Analyzing Trajectory Data

(1)

Analyzing Trajectory Data

Gerasimos Marketos

Information Systems Lab (InfoLab)

University of Piraeus (UniPi), Greece

http://infolab.cs.unipi.gr

Free University of Bolzano

20/3/2009

(2)



Preliminaries



Trajectory Data Warehousing



Our framework for trajectory analysis



Reconstructing trajectories



ETL processing



Addressing the distinct count problem



Traffic Mining



Modeling traffic flow in a road network



Our framework for mining traffic patterns



Detecting traffic flow in a road network

(3)

G. Marketos: Analyzing Trajectory Data 3

(4)

The big picture (the GeoPKDD project)

Traffic Management Accessibility of services Mobility evolution Urban planning …. interpretation visualization trajectory reconstruction p(x)=0.02 warehouse interpretation visualization trajectory reconstruction p(x)=0.02 ST patterns Trajectory warehouse Privacy-aware Data mining Bandwidth/Power optimization

Mobile cells planning … Public administration or business companies Telecommunication provider GeoKnowledge

Aggregative Location-based services Privacy enforcement Traffic Management Accessibility of services Mobility evolution Urban planning …. interpretation visualization trajectory reconstruction p(x)=0.02 warehouse interpretation visualization trajectory reconstruction p(x)=0.02 ST patterns Privacy-aware Data mining Bandwidth/Power optimization

Mobile cells planning …

Public administration or business companies

GeoKnowledge

Aggregative Location-based services

(5)

A tour on GeoPKDD



Mobility data management



Acquiring and storing trajectories in MODs



Location-aware querying



Trajectory indexing



Mobility data mining and the geographic KDD process



Trajectory warehousing and OLAP



Mobility data mining and reasoning



Visual analytics for mobility data



Privacy aspects on mobility data

(6)

Key questions (for this talk)



How to

store

and

query

trajectory data?



Database technology is extended: Moving Object Databases



How to

reconstruct

a trajectory from raw logs?



Position devices provide us information just about location points

and not about trajectories



How to

analyze

trajectory data



Data Warehousing technology is adapted to handle trajectory

data



Are there any

spatio-temporal patterns

in my data?



New Data Mining algorithms are needed so as to discover such

patterns

(7)

Mobility Data



Typical structure and size:

N;Time;Lat;Lon;Height;Course;Speed;PDOP;State;NSat

… 8;22/03/07 08:51:52;50.777132;7.205580; 67.6;345.4;21.817;3.8;1808;4 9;22/03/07 08:51:56;50.777352;7.205435; 68.4;35.6;14.223;3.8;1808;4 10;22/03/07 08:51:59;50.777415;7.205543; 68.3;112.7;25.298;3.8;1808;4 11;22/03/07 08:52:03;50.777317;7.205877; 68.8;119.8;32.447;3.8;1808;4 12;22/03/07 08:52:06;50.777185;7.206202; 68.1;124.1;30.058;3.8;1808;4 13;22/03/07 08:52:09;50.777057;7.206522; 67.9;117.7;34.003;3.8;1808;4 14;22/03/07 08:52:12;50.776925;7.206858; 66.9;117.5;37.151;3.8;1808;4 15;22/03/07 08:52:15;50.776813;7.207263; 67.0;99.2;39.188;3.8;1808;4 16;22/03/07 08:52:18;50.776780;7.207745; 68.8;90.6;41.170;3.8;1808;4 17;22/03/07 08:52:21;50.776803;7.208262; 71.1;82.0;35.058;3.8;1808;4 18;22/03/07 08:52:24;50.776832;7.208682; 68.6;117.1;11.371;3.8;1808;4 …

(8)

Location data producers: GSM, GPS, WiFi

) , , ( ),..., , , ( 1 1 1 i i ini ini ini i i x y t x y t T

Location data (id, x, y, t)

are generated

Moving

Object

Database

trajectory data

(obj-id, traj-id, (x, y, t)

*

₎

are reconstructed

Trajectory stream manager +

Trajectory reconstruction

)

,

(

),...,

,

(

1

1 i

i

n

_i

i

n

_i

i

n

_i

i

x

y

t

x

y

t

T

(9)

Moving Objects Databases



The traditional database technology has been extended into

Moving

Object Databases

(MODs) that handle modeling, indexing and

query processing issues for trajectories



Spatial and temporal dimensions are considered as first-class

citizens.



