An Intelligent & Incremental Approach to kNN using R-trees

An Intelligent & Incremental Approach to kNN using R-trees DJ Oneil & Esten Rye (G01)

Presentation Outline • Motivation • Related Work • Problem Definition • Approach • Validation • Conclusion

Motivation • kNN is a popular (GIS, AI, Pattern Recognition, Clustering, Outlier Detection) • kNN is a hard problem • R-tree is the industry standard (Oracle, Microsoft SQL Server, DB2, and MySQL) • Problems with higher dimensional spaces • GIS

Related Work • Voronoi Diagram • Incremental approach (find k+1 using k) • High dimensions (X-tree) • New data structures (k-d tree, P-range tree, X-tree, SS-tree, …)

What’s Missing??? • Domain specific classifications • Informed, incremental approach to R-tree kNN

Problem Definition • Given: Spatial database with n objects and query point, q. • Find: The k ≤ n ranked nearest neighbors. • Objective: • Use object classifications • Incremental • Constraints: • Spatial objects are stored in an R-Tree

Key Ideas • Allow users to define domain-specific classifiers to decrease search space • Use informed, incrementally increasing query region to decrease search space • Don’t worry about finding exactly k nearest neighbors.

Approach • Object Classification • Distance Classification • Incrementally increasing concentric circle query regions

Detour: R-tree

Object Classification • Domain specific classifiers. • Only search MBBs that contain classifications • Adds classification dimensions. • Example: Zoning Classifier • {“Residential”, “Industrial”, Commercial”}

Distance Classification • Maps Euclidean distance/increment generator to region • Default function • Separate R-tree

Concentric Circles • Decrease candidate regions • Only consider MBBs that are completely contained in query region • Ignore previously searched MBBs

Algorithm Example: 3 nearest squares • Get distance function • Search…

Validation • Find nearest gas stations (Zoning example) • 1.7% total searchable area of Minneapolis • Complexity: • p classifiers with q classifications • Computational: O(p*logα(q))* O(logα(n)) ≈ O(logα(n)) • Spatial: (p*q*s + t)(n + α*logαn + α)

Conclusion • Expand R-trees for kNN • User-defined, domain specific classifiers to decrease search space • User defined incremental distance function • Increasing Euclidean distance, Concentric Circles

Future Work • Extend distance classifier to include many classifiers • Non-Euclidean distance (e.g. speed limit) • Combine distance classification tree with data tree • Experiment • Plan for incrementally upgrading existing R-tree implementations • Determine threshold for number of classifiers and classifications

Any Questions???

An Intelligent & Incremental Approach to kNN using R-trees