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Shape-based Similarity Shape-based Similarity Query forQuery forTrajectory of Mobile Trajectory of Mobile ObjectObject

Shape-based Similarity Shape-based Similarity Query forQuery forTrajectory of Mobile Trajectory of Mobile ObjectObject

NTT Communication NTT Communication Science Laboratories, Science Laboratories, NTT Corporation, JAPAN.NTT Corporation, JAPAN.

Yutaka Yanagisawa Yutaka Yanagisawa Jun-ichi AkahaniJun-ichi AkahaniTetsuji SatohTetsuji Satoh

“Rickshaw” (NARA/KYOTO)

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BackgroundBackgroundBackgroundBackground• The Recent technologies allow us to track moving

objects using highly accurate positioning devices.• There are many applications using such location

information have been developed.– Navigation Systems, Location-based Information Systems,

etc.

A Navigation SystemDigital City Kyoto:

A Location-based Information System

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Motion Pattern AnalysisMotion Pattern AnalysisMotion Pattern AnalysisMotion Pattern Analysis

• Motion pattern analysis is one of the most interesting technologies of these applications.– By analyzing their motion patterns, it is possible to extract

the behavioral characteristics of moving objects.– The applications can predict the future behavior of the

moving objects using extracted characteristics.

• Single Motion Analysis– focuses on the statistical characteristics of a moving object.

• Relative Motion Analysis– focuses on the similarity between motion patterns.

We discuss the approach based on the similarity of trajectory shapes because it is a simple and intuitive approach.

/ 314Similarity of Trajectory Similarity of Trajectory ShapesShapes

Similarity of Trajectory Similarity of Trajectory ShapesShapes

Entrance Exit

A

B

C

D

Show informationabout B, C, and

D.

The trajectories of visitors are stored in a database.

It retrieves trajectories that are similar to A …

It is possible to predict the future route of the new visitor.

• This approach is called shape-based approach.

Exhibition hall

An example of an information providing system.

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ProblemProblemProblemProblem• However, there are few database systems

which can search trajectories based on shapes.– Many database systems retrieve moving objects

based on only “distance”.

D1

L L1

L2D2

X

Y The minimum distance between L and L2 is less than the distance between L and L1.

However, L2 is more similar in shape to L than L1 intuitively.

Not appropriate for shape-based approach

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Our ApproachesOur ApproachesOur ApproachesOur Approaches

• We propose a shape-based similarity query for searching trajectories from moving object databases.

• Moreover, we present an efficient indexing method for retrieving moving objects based on our proposed query.

Shape-based Similarity Shape-based Similarity QueryQuery

Shape-based Similarity Shape-based Similarity QueryQuery

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Data Model for TrajectoryData Model for TrajectoryData Model for TrajectoryData Model for Trajectory• In real world, a trajectory of a moving object can be

modeled as a continuous line in space.– However, positioning devices can not track a moving

object continuously.

• In our work, a trajectory is stored as a sequence of points (discrete line) in databases.– This model is used as a popular data model.

In Real World In Databases

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A Similarity of Time Series A Similarity of Time Series DataData


• The key idea have been proposed in the technique for time series database.

• The similarity between two time series data is defined as the Euclidean distance between the points in n dimensional space.

W = <w1, w2, …, w9>W’ = <w’1, w’2, …, w’9>

t

x

t1t8 t

x

D(W, W’)

w1w2

w9

w’1

w’9

)',( WWD

n

iii ww

0

2)'(

(n=9)

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1

2

3

4

5W = <2, 3, 4, 3>W’ = <1, 1, 2, 3>

1

2

3

4

5

1 2

20

Distance between W and W’ is

2222 0221

= 3

• The key idea have been proposed in the techniques for time series database.


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1

2

3

4

5W = <2, 2, 2, 3>W’ = <2, 2, 2, 3>

In this case, the distance is zero.

Smaller distance means higher similarity

• The key idea have been proposed in the techniques for time series database.


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A Similarity of Time Series A Similarity of Time Series Data Data

A Similarity of Time Series A Similarity of Time Series Data Data

• The distance fits to intuitive similarity of line shapes.

• There is an effective search algorithm to calculate this distance.

• We will extend the similarity for trajectory in 2 or more dimensional space.

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Our Proposed Similarity Our Proposed Similarity of Trajectoriesof Trajectories

Our Proposed Similarity Our Proposed Similarity of Trajectoriesof Trajectories

• The similarity of trajectories can be defined as an extension of the distance of time series data.– The distance can be given as the following expression.

X

Y

’

p7

p1

p’7

p’1

)',( D

22 )'()'()',( iiiiii yyxxppD

n

iii ppD

1

2)',(

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Shape-based Similarity QueryShape-based Similarity Queryfor Trajectoriesfor Trajectories


• We define a shape-based similarity query for trajectories as a subsequence matching query.– Because the length of trajectories are often difference.

＋

Stored trajectoriesStored trajectories A given trajectoryA given trajectory Answer trajectoriesAnswer trajectories

SSQ(, , ) : A set of stored trajectories in database.: A trajectory to be compared.: The distance from .

Answer a: A set of sub-trajectories

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- The database calculates the distance between the given trajectory and each sub-trajectory.

- If the distance is less than the given distance , the database adds the sub-trajectory to the answer set of trajectories a.

A Given Trajectory

An Answer Sub-Trajectory

IndexingIndexingIndexingIndexing

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ApproachApproachApproachApproach• The existing spatial structures are appropriate for

retrieving an object based on the distance.– However, these structures have no method for searching

the data based on the similarity between trajectories.