Both past and current (as well as anticipated future) positions of

moving objects are of interest.



Several prototype MODs



DOMINO (Wolfson

et al.) EDBT‟02



PLACE (Mokbel

et al.) VLDB‟04



SECONDO (Güting et. al.) ICDE‟05

(10)

Hermes MOD engine



Built-in ORACLE ORDBMS



Data model: absolute vs. relative location coordinates



Current location as a function in time over the starting

location



linear and arc movement functions



MOD management



Insert / Update / Delete a moving object or a segment of its

trajectory



Functions over trajectories or sets of trajectories



Indexing support



Supported indices: R-tree (for stationary data)

(11)

(12)

(13)

Hermes: trajectory data type



Primitive definition:



Unit_Function =

_d

x

_i

:double, y

_i

:double, x

_e

:double, y

_e

:double, x

_c

:double, y

_c

:double, v:double,

a:double, flag:TypeOfFunction , where



TypeOfFunction={ CONST, PLNML_1, ARC_<1..8> }



Unit_Moving_Point =

_d

p: Period SEC , m: Unit_Function



Moving_Point =

_d

{ tab: set Unit_Moving_Point

| …

constraints

…}

yy' xx' tt' t1 t2 t3 t4 t ε [t1, t2) -> Linear movement t ε [t2, t3) -> Arc movement t5 t ε [t3, t4) -> Const movement t ε [t4, t5) -> Linear movement Y X o YY' XX' (x_t,y_t,t) (x_e,y_e,t_e) (x_i,y_i,t_i) (x_c,y_c)

(14)

t3

t1 t7

t11

t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 t11 t12

TB-Tree support in Hermes MOD engine



TB-Tree Index (Pfoser et al., 2000)



Maintains the „trajectory‟ concept



Each node consists of segments

of a single trajectory



Nodes are linked together in a chain



Effective for trajectory-oriented queries



Implemented in Hermes using

(15)

Trajectory Data Warehousing &

OLAP

(16)

Trajectory data warehousing



The

analysis

of

trajectory data

raises opportunities for discovering

behavioral patterns that can be exploited in various applications



TDW should



extract aggregate information from MOD



support a variety of dimensions (temporal, spatial, thematic, …) and

measures (about space, time and their derivatives)



Storing

measures

associated with facts, concerning the

set of trajs

crossing the cell

aggregate

information in base cells



Challenges



design of a trajectory-oriented data cube



high volume and complex nature of data; special query processing

requirements



extensions of traditional aggregation techniques to produce summary

(17)

Reconstructed trajectory data are stored in MOD

Trajectory data warehousing



A

Trajectory Reconstruction process

is applied on the raw

time-stamped location data in order to generate trajectories, which are then

stored into a MOD



An

Extract-Transform-Load

(

ETL)

procedure

is activated that feeds

the data cube(s) with aggregate information on trajectories



The final step of the process offers

OLAP

(and, eventually, DM)

capabilities over the aggregated information contained in the trajectory

cube model

trajectory data analyst location data producers

Location data (id, x, y, t) are recorded

Aggregates are loaded in the data cube (ETL procedure) Trajectory

Data Cube MOD

Trajectory reconstruction module Analysis over aggregate data is performed (OLAP)

(18)

Related work



Data Warehousing (DW) is widely investigated for conventional,

non-spatial data.



Some research work has been done in the area of Spatial Data

Warehousing (Han et al., 1998).



(Shekhar et al., 2001) extend the idea of cube dimensions so

as to include spatial and non-spatial ones, and of cube

measures so as to represent space regions and/or calculate

numerical data



One step beyond Spatial DW is modeling a TDW (Pelekis et al.,

2007). A simple TDW model is presented in (Orlando et al.,

2007).



