An Interactive-Voting Based Map Matching Algorithm

Jing Yuan1, Yu Zheng2, Chengyang Zhang3, Xing Xie2 and Guangzhong Sun1

1University of Science and Technology of China2Microsoft Research Asia

3University of North Texas

Outline

• Introduction• Our Contributions• Related Work• Interactive-Voting Algorithm• Evaluation• Conclusion and Future Work

Introduction

• Popular GPS-enabled devices enable us to collect large amount of GPS trajectory data

Introduction

• These data are often not precise–Measurement error: caused by limitation of

devices– Sampling error: uncertainty introduced by

sampling– It is desirable to match GPS points with road

segments on the map

Introduction

• In practice there exists large amount of low-sampling-rate GPS trajectories

Distribution of sampling intervals of Beijing taxi dataset

0~1 minutes34%

1~2 minutes8%

2~6 minutes86%

6~20 minutes14%

2~20 minutes58%

Outline

• Introduction• Our Contributions• Related Work• Interactive-Voting Algorithm• Evaluation• Conclusion and Future Work

Our Contributions

• We study the interactive influence of the GPS points and propose a novel voting-based IVMM algorithm

• Extensive experiments are conducted on real datasets

• The evaluation results demonstrate the effectiveness and efficiency of our approach for map-matching of low-sampling rate GPS trajectories

Outline

• Introduction• Our Contributions• Related Work• Interactive-Voting Algorithm• Evaluation• Conclusion and Future Work

Related Work

• Information utilized in the input data– Geometric, topological, probabilistic, …– Usually performs poor for low-sampling rate

trajectories• Range of sampling points considered– Incremental/Local algorithms– Global algorithms

A screen shot of ST-Matching result (green pushpins are the matched points of the red trace)

Related Work

• Sampling density of the tracking data– Dense-sampling-rate approach– Low-sampling-rate approach

A screen shot of ST-Matching result (green pushpins are the matched points of the red trace)

Related Work

• Problem with ST-Matching– The similarity function only considers two

adjacent candidate points– The influence of points is not weighted– The mutual influence is not considered

Outline

• Introduction• Our Contributions• Related Work• Interactive-Voting Algorithm• Evaluation• Conclusion and Future Work

Problem Definition

• Given a low-sampling rate GPS trajectory T and a road network G(V,E), find the path P from G that matches T with its real path.

Key Insights

• Position context influence

• Mutual influence• Weighted

influence a

b c d e

f

System Overview

Candidate Road Segments / Points

Range Query

Spatial Analysis

Candidate Graph

Static Score Matrix Building Find SequenceRoad Network

I. Candidates Preparation II. Position Context Analysis III. Mutual Influence Modeling IV. Interactive Voting

Raw GPS data

Temporal Analysis Weighted Influence Modeling

Weighted Score Matrix

Parallel Voting

Matched Road Segments

Step 1: Candidate Preparation

• Candidate Road Segments (CRS) • Candidate Points (CP)

• Candidate Graph G’=(V’,E’)

𝑒𝑖3

𝑒𝑖1

𝑒𝑖2

𝑐𝑖3

𝑝𝑖

𝑐𝑖2

𝑐𝑖1

r

11c

21c

31c

12c

22c

13c

23c

14c

24c

34c

1p

2p3p

4p11e

21e

31e

12e

22e

13e

23e 1

4e

24e

34e

p1's candidates p2's candidates p3's candidates p4's candidates

11c

21c

31c

12c

22c

13c

23c

14c

24c

34c

Step 2: Position Context Analysis

• Spatial Analysis– Measure the similarity between the candidate paths

with the shortest path of two adjacent candidate points

11

1, ( , )

.t s i ii i

i t i s

dV c c

w

'1, ( , )

11 2' 2

1, ( , )1 1

( . )

( . )

ki t i sut s u

t i ik k

i t i suu u

e v vF c c

e v v

1 1 1t s t s t si i s i i t i iF c c F c c F c c

p1's candidates p2's candidates p3's candidates p4's candidates

11c

21c

31c

12c

22c

13c

23c

14c

24c

34c

Step 2: Position Context Analysis

• Spatial Analysis

11

1, ( , )

.t s i ii i

i t i s

dV c c

w

1 1 1t s t s t si i s i i t i iF c c F c c F c c

Step 2: Position Context Analysis

• Temporal Analysis– Considers the speed constraints of the road segment

• Spatial Temporal Function

11

1, ( , )

.t s i ii i

i t i s

dV c c

w

1 1 1t s t s t si i s i i t i iF c c F c c F c c

Step 3: Mutual Influence Modeling

• Static Score Matrix– represents the probability of candidate points to be

correct when only considering two consecutive points– e.g.