We extend the spatial data structure for our proposed query.

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An Efficient Calculation ProcessAn Efficient Calculation Processfor the Shape-based Similarity: 1for the Shape-based Similarity: 1An Efficient Calculation ProcessAn Efficient Calculation Process

for the Shape-based Similarity: 1for the Shape-based Similarity: 1• The essential idea was presented as a PAA:

Piecewise Aggregate Approximation [Keogh01]．– PAA is an efficient method of approximating the time series

data for a similarity search.

W

W ‘

t

xUsing the `average sequences’ of a sub-sequences.

t

x

1w 2w3w

1'w 2'w 3'w

W

'W

(N=3)

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for the Shape-based Similarity: 2for the Shape-based Similarity: 2• The distance between the average

sequences is the lower bound of the distance between the original two sequences.

W

W’

t

x

t

D( W, W’)D( W, W’)

)',()',( WWDWWD

By comparing average sequences, we can know the lower bound of the distance between original sequences.

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for the Shape-based Similarity: 3for the Shape-based Similarity: 3• In the case of trajectories, the distance between

the center points of trajectories is the lower bound of the distance between the original trajectories.

X

Y

L’

L

v1

v7

v’1

v’7

Calculating center points

X

Y

The distance between thesecenter points is the lower bound of the original distance.

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• For making indexes, the database calculates the center points of sub-trajectories.– The length of each sub-trajectory must be fixed

to the system parameter N.– In this example, N is four.

X

Y

Y

p1

p8

The center point offrom p5 to p8

The center point offrom p1 to p4

Combination of PAA and Combination of PAA and Spatial Data Structure: 1Spatial Data Structure: 1Combination of PAA and Combination of PAA and Spatial Data Structure: 1Spatial Data Structure: 1

p2

p3p4

p5

p6

p7

X

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Combination of PAA and Combination of PAA and Spatial Data Structure: 2Spatial Data Structure: 2Combination of PAA and Combination of PAA and Spatial Data Structure: 2Spatial Data Structure: 2

• Next, the database makes indexes to the points using a traditional spatial data structure.– Our implemented system makes an index to every

center point using R+-Tree.

X

Y

XX

YY

Normal R+-TreeOur Proposed Index Structure

The database can search objects based on the similarity of trajectories using the spatial data structure.

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Query Processing: 1Query Processing: 1Query Processing: 1Query Processing: 1

• When a SSQ(,Q,) is given, the database calculates the center point of Q at first.– Suppose that the length of stored center points is

fixed to 4 (N=4) in the following example.

Q

X

Y

X

Y

pQ is the center point of a given trajectory.

pQ

If a query SSQ(,Q,) is given..

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X

YA

B

C

B C

A

An index tree (R+-Tree)

pQ

Candidate points

The region within the distance from pQ

• Next, the database searches stored points within the distance from the calculated point pQ using the spatial data structure.

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X

Y

pQ

• Finally, the database checks the distance between a given trajectory Q and each candidate trajectory.

• If the distance is less than a given threshold , the candidate trajectory is added to the answer set a.

Q

Y

p1

p2

1

1 is the original trajectory of p1.

),( 1QDIf ,

1 is added to a

Performance StudyPerformance StudyPerformance StudyPerformance Study

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Performance StudyPerformance StudyPerformance StudyPerformance Study

• We conducted an experiment for evaluating our proposed query and indexing method.– Measuring the processing time for retrieving

trajectories required by a shape-based similarity query.

• For this evaluation, two types of trajectories are stored in a database.– tracked by GPS and generated by a simulator.

We compared the processing time using both methods:

- Our indexing method,- A spatial data structure (R+-Tree).

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Trajectory Data: 1Trajectory Data: 1Trajectory Data: 1Trajectory Data: 1

RickshawA GPS Receiver (eTrex/GARMIN)

• This is an example of trajectory data captured by GPS receivers on rickshaws (in Nara city).– Rickshaw is tour guide, they work in Nara / Kyoto.

A trajectory of a rickshaw in all day

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Trajectory Data: 2Trajectory Data: 2Trajectory Data: 2Trajectory Data: 2

• This figure displays trajectories generated by our implemented simulator.

The simulator can generate trajectoriessuch that people walk on a plane freely.

Velocity and direction of each object are given as random values. But the changes of these values are slow and continuous.

/ 3130The Result of the The Result of the ExperimentExperiment

The Result of the The Result of the ExperimentExperiment

4 8 16 32 64 128 2562000

8000

320000

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

Time(msec)

Length

Points

4 8 16 32 64 128 2562000

8000

320000

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

Time(msec)

Length

Points

Using our index structure Using R+-Tree

For retrieving longer trajectories from stored data, our proposed method has high advantages to existing methods.

The processing time to calculate 10 random queries is displayed:

Amount of Stored Points

Length of Q (=N)

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ConclusionsConclusionsConclusionsConclusions

• We have proposed a shape-based similarity query to find moving objects.– Database users can find moving objects for

analyzing their motion patterns.

• Moreover, we have presented an effective indexing method to search for the trajectories required by our proposed queries.– We demonstrated the advantage of our proposed

method to existing spatial data structures.

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Future WorkFuture WorkFuture WorkFuture Work

[Human Tracking by using Laser Scanners]- University of Tokyo (Dr. Zhao and Prof. Shibasaki)- Captured at Geoinformation Forum Japan 2002 (32.096 people visited)

[Motion Capture Data]- Tokyo University of Technology (Creative Labo)- 76 moving points on bodies (120fps)- Playing football and judo

• We will evaluate our proposed method using these data.

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