1 / 14

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.

nijole
Télécharger la présentation

Nearest-Neighbor Searching Under Uncertainty II

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related