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Managing Sensor Data of Urban Traffic

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ACI Masses de Donn es CADDY (2003-2007) (1) MAS, Ecole ... Grande. circulation. Occupancy Rate. Flow Rate. SeCoGIS 2008. 34. Continuous traffic state variable ... – PowerPoint PPT presentation

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Title: Managing Sensor Data of Urban Traffic


1
Managing Sensor Data of Urban Traffic
  • M. Joliveau1, F.De Vuyst1, G. Jomier2,
  • C.M. Bauzer Medeiros3
  • ACI Masses de Données CADDY (2003-2007)
  • (1) MAS, Ecole Centrale de Paris
  • (2) LAMSADE, Université Paris-Dauphine
  • (3) IC, UNICAMP

2
Goals
  • Urban road traffic analysis
  • congestions
  • Query the past behavior
  • Foresee the future
  • behavior
  • Show understandable résults

(Google Maps)
3
Outline
  • Received Data
  • Exploratory studies
  • Deeper Analysis
  • Work to do
  • Concluding remarks

(Google Maps)
4
Data about the system to be studied
From INRETS
  • - Graph with hundreds of sensors
  • - Flow rate, occupancy rate, 3
  • - States fluid (0) / congestion (1)
  • - Annotations

5
Mass of Data
  • High rate of missing data
  • Bad quality of data
  • Size order of the volume
  • O(109) as I, J, K O(103)

6
Exploratory study
Hours 0-gt24h
  • Temporal view
  • Space-time view dynamic vizualization of the
    sensor state map

7
Traffic States fluid/congestion
Spatio-temporal patterns
It appears 2 states are not enough to
characterize the dynamic behavior of the system
Urban Traffic 
8
Space-Time Vizualization flow rate
9
Analysis of temporal series
Extract of one week for a sensor among 400
Regularity of the human activity generating
traffic
10
Schema of Data Base for Analysis
Sensors
Annotation
sensor-id
annotation-id
Traffic
sensor-id day-id hour-id annotation-id weather-id
Days
day-id
Weather
Hours
flow rate occupancy rate traffic state
weather-id
hour-id
11
Symbolic representation of sets of temporal
series
Episod partition Symbol Alphabet Symbolic
Representation
  • Symbol label associated to a class
  • ? reduction of size and intelligibility
  • Class ?identification of typical behavior,
  • detection of atypical
    behaviors

12
Plan
  • Received Data
  • Exploratory studies
  • Deeper Analysis
  • STPCA
  • Continuous Traffic
  • State Variable
  • Concluding remarks

13
STPCA Spatio-Temporal Principal Component Analysis
  • Goal data representation in a reduced number
    of
  • spatial dimensions gt sensors
  • temporal dimensions gt daily instants
  • Result
  • Data projection simultaneously on the first
    spatial and temporal eigenmodes
  • 1st experiment
  • Flow rate (Monday to Friday) for a family of
    reliable sensors

14
Spatial Reduction
  • Xd (complete) matrix of daily realizations
  • element xi,t ,i sensor , t instant , d day
  • T number of instants by day
  • N number of days
  • I number of sensors
  • Y assembles horizontally N matrices Xd
  • Y col (X1, X2,...... ,XN)

15
Matrix Y for spatial reduction
Number of Measure Instants
Sensors Number
Daily Data
16
Spatial Reduction
  • Y assembles horizontally N matrices Xd
  • Y col (X1, X2,... ,XN)
  • Each line is a temporal serie for 1 sensor
  • Singular value decomposition of Y
  • Spatial correlation matrix MS YYT
  • Eigenvalues l1 gt l2 gt ... lKM
  • Eigenvectors (Fk) for k 1KM

17
Spatial Reduction
  • Spatial correlation matrix Ms YYT
  • Eigenvalues ?1 ?2 ... ?KM
  • Eigenvectors ?k for k 1KM
  • P matrix of the K first eigenvectors ?k
  • P col (?1, ?2, ... ?K) for Kltlt
    KM

18
Spatial Reduction
  • Estimate Xd of each realization Xd
  • Xd P PT Xd
  • K reduced spatial order
  • Reduced order matrix Xr PT X
  • contains latent (hidden) variables of X
  • size K T (T instants)
  • If T is large, the dimension of the reduced order
    representation is too large