The notion of multiple aggregation paths is defined in (Jensen et

al., 2004)



The integration of spatial and temporal dimensions is proposed in

(19)

Conventional DWs



In conventional DWs, measures about entities (e.g. shopping

baskets, customers etc.) refer to a specific base cell that are

formed by the dimensions



distinct objects appear only once at the minimum abstraction

level of the cube

Time

S

tor

e

count

Count of transactions

TV

VCR

PC

1/1

2/1 3/1

…

101

201

301 sum

A transaction cannot be

(20)

Trajectory DW



The challenge: In TDW, measures regarding trajectories may

affect more than one base cell



the same object might affect measures in several base cell due to

its movement (!!)

Time

L

ocat

io

n

count

Count of trajectories

50 < Age

Age 30

30 < Age 50

12.00 13.00 14.00

…

R1

R2

R3

sum

A trajectory can be found

in both base cells (the

distinct counting problem)

(21)



Moving Object Database



Trajectory Data Warehouse



Dimensions:

Spatial,

Temporal, Object Profile



Measures:

count

(trajectories), count (users),

avg (distance traveled), avg

(travel duration), avg (speed),

avg (abs (acceler) )

Sample schemas

OBJECT_PROFILE_DIM PK OBJPROFILE_ID GENDER BIRTHYEAR PROFESSION MARITAL_STATUS DEVICE_TYPE FACT_TBL PK,FK3 INTERVAL_ID PK,FK2 PARTITION_ID PK,FK1 OBJPROFILE_ID COUNT_TRAJECTORIES COUNT_USERS AVG_DISTANCE_TRAVELED AVG_TRAVEL_DURATION AVG_SPEED AVG_ABS_ACCELER SPACE_DIM PK PARTITION_ID PARTITION_GEOMETRY DISTRICT CITY STATE COUNTRY TIME_DIM PK INTERVAL_ID INTERVAL_START INTERVAL_END HOUR DAY MONTH QUARTER YEAR DAY_OF_WEEK RUSH_HOUR

OBJECTS(object-id: identifier, description: text, gender: {M | F}, birth-date: date, profession: text, device-type: text)

RAW_LOCATIONS(object-id: identifier, timestamp: datetime, eastings-x: numeric, northings-y: numeric, altitude-z: numeric)

MOD_TRAJECTORIES (trajectory-id: identifier, object-id:

(22)

Our framework for trajectory analysis



We focus our research on three issues that are critical to

trajectory data warehousing:



The preprocessing phase that deals with the explicit

reconstruction

of the trajectories, which are then stored into a

MOD



Alternative ETL processes

that feed the trajectory data

warehouse



The solutions proposed on the challenging issue of

measure

(23)

G. Marketos: Analyzing Trajectory Data 24 y

t

x

Reconstructing trajectories



Collected raw data represent time-stamped geographical

locations



Apart from storing raw data in the MOD, we are also

interested in reconstructing trajectories:



Raw points arrive in bulk sets



We need a filter that decides if the new series of data is to be

appended to an existing trajectory or not:



Tolerance distance



Temporal gap



Spatial gap



Maximum speed



Maximum noise duration

t

y

(24)

Reconstructing trajectories: parameters



Tolerance distance



The tolerance of the transmitted time-stamped positions. In other

words, it is the

maximum distance between two consecutive

time-stamped positions

of the same object in order for the

object to be

considered

as

stationary

t

y y

t

(25)

Reconstructing trajectories: parameters



Tolerance distance



Temporal gap between trajectories



The

maximum allowed time interval

between two consecutive

time-stamped positions of the same trajectory for a single moving

object

t y y t x x

temporal gap

(26)

Reconstructing trajectories: parameters



Tolerance distance



Temporal gap between trajectories



Spatial gap between trajectories



The

maximum allowed distance

in 2D plane between two

consecutive time-stamped positions of the same trajectory

t

y y

t

x x

(27)

Reconstructing trajectories: parameters



Tolerance distance



Temporal gap between trajectories



Spatial gap between trajectories



Maximum speed



It is used in order to determine whether a reported time-stamped

position must be considered as

noise

and consequently

discarded from the output trajectory

t

y y

t

(28)

Reconstructing trajectories: parameters



Tolerance distance



Temporal gap between trajectories



Spatial gap between trajectories



Maximum speed



Maximum noise duration



The

maximum duration of a noisy part

of a trajectory. Any

sequence of noisy time-stamped positions of the same object will

result in a new trajectory given that its duration exceeds

noise

_max

t

y y

t

(29)

Reconstructing trajectories: algorithm

Algorithm Trajectory-Reconstruction

(PartialTrajectories List, P Point, OId ObjectId) 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32.

