Nearest Neighbors by Neighborhood Counting

1. Nearest Neighbors by Neighborhood Counting Author : Hui Wang Reporter : Tze Ho-Lin 2006/11/13 PAMI, 2006

2. Outline • Motivation • Objectives • Method (NCM) • Evaluation • Conclusion • Personal Comments

3. Motivation • Finding nearest neighbors is a general idea that underlies many artificial intelligence tasks. • Complex real-world applications may generate new types of data or new combinations of existing types of data. • This may call for new distance/similarity functions.

4. Objectives • We propose using the number of neighborhoods as a generic measure of similarity which can then serve as a methodology.

5. Method: NCM Assumption: the domains of attributes a1 and a2 are both {1,2,3,4,5} the domain of c is {+,-}

6. Method: NCM Ex. 5 5 t1 x3=t3 t2 x1 4 4 x2 1 1 (5-5+1)*(4-1+1) =4 (5-4+1)*(4-1+1) =8

7. Experimental result Fig. 4. With weighting • NCM generally performed well under relatively large k. • NCMconsistentlyoutperformedHEOMwhen k> 1 withoutweightingandwhen k> 11 withweighting. PS. HEOM: Heterogeneous Euclidean-Overlap Metric Table 3 Runtime, in Seconds, where k = 11 and There Is No Weighting

8. Conclusion • Uniform approach for both numerical and categorical attributes • It can be used for classification and clustering. • Efficient–computational complexity is O(n), in the same order as Euclidean distance, where n is the number of attributes.

9. Personal Comments • Application • A lot of nearest-neighbors-required algorithms. • Advantage • It can be used for classification and clustering. • This function has a simple, easy-to-implement formula. • Disadvantage • This function can’t really measure different categorical data.

10. Hypertuples of numerical case Count: 8 (max(ai)-t(ai)+1)* (t(ai)-min(ai)+1) (5-2+1)*(2-1+1) =4*2=8 t(ai) ai Hypertuples of 1

11. Hypertuples of categorical case • Domain :{+,-} • All hypertuple • {Ø} {+} {-} {+,-} • All hypertuple of {+} • {+} {+,-}