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

2. Presentation Outline Motivation Related Work Problem Definition Approach Validation Conclusion

3. 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

4. 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, …)

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

6. 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

7. 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.

8. Approach Object Classification Distance Classification Incrementally increasing concentric circle query regions

9. Detour: R-tree

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

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

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

13. Algorithm Example: 3 nearest squares 1) Get distance function 2) Search…

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

15. 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

16. 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

17. Any Questions???