k-nearest neighbor temporal aggregate queries · of people now find a good restaurant not far away...

Motivation and Related WorkQuery kNNTA and Index TAR-tree

Entry Grouping StrategiesExperiments and Conclusion

K-Nearest Neighbor Temporal Aggregate

Queries

Yu Sun † Jianzhong Qi † Yu Zheng ‡ Rui Zhang †

†Department of Computing and Information SystemsUniversity of Melbourne

‡Microsoft Research, Beijing

March 26th 2015

Yu Sun, Jianzhong Qi, Yu Zheng and Rui Zhang K-Nearest Neighbor Temporal Aggregate Queries


Entry Grouping StrategiesExperiments and Conclusion

Outline

1 Motivation and Related Work

Motivating Examples

Previous Work

2 Query kNNTA and Index TAR-tree

Definition of kNNTA

Structure and Usage of TAR-tree

3 Entry Grouping Strategies

The Proposed Strategy

Analysis of Different Strategies

4 Experiments and Conclusion



Entry Grouping StrategiesExperiments and Conclusion Motivating Examples Previous Work

Examples in Our Daily Life

Find some walking-distanceattractions

Find a nearby club gathering lotsof people now

Find a good restaurant not faraway and has few customers now




Answering Such Questions Has Wide Applications

Foursquare or Facebook: placesnearby

Flickr or Instagram: photos takennearby having many Likes

Urban computing




No Existing Queries Can Effectively Answer Such

Questions

Ranking locations on

Spatial distanceTemporal aggregate on visits or likes

Range aggregate does not 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



Entry Grouping StrategiesExperiments 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, Iq))

K-Nearest Neighbor Temporal Aggregate Queries(kNNTA): returns the k locations with the minimumranking scores




A Query Example

a

bc

de

f

gh

i

jk

l

q t0→ t1→ t2→

a 1 1 0

. . .

e 1 1 0

f 3 5 4

. . .

l 1 0 1

Query: q, [t0, now], α = 0.3, k = 1

f (e) = 0.3 ·2.2415.6

+ (1 − 0.3) · (1 −2

12) = 0.626

f (f) = 0.3 ·3

15.6+ (1 − 0.3) · (1 −

1212) = 0.058




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




A Brief Reminder of R-tree

a

b

c

d

ef

gh

ij

kl R1

R2

R3

R4

R5

R6

R7

c g l a b d h j f e i k

R1 R2 R3 R4 R5

R6 R7


Basic Structure of TAR-tree

a

bc

de

fg

h

i

j kl

R1R2

R3

R4R5

R6

R7

Temporal Indexes

f c g b a e d h k i l j

R1 R2 R3 R4 R5

R6 R7

(3,5,4)

(2,2,2)

(2,3,1)

(1,*,1)

(3,5,4)

(2,3,2)



kNNTA Query Processing using TAR-tree

Best-First Search:

R6 (0.000) R7 (0.427)

R1 (0.058) R2 (0.352) R3 (0.408) R7 (0.427)

f (0.058) R2 (0.352) R3 (0.408) R7 (0.427)


R1 R2 R3 R4 R5

R6 R7(3,5,4) (2,2,2)

(3,5,4)

(2,3,2)

(2,3,*)




Maintenance of TAR-tree

Insert Visits or Likes

Insert location

Re-Insert

Note split


R1 R2 R3 R4 R5

R6 R7



Entry Grouping StrategiesExperiments and Conclusion The Proposed Strategy Analysis of Different Strategies

The Importance of Entry Grouping Strategy

R2

R6

R7

Root, R6, R7, R2

Four node accesses




The Importance of Entry Grouping Strategy

R2

R6

R7

Root, R6, R7, R2

Four node accesses

R3

R6

Root, R6, R3

Three node accesses




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 dimensionsthird is the aggregate dimension

Coordinate of the aggregate dimension

λ̂p =1

m

m∑

i=1

vi

Example: (1, 0, 1) → 0.67 and (10, 2, 9, 8) → 7.25




Power-law Distribution of the Aggregate Data

Roughly 80% of the visits are at 20% of the locations

100

101

102

10310

-5

10-4

10-3

10-2

10-1

100

Pr(

X ≥

x)

x

(a) NYC

100

101

102

10310

-5

10-4

10-3

10-2

10-1

100

Pr(

X ≥

x)

x

(b) LA

100

101

102

103

10410

-7

10-5

10-3

10-1

Pr(

X ≥

x)

x

(c) GW

100

101

102

103

104

10510

-6

10-4

10-2

100

Pr(

X ≥

x)

x

(d) GS




Estimation of the Query Search Region and Number

of Node Accesses

l jh

kb

da e

c

gi

f 0.00

0.50

0.83

g′

aggre

gate

dim

ensio

n

Conic shape search region




Estimation of the Query Search Region and Number

of Node Accesses

l jh

kb

da e

c

gi

f 0.00

0.50

0.83

g′

aggre

gate

dim

ensio

n

Conic shape search region

search region

nodes

aggre

gate

dim

ensio

n

Power-law like node extents




Bad Behavior of the Two Straightforward Strategies

lj

h k

bd

a

e

c

gi

f

Spatial grouping




Bad Behavior of the Two Straightforward Strategies

lj

h k

bd

a

e

c

gi

f

Spatial grouping

l j hk

bd

ae

c

gi

f

Aggregate grouping



Entry Grouping StrategiesExperiments and Conclusion Experiments Conclusion

Experiment Set Up

Table: Data Set

Name Time Locations Check-ins

NYC 05/2008-06/2011 72,626 237,784

LA 02/2009-07/2011 45,591 127,924

GW 02/2009-10/2010 1,280,969 6,442,803

GS 01/2011-07/2011 182,968 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.




Validation of The Analysis

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

1 5 10 50 100

f(pk)

k

measuredestimated

0

200

400

600

800

1000

1 5 10 50 100

node accesses

k

measuredestimated

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.1 0.3 0.5 0.7 0.9

f(pk)

α0

measuredestimated

0

100

200

300

0.1 0.3 0.5 0.7 0.9

node accesses

α0

measuredestimated




Performance of the TAR-tree

1

10

100

1000

10000

20% 40% 60% 80% 100%

CPU time (ms)

time

baselineIND-aggIND-spaTAR-tree

1

10

100

1000

10000

1 5 10 50 100

CPU time (ms)

k


1

10

100

1000

10000

0.1 0.3 0.5 0.7 0.9

CPU time (ms)

α0


1

10

100

1000

10000

1 3 7 14 28

CPU time (ms)

epoch length (day)





Conclusion

The kNNTA query can provide highly customizedlocation retrieval and has wide applications.

The TAR-tree index efficiently processes the kNNTAquery.




Questions?


k-nearest neighbor temporal aggregate queries · of people now find a good restaurant not far away...

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