IF NOT PartialTrajectories.Contains(OId) THEN CTrajectory=New Trajectory;

CTrajectory.AddPoint(P);

PartialTrajectories.Add(CTrajectory);

ELSE

CTrajectory=PartialTrajectories(OId);

IF Distance(CTrajectory.LastPoint,P)<= DTOL THEN

IF P.T – CTrajectory.LastPoint.T > gapTime THEN

Report Ctrajectory.LastPoint;

CTrajectory.Id=CTrajectory.Id+1; CTrajectory.AddPoint(P);

ENDIF

ELSEIF Speed(CTrajectory.LastPoint,P)> Vmax THEN

IF P.T – CTrajectory.LastPoint.T > noisemax THEN

Report CTrajectory.Noise; ELSE

CTrajectory.AddNoise(P); ENDIF

ELSEIF Distance(CTrajectory.LastPoint,P)> gapspace THEN

Report Ctrajectory.LastPoint; CTrajectory.Id=CTrajectory.Id+1; CTrajectory.AddPoint(P);

ELSE

IF P.T – CTrajectory.LastPoint.T > gapTime THEN

Report Ctrajectory.LastPoint; CTrajectory.Id=CTrajectory.Id+1; CTrajectory.AddPoint(P); ELSE CTrajectory.AddPoint(P); ENDIF ENDIF ENDIF



As a first step (lines 1-6),

the algorithm checks

whether the object has been

processed



if so, it retrieves its partial

trajectory from the

corresponding list



otherwise, it creates a new

trajectory and adds it to list



Then (lines 7-31), it

compares the incoming

point P with the tail of the

partial trajectory (LastPoint)

by applying the trajectory

reconstruction parameters

(30)

Our framework for trajectory analysis



We focus our research on three issues that are critical to

trajectory data warehousing:



The preprocessing phase that deals with the explicit

reconstruction

of

the trajectories, which are then stored into a MOD



Alternative ETL processes

that feed the trajectory

data warehouse



The solutions proposed on the challenging issue of

measure

(31)

ETL processing: loading



Loading data into the dimension tables



straightforward



Loading data into the fact table



complex



Fill in the measures with the appropriate numeric values



In order to calculate the measures, we have to extract the

portions of the trajectories that fit into the base cells of the cube



We propose two alternative solutions to this problem:



cell-oriented



trajectory-oriented

y

(32)

ETL processing: measures

Measure

Formula

COUNT_

TRAJECTORIES

count all distinct trajectory ids that pass through

base cell (bc)

COUNT_USERS

count all the distinct object ids that pass through

bc

AVG_DISTANCE_

TRAVELED

AVG_TRAVEL_

DURATION

AVG_SPEED

AVG_ABS_

ACCELER

) ( _ ) ( _ ) ( _ _ bc ES TRAJECTORI COUNT bc DISTANCE SUM bc TRAVELED DISTANCE AVG bc TP i i

TP

len

bc

DISTANCE

SUM

_

(

)

(

)

) ( _ ) ( _ ) ( _ _ bc ES TRAJECTORI COUNT bc DURATION SUM bc DURATION TRAVEL AVG bc TP i i TP lifespan bc DURATION SUM_ ( ) ( ) ) ( _ ) ( _ ) ( _ bc ES TRAJECTORI COUNT bc SPEED SUM bc SPEED AVG bc TP i i i lifespanTP TP len bc SPEED SUM ) ( ) ( ) ( _ ) ( _ ) ( _ _ ) ( _ _ bc ES TRAJECTORI COUNT bc ACCELER ABS SUM bc ACCELER ABS AVG TP speed TP speed ( ) ( )

(33)

ETL processing: algorithms

Cell-oriented approach

(COA)



