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Nearest-Neighbor Searching Under Uncertainty II

Nearest-Neighbor Searching Under Uncertainty II. Nearest Neighbor (NN) Searching. Post office problem. : a set of points. : any query point. Find the closest one. Voronoi Diagram. Voronoi cell : Voronoi diagram : decomposition induced by . Data Uncertainty.

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Nearest-Neighbor Searching Under Uncertainty II

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  1. Nearest-Neighbor Searching Under Uncertainty II

  2. Nearest Neighbor (NN) Searching Post office problem : a set of points : any query point Find the closest one

  3. Voronoi Diagram • Voronoi cell: • Voronoi diagram : decomposition induced by

  4. Data Uncertainty • Location of data is imprecise: Sensor databases, face recognition, mobile data, etc. What is the “nearest neighbor” of now?

  5. Uncertainty Models • Existential model. Each uncertain point appears with some probability. • Locational model. Each uncertain point is represented by a probability distribution function (pdf) . Uncertainty region

  6. Probabilistic Nearest Neighbor (PNN) in : the pdf of : any given query point : the pdf of : the cdfof The qualification probability

  7. Problem Definition Two sub-problems: • Nonzero NNs. Nonzero Voronoi Diagram : for any , . • Computing . :

  8. Prior Work • Nonzero NNs. • in the case of disks: [Evans et al. 2008] • Voronoi-based heuristics [Zhang et al. 2013] • Computing • Best-effort based [Kriegel et al. 2007][Cheng et al. 2008] • Other variants. • Expected Nearest Neighbor [Agarwal et al. 2012] • Superseding Nearest Neighbor [Yuen et al. 2010] • Top- NNs [Ljosa et al. 2007][Beskales et al. 2008]

  9. Our ResultsNonzero NNs Complexity of • if assuming general disks. • if pairwise disjoint disks of same radii. • if has locations. In all the cases, where , and is the output size.

  10. Our ResultsNonzero NNs Indexing schemes (using less space) • If each uncertainty region is a disk, • If each has possible locations,

  11. Our ResultsComputing • Monte Carlo method The number of instantiations is . If each has a discrete pdf of size : , with probability at least • Spiral Search method Only need to look at a small number of closest points

  12. Nonzero NNsbound for iff. An (curved) edge: Vertices: Only

  13. Computing Spiral Search method Each has equally likely locations. Estimate using closest points. Independent of !

  14. Future Work • The PNN problem under the existential model • The non-zero NN definition does not make sense • Solutions here cannot be directly adapted

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