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Reverse Spatial and Textual k Nearest Neighbor Search

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Outline Motivation & Problem Statement Related Work RSTkNN Search Strategy Experiments Conclusion 1

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If add a new shop at Q, which shops will be influenced? Influence facts –Spatial Distance Results: D, F –Textual Similarity Services/Products... Results: F, C Motivation food clothes sports food clothes 2

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Problems of finding Influential Sets Traditional query Reverse k nearest neighbor query (RkNN) Our new query Reverse spatial and textual k nearest neighbor query (RSTkNN) 3

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Problem Statement Spatial-Textual Similarity describe the similarity between such objects based on both spatial proximity and textual similarity. Spatial-Textual Similarity Function 4

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Problem Statement (cont) RSTkNN query –is finding objects which have the query object as one of their k spatial-textual similar objects. 5

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Outline Motivation & Problem Statement Related Work RSTkNN Search Strategy Experiments Conclusion 6

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Related Work Pre-computing the kNN for each object (Korn ect, SIGMOD2000, Yang ect, ICDE2001) (Hyper) Voronio cell/planes pruning strategy (Tao ect, VLDB2004, Wu ect, PVLDB2008, Kriegel ect, ICDE2009) 60-degree-pruning method (Stanoi ect, SIGMOD2000) Branch and Bound ( based on Lp-norm metric space ) (Achtert ect, SIGMOD2006, Achtert ect, EDBT2009) Pre-computing the kNN for each object (Korn ect, SIGMOD2000, Yang ect, ICDE2001) (Hyper) Voronio cell/planes pruning strategy (Tao ect, VLDB2004, Wu ect, PVLDB2008, Kriegel ect, ICDE2009) 60-degree-pruning method (Stanoi ect, SIGMOD2000) Branch and Bound ( based on Lp-norm metric space ) (Achtert ect, SIGMOD2006, Achtert ect, EDBT2009) 7 Challenging Features: Lose Euclidean geometric properties. High dimension in text space. k and α are different from query to query. Challenging Features: Lose Euclidean geometric properties. High dimension in text space. k and α are different from query to query.

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Baseline method Precompute Spatial NNs Textual NNs Threshold Algorithm Spatial-textual kNN o q is no more similar than o Object o q is more similar than o Give query q, k & α Inefficient since lacking a novel data structure For each object o in the database 8

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Outline Motivation & Problem Statement Related Work RSTkNN Search Strategy Experiments Conclusion 9

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Intersection and Union R-tree (IUR-tree) 10

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Main idea of Search Strategy Prune an entry E in IUR-Tree, when query q is no more similar than kNN L (E). Report an entry E to be results, when query q is more similar than kNN U (E). 11

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How to Compute the Bounds Similarity approximations MinST(E, E): TightMinST(E, E): MaxST(E, E): 12

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Example for Computing Bounds Current traveled entries: N1, N2, N3 Given k=2, to compute kNN L (N1) and kNN U (N1). TightMinST(N1, N3) = 0.564 MinST(N1, N3) = 0.370 TightMinST(N1, N2) = 0.179 MinST(N1, N2) = 0.095 N1N3 effect N1N2 Compute kNN L (N1) decrease kNN L (N1) = 0.370 Compute kNN U (N1) decrease kNN U (N1) = 0.432 MaxST(N1, N3) = 0.432 MaxST(N1, N2) = 0.150 13

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Overview of Search Algorithm RSTkNN Algorithm: –Travel from the IUR-tree root –Progressively update lower and upper bounds –Apply search strategy: prune unrelated entries to Pruned; report entries to be results Ans; add candidate objects to Cnd. –FinalVerification For objects in Cnd, check whether to results or not by updating the bounds for candidates using expanding entries in Pruned. 14

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N4 N1 p1 N2 p2 p3 N3 p4 p5 EnQueue(U, N4); Initialize N4.CLs; Example: Execution of the RSTkNN Algorithm on IUR-tree, given k=2, alpha=0.6 U N4, (0, 0) 15

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Example: Execution of the RSTkNN Algorithm on IUR-tree, given k=2, alpha=0.6 U N4(0, 0) DeQueue(U, N4) Mutual-effect N1 N2 N1 N3 N2 N3 N4 N1 p1 N2 p2 p3 N3 p4 p5 EnQueue(U, N2) EnQueue(U, N3) Pruned.add(N1) Pruned N1(0.37, 0.432) N3(0.323, 0.619 )N2(0.21, 0.619 ) 16

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Example: Execution of the RSTkNN Algorithm on IUR-tree, given k=2, alpha=0.6 U DeQueue(U, N3) Mutual-effect p4 N2 p5 p4,N2 Answer.add(p4) Candidate.add(p5) Pruned N1(0.37, 0.432) N3(0.323, 0.619 )N2(0.21, 0.619 ) Answer Candidate p4(0.21, 0.619 ) p5(0.374, 0.374) N4 N1 p1 N2 p2 p3 N3 p4 p5 17

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Example: Execution of the RSTkNN Algorithm on IUR-tree, given k=2, alpha=0.6 U DeQueue(U, N2) Mutual-effect p2 p4,p5 p3 p2,p4,p5 Answer.add(p2, p3) Pruned.add(p5) Pruned N1(0.37, 0.432) N2(0.21, 0.619 ) Answer Candidate p4 p5(0.374, 0.374) N4 N1 p1 N2 p2 p3 N3 p4 p5 p2p3 So far since U=Cand=empty, algorithm ends. Results: p2, p3, p4. So far since U=Cand=empty, algorithm ends. Results: p2, p3, p4. 18

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Cluster IUR-tree: CIUR-tree IUR-tree: Texts in an index node could be very different. CIUR-tree: An enhanced IUR-tree by incorporating textual clusters. 19

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Optimizations Motivation –To give a tighter bound during CIUR-tree traversal –To purify the textual description in the index node Outlier Detection and Extraction (ODE-CIUR) –Extract subtrees with outlier clusters –Take the outliers into special account and calculate their bounds separately. Text-entropy based optimization (TE-CIUR) –Define TextEntropy to depict the distribution of text clusters in an entry of CIUR-tree –Travel first for the entries with higher TextEntropy, i.e. more diverse in texts. 20

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Experimental Study Experimental Setup –OS: Windows XP;CPU: 2.0GHz; Memory: 4GB –Page size: 4KB;Language: C/C++. Compared Methods –baseline, IUR-tree, ODE-CIUR, TE-CIUR, and ODE-TE. Datasets –ShopBranches(Shop), extended from a small real data –GeographicNames(GN), real data –CaliforniaDBpedia(CD), generated combining location in California and documents from DBpedia. Metric –Total query time –Page access number StatisticsShopCDGN Total # of objects304,0081,555,2091,868,821 Total unique words in dataset393321,578222,409 Average # words per object45474 21

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Scalability (1) Log-scale version (2) Linear-scale version 22

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Effect of k (a) Query time(b) Page access 23

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Conclusion Propose a new query problem RSTkNN. Present a hybrid index IUR-Tree. Present the efficient search algorithm to answer the queries. Show the enhancing variant CIUR-Tree and two optimizations ODE-CIUR and TE-CIUR to further improve search processing. Extensive experiments confirm the efficiency and scalability of our algorithms. 24

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Reverse Spatial and Textual k Nearest Neighbor Search Thanks! Q & A

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A straightforward method 1.Compute RSkNN and RTkNN, respectively; 2.Combine both results of RSkNN and RTkNN get RSTkNN results. No sensible way for combination. (Infeasible)

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