Search for the portions of trajectories

that they reside inside a

spatiotemporal cell



Perform a

spatiotemporal

range query

that returns the

portions of trajectories that

satisfy the range constraints



This is efficiently supported by

the

TB-tree



Decompose the trajectory portions

with respect to the user profiles they

belong to



Compute measures for this cell



Repeat for the next cells

x

y

COUNT

_{_}

TRAJECTORIES

_{= 2}

COUNT

_{_}

USERS

_{= 2}

(34)

COUNT

_{_}

TRAJECTORIES

_{= 1}

COUNT

_{_}

USERS

_{= 1}

…

ETL processing: algorithms

Trajectory-oriented approach

(TOA)



Discover the spatiotemporal cells

where each trajectory resides in



In order to avoid checking all

cells, use the trajectory MBR



Identify the cells that overlap with the

MBR and contain portions of the

trajectory



Compute measures for each cell

…



Repeat for the next trajectories

…

x

y

COUNT

_{_}

TRAJECTORIES

_{= 2}

COUNT

_{_}

USERS

_{= 2}

…

(35)

Our framework for trajectory analysis



We focus our research on three issues that are critical to

trajectory data warehousing:



The preprocessing phase that deals with the explicit

reconstruction

of

the trajectories, which are then stored into a MOD



Alternative ETL processes

that feed the trajectory data warehouse



The solutions proposed on the challenging issue of

(36)

The distinct count problem: definition



During the ETL process, measures can be computed in an

accurate way by executing MOD queries



Once the fact table has been fed, aggregate-only information is

stored inside the TDW (no trajectory / user ids)



When rolling up,

COUNT_USERS, COUNT_TRAJECTORIES

and,

hence, all other measures defined over

COUNT_TRAJECTORIES

are subject to the distinct count problem (Tao et al., 2004):



if an object remains in the query region

for several timestamps during the query

interval, instead of counting this object

once, it is counted multiple times in the

result

y

(37)

G. Marketos: Analyzing Trajectory Data

38

The distinct count problem: solution

(1/3)



We store in the base cells (

C

_(x,y),t,p

) a tuple of auxiliary

measures that help us correct the errors due to the duplicates

when rolling-up:



C

_(x,y),t,p

.

Traj

: number of distinct trajectories of profile

p

intersecting the cell



C

_(x,y),t,p

.

cross-x

: number of distinct trajectories of profile

p

crossing the

spatial

border between

C

_(x-1,y),t,p

and

C

_(x,y),t,p



C

_(x,y),t,p

.

cross-y

: number of distinct trajectories of profile

p

crossing the

spatial

border between

C

_(x,y-1),t,p

and

C

_(x,y),t,p



C

_(x,y),t,p

.

cross-t

: number of distinct trajectories of profile p crossing

the

temporal

border between

C

_(x,y),t-1,p

and

C

_(x,y),t,p

X

Y

T

(38)

The distinct count problem: solution

(2/3)



Let

C

_{(x’,y’),t’,p’}

be a cell consisting of the union of two adjacent

cells (i.e.

C

_(x,y),t.p

C

_(x+1,y),t,p

)



In order to compute the

number of distinct trajectories

:

C

_{(x’,y’),t’,p’}

.

Traj = C

_(x,y),t,p

.

Traj + C

_(x+1,y),t,p

.

Traj – C

_(x+1,y),t,p

.

cross-x



application of the well-known Inclusion/Exclusion principle for

sets: A B = A + B

A B



BUT

in some cases it holds that

C

_(x+1,y),t,p

.

cross-x

A B



(39)

The distinct count problem: solution

(3/3)

C

_x,y,t,p

C

_x+1,y,t,p

C

_x,y+1,t,p

C

_x+1,y+1,t,p

(a)

C

_x,y,t,p

C

_x+1,y,t,p

C

_x,y+1,t,p

C

_x+1,y+1,t,p

(b)

Correct!

Not Correct!

