Trajectories Simplification Method for Location-Based Social Networking Services

Presenter: Yu Zheng

on behalf of Yukun Cheng, Kai Jiang, Xing Xie

Microsoft Research Asia

March 16, 2009

Background

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GPS devices enable us to record our location history with GPS trajectories

Location-based social networking services using web mapsBikely, GeoLife,

Sharing life experiences with GPS trajectories

Many GPS trajectories are too dense to be displayedCost lots of hardware resource.

Make an application very slow

IE browser could crash

It is not necessary to show so many details to users

Motivation

We need to simplify a trajectory from n point to m point (m<<n)

Traditional line simplification methodsonly maintain the skeleton (geospatial shape) information of a trajectory while missing the semantic meanings

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n points

m points

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c) overallb) walking detail 1a) walking detail 2

• A travel route consists of 10,000+ points• contains one driving segment and one walking segment

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b) walking detail 1 c) overalla) walking detail 2 d) driving

A result returned by the DP algorithm

a) walking detail 2 c) overallb) walking detail 1 d) driving

A result returned by our method

Our Goal

TS algorithm: Simplify a trajectory with N points to a m-point oneWhile maintain not only the skeleton informationBut also the semantic meanings for trajectory sharing

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Framework of TS

Partition a trajectory into some segmentsAssign the headcount of points to each segmentRank the points in a segment according to some factorsRetrieve the high-rank points from each segment and formulate a simplified a trajectory

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Preliminaries

Distance between a point and its nearest neighbors

Heading direction of a point

Heading change of a point

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p2.hp3.h

p2

p3.Θp1 p4 p5

d1

d2

a)

p3

p2

p3.Θp1 p4 p5

b)

p3

p2.Θ

p4.Θ

𝑝𝑖.𝑑= 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒ሺ𝑝𝑖−1,𝑝𝑖ሻ+ 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒(𝑝𝑖,𝑝𝑖+1)

𝜃 = 𝑝𝑖.ℎ− 𝑝𝑖−1.ℎ

𝜃 = 𝑝𝑖.ℎ− 𝑝𝑖−1.ℎ

1. Trajectory Segmentation

See our WWW2008 publication for details

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WalkBus

Certain Segment

Denotes a non-walk Point: P.V>Vt or P.a>atDenotes a possible walk point: P.V<Vt and P.a<at

(b)

(c)

Backward ForwardCar

(a)

Certain Segment3 Uncertain Segments

Car

2. Assign Points to a Segment

The weight of a segment depends on The length of a segment

The average heading change

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𝑆.𝑑 = 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒(𝑝𝑘,𝑝𝑘−1)𝑗𝑘=𝑖+1

𝑆.𝛼= ( |𝑝𝑘.𝑗𝑘=𝑖 𝜃|) / (𝑗− 𝑖 + 1)

𝑆.𝑤= 𝑆.𝑑∗ 𝑆.𝛼

,

3. Ranking Points in a Segment

Factors 1: Distance between a point and its nearest neighbors

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𝑝𝑖.𝑑= 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒ሺ𝑝𝑖−1,𝑝𝑖ሻ+ 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒(𝑝𝑖,𝑝𝑖+1)

Example 1

𝑝𝑖−1

𝑝𝑖−1

𝑝𝑖+1

Example 2

𝑝𝑖−1

𝑝𝑖−1

𝑝𝑖+1

3. Ranking Points in a Segment

Factors 2: Heading change of a point

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𝜃 = 𝑝𝑖.ℎ− 𝑝𝑖−1.ℎ

Example 1

𝑝𝑖−1

𝑝𝑖−1

𝑝𝑖+1

𝜃 = 𝑝𝑖.ℎ− 𝑝𝑖−1.ℎ

𝜃 = 𝑝𝑖.ℎ− 𝑝𝑖−1.ℎ

𝜃 = 𝑝𝑖.ℎ− 𝑝𝑖−1.ℎ

Example 2

𝑝𝑖−1

𝑝𝑖−1

𝑝𝑖+1

3. Ranking Points in a Segment

Factors 3: Accumulated Heading Change

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𝑝𝑖.𝛽 = 𝑝𝑘.𝜃𝑖+𝜏𝑘=𝑖−𝜏

Factors Determine the Weigth of a Point

Distance between a point and its nearest neighbors

Heading change of a point

Accumulated Heading Change

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p2.hp3.h

p2

p3.Θp1 p4 p5

d1

d2

a)

p3

p2

p3.Θp1 p4 p5

b)

p3

p2.Θ

p4.Θ

𝑝𝑖.𝑑= 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒ሺ𝑝𝑖−1,𝑝𝑖ሻ+ 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒(𝑝𝑖,𝑝𝑖+1)

𝜃 = 𝑝𝑖.ℎ− 𝑝𝑖−1.ℎ

𝑝𝑖.𝛽 = 𝑝𝑘.𝜃𝑖+𝜏𝑘=𝑖−𝜏

𝑝.𝑤= 𝑝.𝑑∗(ȁ"𝑝.𝜃ȁ"+ ȁ"𝑝.𝛽ȁ")

An example of our method

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S1 S2

P1

P2

P3

P4

P5

P7

P6

P8

P9P10

P11

P12

P13 P14

P15

P16

P17P19 P18P20P21

P22

S1 S2

P1

P7

P10

P11 P13

P15

P16

P17P20

P22a) original trajectory b) simplified trajectory

Experiments

GPS trajectory data335 travel routes generated by 65 usersThe distance of each trajectory is over 5kmOn average each trajectory

has 2,100+ points, a distance of 63 km and a 4-hour time span

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Evaluation on EffectivenessAverage normalized perpendicular:

Calculate the perpendicular distance of each point to the simplified resultsCompute the root mean square value of these perpendicular distance

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a f

ec

bPerpendicular distance from point c to line ab

Evaluation on Effectiveness

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0

0.1

0.2

0.3

0.4

0.5

0.6

0.05 0.

10.

15 0.2

0.25 0.

30.

35 0.4

0.45 0.

50.

55 0.6

0.65 0.

70.

75 0.8

0.85 0.

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Nor

mal

ized

Dev

iati

on

Simplification Rate

Average Normalized Perpendicular Deviation

Deviation of TS

Deviation of DP

Evaluation on Effectiveness

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0

0.2

0.4

0.6

0.8

1

1.2

0.05 0.

10.

15 0.2

0.25 0.

30.

35 0.4

0.45 0.

50.

55 0.6

0.65 0.

70.

75 0.8

0.85 0.

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Cor

rect

Rat

e

Simplification Rate

Correct Rate for TS and DP

Correct rate of TS

Correct rate of DP

EfficiencyThe average computing complexity

DP:TS :

20

0

0.5

1

1.5

2

2.5

0.05 0.

10.

15 0.2

0.25 0.

30.

35 0.4

0.45 0.

50.

55 0.6

0.65 0.

70.

75 0.8

0.85 0.

90.

95

Seco

ns(s

)

Simplification Rate

Time cost of TS and DP

Time of TS

Time of DP

𝑂(𝑛∗𝑙𝑜𝑔𝑛∗𝑙𝑜𝑔𝑚) 𝑂(𝑛∗𝑙𝑜𝑔𝑚)

Conclusion & Future work

ConclusionTS care not only the skeleton information but also the semantic meanings of travel (user behaviors)TS is more effective than DP in simplifying travel routesTS is also more efficient than DP

Future workDynamic simplification:

display the top k points in present viewCost lots of online computation

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Thanks!

yuzheng@microsoft.com

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