19
Temporal Reduction
  • Z assembles vertically N day realizations Xd
  • Z row (X1, X2,... ,XN)
  • one colon corresponds to one instant t
  • one line corresponds to one sensor i for one day
    d
  • the data of one day d are grouped
  • I N lines

20
Matrix Z for temporal reduction
Number of Measure Instants
Sensors Number
Daily Data
21
Temporal Reduction
  • Z assembles vertically N day realizations Xd
  • Z row (X1, X2,... ,XN)
  • Singular value decomposition of Z
  • Temporal correlation matrix Mt ZTZ
  • Eigenvalues µ1 µ2 ... µLM
  • Eigenvectors (Fl) for l 1, 2LM
  • Q matrix of the L first eigenvectors Fl
  • Q col (F1, F2, ...FL) for L ltlt
    LM

22
Temporal Reduction
  • Estimate X for each realization X
  • X X Q QT
  • Reduced order matrix Xr XQ
  • contains the latent variables of X
  • size I L
  • If I (space number of sensors) is large the
    dimension
  • of the reduced order representation is too high

23
Results of temporal component analysis
The 6 first temporal modes (ACP-t)-order
colon- definethe matrix Q (Jr6)
24
Reduction projection on the first temporal mode
  • Flow rates,
  • 1 work day, 6 sensors - Observed flow rate
  • Projection on the
  • 1rst temporal mode

Sensor 1
Sensor 2
Time
Time
Sensor 3
Sensor 4
Time
Time
Sensor 5
Sensor 6
Time
Time
25
Spatio-Temporal Reduction
  • Combines spatial and temporal analysis
  • new estimate of each realization X
  • X PPTXQQT
  • Reduced order matrix
  • Xr PTXQ
  • contains the latent variables of X
  • size KL

26
Cumulative Energy
Cumulative Energy
Cumulative Energy
Spatial correlation matrix Eigenvalue Index
Eigenvalue Index
Temporal correlation matrix
27
Sensor 3
Sensor 1
Sensor 2
Sensor 4
Sensor 6
Sensor 7
Sensor 5
Sensor 8
Sensor 10
Sensor 11
Sensor 9
Sensor 12
Sensor 14
Sensor 15
Sensor 13
Sensor 16
Work days K3, L3
28
Mean Direct Error
Standard Deviation
Reduced-order Matrix Size
Mean Direct Error
Standard Deviation
Reduced-order Matrix Size
Mean Direct Error
Standard Deviation
Reduced-order Matrix Size
29
g
Sensor 1
Sensor 2
Sensor 3
Sensor 4
Sensor 5
Sensor 6
Sensor 7
Sensor 8
Sensor 9
Sensor 10
Sensor 11
Sensor 12
Sensor 13
Sensor 14
Sensor 15
Sensor 16
Chrismas Day K3, L3
30
Error Distribution FunctionSensors
Number of Sensors
31
Error Distribution Function Days
Number of days
32
Plan
  • Received Data
  • Exploratory studies
  • Deeper Analysis
  • STPCA
  • Continuous Traffic State Variable
  • Concluding remarks

33
Generation of 7 new traffic states using
analysis in phase space
Occupancy Rate
Flow Rate
34
Continuous traffic state variable
Occupancy rate
Throughput
35
Sensor 1
Flow Rate (nb vehicles)
Time (hour)
Occupancy Rate ()
Time (hour)
Circulation State ()
Time (hour)
36
New circulation states
State Name
Symb. State
Num. Symbol
E value at t
Deriv. Sign in t
Calm
Negative
Back to Calm
Very high level circ.
Positive
High level circul.
Saturation level 1
Saturation level 2
Saturation level 3
37
Dynamic Visualization of the Traffic State
Animation spatio-temporal patterns appear
38
Other results
  • Missing Data
  • STPCA for state variables
  • Spatio-temporal patterns
  • See Marc Joliveau s PhD Thesis

39
Work to be done
  • Enrich the datawarehouse with summaries, GIS,
    results of STPCA
  • Symbolic spatio-temporal analysis
  • Adaptation to evolution
  • Visualization, user interaction
  • Refinement on types of days, episodes
  • Datawarehouse queries

40
Concluding Remarks
  • Reduction from data masses to intelligible and
    manipulable elements
  • Generic Approach
  • For spatio-temporal analysis of flow systems,
  • described by data coming from a network of
    static georeferenced sensors
  • with diffuse sources and wells

41
Future Prospects
  • Data coming from embarked sensors
  • Go farther in spatio-temporal reduction
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