C

_x,y,t,p

.Traj

=

1 C

_x+1,y,t,p

.Traj

=

1 C

_x+1,y,t,p

.cross-x

=

1 C

_x+1,y,t,p

.cross-x

=

0 Compute the number of distinct trajectories:

(40)

Conclusions (for this part)



We explored solutions for the efficient and effective

development of trajectory warehouses



Related work does not include research work on the complete

flow of processes in a TDW



In particular, we discussed about techniques for:



the solution of the

trajectory reconstruction

problem



efficient

ETL support

for trajectory data



handling measure aggregation issues, with a special attention to

(41)

Future work



Extend the proposed framework by applying OLAP analysis

and DM techniques over the aggregated data



Examine new measures for TDW, specifically suited for

trajectories. Two examples:



A

typical trajectory

describing the trend of movement within a cell

(42)

(43)

The ‘traffic’ problem and challenges



Traffic in cities is a well-known problem:



the majority of people living in large cities and use cars for their

transportation



the number of cars moving in a city increases from year to year



Recently, the technology achievements allow us to collect

huge amount of traffic related data:



mobile phones, traffic cameras, sensors, GPS devices …



How can we exploit this huge volume of data so as to gain

insights on the traffic problem?



The focus of our work is to detect how the different road segments of the

(44)

Related work



(Liu et al, 2006), proposed a distributed traffic stream mining

system



they focus on description of the distributed traffic stream system,

rather on the discovery of traffic related patterns



(Li et al., 2007) proposed a technique for the discovery of hot

routes in a road network



They introduced a density-based algorithm, called FlowScan



The algorithm requires the trajectories of the objects that move

(45)

How can the road segments be related? - 1

(46)

How can the road segments be related? - 2

Syngrou Ave.

Poseidonos Ave.

(47)

How can the road segments be related? - 3

Mesogeion Ave.

Kifissias Ave.

(48)

Network Traffic



We consider a fixed network consisting of a set of

non-overlapping regions



regions = road intersections or landmarks of interest

R

₄

R

₃

(49)

Network Graph



The network is modeled as a directed graph G=(V,E)



nodes V



regions



edges E



direct connections between regions

R

₃

R

₁

R

₇

R

₆

R

₁₁

R

₁₀

R

₉

R

₁₅

R

₁₄

R

₁₃

R

₄

R

₈

R

₁₂

R

₁₆

R

₂

R

₅

(50)

Capturing traffic through sensors



Each edge e=(v, v‟) is equipped with sensor technology that

captures the movement from region v to region v‟.



Definition: The

traffic series of a sensor

s

S during a time

period [t

_s

, t

_e

] consists of the number of cars passed through

this sensor during this period, recorded at Δt intervals and

ordered in time:



TS

_s

= {v

_i

, t

_i

}, t

_s

≤ t

_i

≤ t

_e

, Δt=t

_i

-t

_i-1

the transmission rate

of the sensor

v’

v

time

150 ₁₀₀

80 …

90 t

_s

t

_s

+Δ

t

_e

t

_s

+2

Δt

…

(51)

Network Traffic

R

₃

R

₁

R

₇

R

₆

R

₁₁

R

₁₀

R

₉

R

₁₅

R

₁₄

R

₁₃

R

₄

R

₈

R

₁₂

R

₁₆

R

₂

R

₅

(52)

Similarity between edges: value distance



Let e

₁

, e

₂

be two network edges and let

TS

₁

={(v

_1i

,t

_i

)}, TS

₂

={(v

_2i

,t

_i

)}

be their corresponding traffic series, t

_i

[t

_s

, t

_e

]



Definition: The

value-based distance

between e

₁

, e

₂

during

periods p and p‟ is given by the absolute distance of their

corresponding traffic series TS

₁

, TS

₂

at these periods:

)

,

(

)

,

(

₁

p

₂

p

'

_value

₁

p

₂

p

'

value

e

dis

TS

dis

(53)

Similarity between edges: shape distance



Value-based distance is not appropriate for shape similarity

task since it is sensible to:



different baselines



e.g. one series fluctuating around 100 and the other series fluctuating

around 30



different scales



e.g. one series having a small amplitude between 90 and 100 and the other

series having a larger amplitude between 20 and 40



To deal with this problem, different techniques can be

applied for comparing time series, e.g.:



Dynamic Time Warping that allows us to compare time series

either on the same or adjacent time periods



Correlation-Coefficient measure

(54)



Traffic propagation



traffic from e

₁₂

propagates

to e

₂₃



This might indicate objects that continue moving

in a highway



Condition:



