transformation d D, M(s, t1) < d D, M(s, t2) => d M(s, t1) < d M(s, t2) d M(s, t1) >= d M(s, t2) => d D, M(s, t1) >= d D, M(s, t2)

  15. Median-D kNN Query Answering

  16. Majority-D kNN Query Answering • The condition of d which is the exact majority distance should be Pr(d) >= 1 – P, P denotes the sum of visited nodes’ probabilities. • For the node which enters the kNN-set could be possibly replaced by another node with smaller majority distance at a later step.

  17. Experimental Results • Dataset overview • Convergence of D-F Using the distance of a sample of 500 pws as the ground truth

  18. Efficiency of k-NN Pruning The fraction of visited nodes (pruning efficiency) as a function of k Pruning efficiency as a function of sample size

  19. Quality of Results Median-D Pruning efficiency as a function of edge probability Stability as a function of the number of possible worlds

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