Nearest-Neighbor Searching Under Uncertainty Wuzhou Zhang Joint work with Pankaj K. Agarwal, Alon Efrat, and Swaminathan Sankararaman. To appear in PODS 2012.

Nearest-Neighbor Searching Applications Pattern Recognition, Data Compression Statistical Classification, Clustering Databases, Information Retrieval Computer Vision, etc. 2

Data Uncertainty  Location of data is imprecise: Sensor databases, face recognition, mobile data, etc. 3

Our Model and Problem Statement

Previous work and Our contribution 5

Summary of results 6 Distance function SettingsPreprocessing timeSpaceQuery time Squared Euclidean distance Uncertain data Uncertain query Rectilinear metric Uncertain data Uncertain query Uncertain data Uncertain query

Voronoi Diagram 7 Preprocessing time Space Query time

Expected Voronoi Diagram 8

Minimization diagram 9

Squared Euclidean distance Uncertain data 10 Preprocessing timeSpaceQuery time Remarks: Works for any distribution

Rectilinear metric Uncertain data 11

Rectilinear metric Uncertain data (cont.) 12 Linear!

Rectilinear metric Uncertain data (cont.) 13 Preprocessing timeSpaceQuery time Remarks: Extends to higher dimensions

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15 Quadtree: 4-way tree Preprocessing timeSpaceQuery time

Further work 16

Squared Euclidean distance Uncertain query 17 Preprocessing timeSpaceQuery time Remarks: Extends to higher dimensions and works for any distribution

Rectilinear metric Uncertain query 18 Preprocessing time Space Query time

19 Preprocessing time Space Query time Remarks: Extends to higher dimensions