K-Nearest Neighbor Temporal Aggregate Queries

Transcription

1 Experiments and Conclusion K-Nearest Neighbor Temporal Aggregate Queries Yu Sun Jianzhong Qi Yu Zheng Rui Zhang Department of Computing and Information Systems University of Melbourne Microsoft Research, Beijing March 26 th 2015

2 Outline Experiments and Conclusion 1 Motivation and Related Work Motivating Examples Previous Work 2 Definition of knnta Structure and Usage of TAR-tree 3 The Proposed Strategy Analysis of Different Strategies 4 Experiments and Conclusion

3 Examples in Our Daily Life Experiments and Conclusion Motivating Examples Previous Work Find some walking-distance attractions Find a nearby club gathering lots of people now Find a good restaurant not far away and has few customers now

4 Experiments and Conclusion Motivating Examples Previous Work Answering Such Questions Has Wide Applications Foursquare or Facebook: places nearby Flickr or Instagram: photos taken nearby having many Likes Urban computing

5 Experiments and Conclusion Motivating Examples Previous Work No Existing Queries Can Effectively Answer Such Questions Ranking locations on Spatial distance Temporal aggregate on visits or likes Range aggregate does not work

6 Experiments and Conclusion Motivating Examples Previous Work No Existing Algorithms or Indexes Can Efficiently Support Such Rankings Characteristics of such applications Visits or likes arrive continuously Interested periods range from hours to years Explore results of different preferences

7 Experiments and Conclusion Definition of knnta Structure and Usage of TAR-tree A Weighted Sum of the Spatial Distance and Temporal Aggregate The ranking function f(p) = αd(p, q)+(1 α)(1 g(p,i q )) (knnta): returns the k locations with the minimum ranking scores

8 A Query Example Experiments and Conclusion Definition of knnta Structure and Usage of TAR-tree c l a g b j d q t 0 t 1 t 2 e a f i e f h... k l Query: q, [t 0, now], α = 0.3, k = 1 f(e) = (1 0.3) (1 2 ) = f(f) = (1 0.3) ( ) = 0.058

9 Experiments and Conclusion Definition of knnta Structure and Usage of TAR-tree A Straightforward Approach May Encounter Very High Cost Number of locations in Foursquare is 60 million Number of records for each location is 525, 600 Much more for applications like Instagram or Twitter

10 A Brief Reminder of R-tree Experiments and Conclusion Definition of knnta Structure and Usage of TAR-tree R 6 R 2 c g l R 1 a b d j f R 3 h e R 7 R 4 i R 5 k R 6 R 7 R 1 R 2 R 3 R 4 R 5 c g l a b d h j f e i k

11 Basic Structure of TAR-tree l a d j R 3 b c R 1 g R 2 R 5 f e h R 6 i R 4 R 7 k Temporal Indexes (2,3,2) R 6 R 7 (3,5,4) R 1 R 2 R 3 R 4 R 5 f c g b a e d h k i l j (3,5,4) (2,2,2) (2,3,1) (1,*,1)

12 Experiments and Conclusion Definition of knnta Structure and Usage of TAR-tree knnta Query Processing using TAR-tree Best-First Search: R 6 (0.000) R 7 (0.427) R 1 (0.058) R 2 (0.352) R 3 (0.408) R 7 (0.427) f (0.058) R 2 (0.352) R 3 (0.408) R 7 (0.427) (2,3,2) (3,5,4) R 6 R 7 (2,2,2) (3,5,4) R 1 R 2 R 3 (2,3,*) R 4 R 5 f c g b a e d h k i l j

13 Maintenance of TAR-tree Experiments and Conclusion Definition of knnta Structure and Usage of TAR-tree Insert Visits or Likes Insert location Re-Insert Note split R 6 R 7 R 1 R 2 R 3 R 4 R 5 f c g b a e d h k i l j

14 Maintenance of TAR-tree Experiments and Conclusion Definition of knnta Structure and Usage of TAR-tree Insert Visits or Likes Insert location Re-Insert Note split R 6 R 7 R 1 R 2 R 3 R 4 R 5 f c g b a e d h k i l j

15 Experiments and Conclusion The Proposed Strategy Analysis of Different Strategies The Importance of Entry Grouping Strategy R 6 R 2 R 7 Root, R 6, R 7, R 2 Four node accesses

16 Experiments and Conclusion The Proposed Strategy Analysis of Different Strategies The Importance of Entry Grouping Strategy R 6 R 2 R 7 R 3 R 6 Root, R 6, R 7, R 2 Four node accesses Root, R 6, R 3 Three node accesses

17 Experiments and Conclusion The Proposed Strategy Analysis of Different Strategies Properly Integrating the Spatial Distance and Temporal Aggregate Straightforward one: Use the spatial information Straightforward two: Use the aggregate distribution (1, 0, 1) with (1, 1, 0) (1, 0, 1) not with (10, 8, 9) Propose: 3D MBR in R*-tree two spatial dimensions third is the aggregate dimension Coordinate of the aggregate dimension m λ p = 1 m v i i=1 Example: (1, 0, 1) 0.67 and (10, 2, 9, 8) 7.25

18 Experiments and Conclusion The Proposed Strategy Analysis of Different Strategies Power-law Distribution of the Aggregate Data Roughly 80% of the visits are at 20% of the locations Pr(X x) Pr(X x) x (a) NYC Pr(X x) Pr(X x) x (b) LA x (c) GW x (d) GS

19 Experiments and Conclusion The Proposed Strategy Analysis of Different Strategies Estimation of the Query Search Region and Number of Node Accesses aggregate dimension l j c g g a b d e h k i f 0.00 Conic shape search region

20 Experiments and Conclusion The Proposed Strategy Analysis of Different Strategies Estimation of the Query Search Region and Number of Node Accesses aggregate dimension l j c g g a b d e h k i f 0.00 aggregate dimension nodes search region Conic shape search region Power-law like node extents

21 Experiments and Conclusion The Proposed Strategy Analysis of Different Strategies Bad Behavior of the Two Straightforward Strategies b a d e l j h k c g i f Spatial grouping

22 Experiments and Conclusion The Proposed Strategy Analysis of Different Strategies Bad Behavior of the Two Straightforward Strategies l j b a d h e k a d b l j h k e c g i c g i f f Spatial grouping Aggregate grouping

23 Experiment Set Up Experiments and Conclusion Experiments Conclusion Table: Data Set Name Time Locations Check-ins NYC 05/ / , ,784 LA 02/ / , ,924 GW 02/ /2010 1,280,969 6,442,803 GS 01/ / ,968 1,385,223 Temporal index: Multi-version B-tree Desktop with 3.40GHz CPU and 16GB RAM Results are averaged over 1, 000 queries By default k = 10 and α = 0.3.

24 Validation of The Analysis Experiments and Conclusion Experiments Conclusion f(p k ) f(p k ) measured estimated k measured estimated α 0 node accesses node accesses measured estimated k measured estimated α 0

25 Experiments and Conclusion Experiments Conclusion Performance of the TAR-tree CPU time (ms) CPU time (ms) baseline IND-agg IND-spa TAR-tree 1 20% 40% 60% 80% 100% time 10 baseline IND-agg IND-spa TAR-tree α CPU time (ms) CPU time (ms) baseline IND-agg IND-spa TAR-tree k baseline IND-agg IND-spa TAR-tree epoch length (day)

26 Conclusion Experiments and Conclusion Experiments Conclusion The knnta query can provide highly customized location retrieval and has wide applications. The TAR-tree index efficiently processes the knnta query.

27 Experiments and Conclusion Experiments Conclusion Questions?