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Nearest Neighbor Searching Under Uncertainty

Nearest Neighbor Searching Under Uncertainty. Wuzhou Zhang Supervised by Pankaj K. Agarwal Department of Computer Science Duke University. Nearest Neighbor Searching (NNS). http :// en.wikipedia.org /wiki/ Nearest_neighbor_search. Nearest Neighbor Searching Under Uncertainty.

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Nearest Neighbor Searching Under Uncertainty

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  1. Nearest Neighbor Searching Under Uncertainty Wuzhou Zhang Supervised by Pankaj K. Agarwal Department of Computer Science Duke University

  2. Nearest Neighbor Searching (NNS) http://en.wikipedia.org/wiki/Nearest_neighbor_search

  3. Nearest Neighbor Searching Under Uncertainty

  4. Nearest Neighbor In Expectation _________

  5. Bisector In Case Of Gaussian • For Gaussian distribution, bisector is a line! • Hard to get explicit formula! Figure: http://www.cs.utah.edu/~hal/courses/2009S_AI/Walkthrough/KalmanFilters/

  6. Squared Distance Function • bisector is simple and beautiful! In case of discretepdf, bisector is also a line! In both cases, compute the Voronoi diagram, solve it optimally! However, not a metric !

  7. Sampling Continuous Distributions Sometimes working on continuous distributions is hard…. Lower bounds on other metrics and distributions are also possible…. Let’s focus on discrete pdf then….

  8. Expected Nearest NeighborIn L1 Metric (Manhattan metric)

  9. Expected Nearest NeighborIn L1 Metric (cont. ) Source: Range Searching on Uncertain Data [P.K.Agarwalet al. 2009]

  10. Geometric Reduction

  11. Building Block:Half-Space Intersection and Convex Hulls Upper hulls correspond to lower envelopes, an example in 2D Source: page 252 – 253, Computational Geometry: Algorithms and Applications, 3rd Edition[Mark de Berg et al. ]

  12. Segment-tree Based Data Structures for Expected-NNIn L1 Metric

  13. Segment-tree Based Data Structures for Expected-NNIn L1 Metric ( cont. )

  14. Segment-tree Based Data Structures for Expected-NNIn L1 Metric ( cont. ) Summary of the result

  15. ApproximateL2 Metric It’s a metric when P is centrally symmetric!

  16. ApproximateL2 Metric ( cont. ) More complex!

  17. Future Work

  18. Thanks! Main References: [1] Pankaj K. Agarwal, Siu-Wing Cheng, Yufei Tao, Ke Yi: Indexinguncertaindata. PODS 2009: 137-146 [2] PankajK. Agarwal, Lars Arge, Jeff Erickson: IndexingMoving Points. J. Comput. Syst. Sci. 66(1): 207-243 (2003) Questions?

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