Traffic split/ spread



traffic from e

₁₂

splits into e

₂₃

and e

₂₆



This might indicate objects that leave a highway

and follow different directions to their destination



Conditions:



Traffic merge



traffic to e

₂₃

merges traffic from e

₁₂

and e

₆₂ 

This might indicate objects that enter a highway

from different directions



Conditions:

Traffic relationships

R

₃

R

₁

R

₇

R

₆

R

₂

R

₅

R

₄

R

₈

e

₂₃

e

₁₂

R

₃

R

₁

R

₇

R

₆

R

₂

R

₅

R

₄

R

₈

e

₂₃

e

₁₂

e

₂₆

R

₃

R

₁

R

₇

R

₆

R

₂

R

₅

R

₄

R

₈

e

₂₃

e

₁₂

e

₆₂ value p e p e value

TS

dis

(

,

'

)

23 12 shape p e e p e shape

TS

dis

(

,

'_,

)

62 23 12 value p e p e p e value

TS

dis

(

,

(

'

,

'

))

26 23 12 shape p e e p e shape

TS

dis

(

,

'_,

)

62 12 23 p p p

TS

dis

((

'

,

'

),

,

)

(55)

Traffic relationships



Traffic sink



traffic in e

₁₂

is sank because there is

no propagation or split relationship

with its outgoing edges



Traffic source



traffic starts (source) from e

₂₃

because there is no propagation or

merge relationship with its incoming

edges

R

₃

R

₁

R

₇

R

₆

R

₂

R

₅

R

₄

R

₈

e

₁₂

R

₃

R

₁

R

₇

R

₆

R

₂

R

₅

R

₄

R

₈

e

₂₃

e

₃₄

(56)

Conclusions (for this part)



We consider the problem of mining traffic flow in a road

network monitored through sensors placed at regions of

interest (crossroads, etc.).



We employ edge similarity measures based on time series

comparison

(57)

Thank you!

Questions?

Acknowledgement:

Research partially supported by EU

under the GeoPKDD (Geographic Privacy-aware

Knowledge Discovery and Delivery)

(58)

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 Jensen, C.S., Kligys, A., Pedersen, T.B., Dyreson, C.E., and Timko, I. Multidimensional data modeling for location-based services, The VLDB Journal, 13:1–21, 2004.

 Li, X., Han, J., Lee, J.-G. and Gonzalez, H.: “Traffic density-based discovery of hot routes in road networks.” in

Proc. 10th International Symposium on Spatial and Temporal Databases., 2007.

 Liu, Y., Choudhary, A. N., Zhou, J., and Khokhar, A. A.: “A scalable distributed stream mining system for highway

traffic data.” in Proc. 10th European Conference on Principles and Practice of Knowledge Discovery in Databases, 2006, pp. 309–321.

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Warehouses. Proc. DaWaK, 2007.

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Towards Trajectory Data Warehouses. Chapter in Mobility, Data Mining and Privacy: Geographic Knowledge Discovery. Springer-Verlag. 2008.

 Pfoser, D., Jensen, C.S., and Theodoridis, Y. Novel Approaches to the Indexing of Moving Object Trajectories, Proc. VLDB, 2000.

 Shekhar, S.., Lu, C., Tan, X., Chawla, S., Vatsavai, R. Map Cube: a Visualization Tool for Spatial Data Warehouses,

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 Tao, Y., Kollios, G., Considine, J., Li, F., and Papadias, D. Spatio-Temporal Aggregation Using Sketches. Proc. ICDE, 2004.

(59)

Selected literature on …



Mobility Data Modeling & MOD engines

 Nikos Pelekis, Elias Frentzos, Nikos Giatrakos, Yannis Theodoridis: HERMES: aggregative LBS via a

trajectory DB engine. SIGMOD Conference 2008: 1255-1258

 Nikos Pelekis, Yannis Theodoridis, Spyros Vosinakis, Themis Panayiotopoulos: Hermes - A Framework for

Location-Based Data Management. EDBT 2006: 1130-1134

 Güting, R.H. et al. (2000) A Foundation for Representing and Querying Moving Objects. ACM Transactions

on Database Systems, 25(1):1-42.