1 2 1 1

2 31 1 1 1

, , , , , 2,3,...

, , ,

i i ni i i i i

n

diag w w w w w i n

w w w

iW

W ( ( , )) 1,2,...ji i jw f dist p p j n

2 3, , , 1,2,3,...diag i n ni i i i iΦ W M Φ Φ Φ

Step 3: Mutual Influence Modeling

• Distance Weight Matrix– a (n-1) dimensional diagonal matrix for each sampling

point– The value of each element is determined by a distance-

based function f– e.g.

w1=diag{1/2,1/4,1/8} ( ( , )) 1,2,...ji i jw f dist p p j n

2 3, , , 1,2,3,...diag i n ni i i i iΦ W M Φ Φ Φ

Step 3: Mutual Influence Modeling

• Weighted Score Matrix– probability when remote points are also considered– e.g.

1 2 1 1

2 31 1 1 1

, , , , , 2,3,...

, , ,

i i ni i i i i

n

diag w w w w w i n

w w w

iW

W ( ( , )) 1,2,...ji i jw f dist p p j n

2 3, , , 1,2,3,...diag i n ni i i i iΦ W M Φ Φ Φ

Step 4: Interactive Voting

• Interactive Voting Scheme– Each candidate point determines an optimal path

based on weighted score matrix– Each point on the best path gets a vote from that

candidate point– The points with most votes are selected– Can be processed in parallel

Step 4: Interactive Voting

• Find optimal path for one candidate point– The path with largest weighted score summation– Dynamic programming– A value is obtained to break the tie of voting

Step 4: Interactive Voting

• Find Optimal Path

• Voting results

• Matching result

Outline

• Introduction• Our Contributions• Related Work• Interactive-Voting Algorithm• Evaluation• Conclusion and Future Work

Evaluation

• Dataset– Beijing road network– 26 GPS traces from Geolife System

• Evaluation approach (Correct Matching Percentage)

0

2

4

6

8

10

12

0~50 50~100 100~200 200~450

Cou

nts

Number of Sampling Points

012345678

0~10 10~20 20~30 30~40 40~50 50~60 60~

Cou

nts

Average Vehicle Speed (km/h)

CMP = Correct matched pointsNumber of points to be matched× 100%

Evaluation Results

• Visualized results

IVMM

IVMM

ST

ST

Evaluation Results

• Accuracy

50

55

60

65

70

75

80

85

0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5

Cor

rect

Mat

chin

g Pe

rcen

tage

(%)

Sampling Interval (minute)

ST-Matching

IVMM(β=7km)

Evaluation Results

• Running time

0 50 100 150 200

0.51.52.53.54.55.56.57.58.59.5

10.5

Running Time(s)

Sam

plin

g In

terv

al (m

inut

e)

IVMM

ST-Matching

Evaluation Results

• Impact of different distance weight functions

60

62

64

66

68

70

72

2.5 4.5 6.5 8.5 10.5

Cor

rect

mat

chin

g pe

rcen

tage

(%)

Sampling Interval (minute)

IVMM(β=10)

IVMM (exponential)

IVMM (none)

IVMM (linear)

Outline

• Introduction• Our Contributions• Related Work• Interactive-Voting Algorithm• Evaluation• Conclusion and Future Work

Conclusion and Future Work

• Conclusion– Modeling the mutual influence of the GPS sampling points – A voting-based approach for map matching low-sampling-rate GPS

traces– Evaluation with real world GPS traces

• Future Work– The mutual influence related with the topology of the road network– Combination with other statistical methods, e.g., HMM and CRF

models

Thank You!