 Karimi, H. and X. Liu (2003) A Predictive Location Model for Location-Based Services, Proceedings of

ACM-GIS.

 Pelekis, N. et al. (2005) An Oracle Data Cartridge for Moving Objects. UNIPI-ISL-TR-2005-01, Univ. of

Piraeus. Retrieved from http://infolab.cs.unipi.gr/

 Schlieder, C. et al. (2001) Location Modeling for Intentional Behavior in Spatial Partonomies. Proceedings of

Location Modeling for Ubiquitous Computing Workshop.

 Sistla, P. et al. (1997) Modeling and Querying Moving Objects. Proceedings of IEEE ICDE Conference.  Wolfson, O. et al. (1998) Moving Objects Databases: Issues and Solutions. Proceedings of SSDBM

(60)

Selected literature on …



Mobility Data Warehousing

 Han, J., Stefanovic, N., and Koperski, K. Selective Materialization: An Efficient Method for Spatial Data Cube

Construction. Proc. PAKDD, 1998.

 Jensen, C.S., Kligys, A., Pedersen, T.B., Dyreson, C.E., and Timko, I. Multidimensional data modeling for

location-based services, The VLDB Journal, 13:1–21, 2004.

 Leonardi, L., Orlando, S., Raffaetà, A., Roncato, A. and Silvestri, C. Frequent Spatio-Temporal Patterns in

Trajectory Data Warehouses. Proceedings of 24th Annual ACM Symposium on Applied Computing, 2009

 Marketos, G., Frentzos, E., Ntoutsi, I., Pelekis, N., Raffaetà, A., and Theodoridis, Y. Building Real World

Trajectory Warehouses. Proc. MobiDE‟08, Vancouver, Canada

 Orlando, S., Orsini, R., Raffaetà, A., Roncato, A., and Silvestri, C. Spatio-Temporal Aggregations in

Trajectory Data Warehouses. Proc. DaWaK, 2007.

 Pelekis, N., Raffaetà, A., Damiani, M.-L., Vangenot, C., Marketos, G., Frentzos, E., Ntoutsi, I., and

Theodoridis, Y. Towards Trajectory Data Warehouses. Chapter in Mobility, Data Mining and Privacy: Geographic Knowledge Discovery. Springer-Verlag. 2008.

 Pfoser, D., Jensen, C.S., and Theodoridis, Y. Novel Approaches to the Indexing of Moving Object

Trajectories, Proc. VLDB, 2000.

 Shekhar, S., Lu, C., Tan, X., Chawla, S., Vatsavai, R. Map Cube: a Visualization Tool for Spatial Data

Warehouses, Chapter in Geographic Data Mining and Knowledge Discovery. Taylor and Francis, 2001.

 Tao, Y., Kollios, G., Considine, J., Li, F., and Papadias, D. Spatio-Temporal Aggregation Using Sketches.

(61)

Selected literature on …



Mining Traffic Patterns

 Horvitz, E., Apacible, J., Sarin, R., and Liao, L.: “Prediction, expectation, and surprise: Methods, designs,

and study of a deployed traffic forecasting service,” in In Twenty-First Conference on Uncertainty in Artificial Intelligence, 2005.

 Li, X., Han, J., Lee, J.-G. and Gonzalez, H.: “Traffic density-based discovery of hot routes in road

networks.” in Proc. 10th International Symposium on Spatial and Temporal Databases., 2007.

 Liu, Y., Choudhary, A. N., Zhou, J., and Khokhar, A. A.: “A scalable distributed stream mining system for

highway traffic data.” in Proc. 10th European Conference on Principles and Practice of Knowledge Discovery in Databases, 2006, pp. 309–321.

 Nakata T., and Takeuchi, J.: “Mining traffic data from probe-car system for travel time prediction,” in Proc.

10th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2004, pp. 817–822.

 Ntoutsi, I., Mitsou, N., Marketos, G.: Traffic mining in a road-network: How does the traffic flow? IJBIDM

3(1): 82-98 (2008)

 Shekhar, S., Lu, C.-T., Chawla, S., and Zhang, P.: “Data mining and visualization of twin-cities traffic data,”