Download presentation
Presentation is loading. Please wait.
Published byLilian Watkins Modified over 9 years ago
1
SeCoGIS 20081 Managing Sensor Data of Urban Traffic M. Joliveau 1, F.De Vuyst 1, G. Jomier 2, C.M. Bauzer Medeiros 3 ACI Masses de Données CADDY (2003-2007) (1) MAS, Ecole Centrale de Paris (2) LAMSADE, Université Paris-Dauphine (3) IC, UNICAMP
2
SeCoGIS 20082 Goals Urban road traffic analysis congestions Query the past behavior Foresee the future behavior Show understandable résults (Google Maps)
3
SeCoGIS 20083 Outline Received Data Exploratory studies Deeper Analysis Work to do Concluding remarks (Google Maps)
4
SeCoGIS 20084 Data about the system to be studied - Graph with hundreds of sensors - Flow rate, occupancy rate, 3’ - States: fluid (0) / congestion (1) - Annotations From INRETS
5
SeCoGIS 20085 Mass of Data Sensor number (I) Day number (J) Number of measures in a day (K) High rate of missing data Bad quality of data Size order of the volume O(10 9 ) as I, J, K : O(10 3 )
6
SeCoGIS 20086 Exploratory study Temporal view Space-time view : dynamic vizualization of the sensor state map Flow rateOccupancy Rate Hours 0->24h
7
SeCoGIS 20087 Traffic States: fluid/congestion It appears : 2 states are not enough to characterize the dynamic behavior of the system Urban Traffic Spatio-temporal patterns
8
SeCoGIS 20088 Space-Time Vizualization flow rate x Time y
9
SeCoGIS 20089 Analysis of temporal series Extract of one week for a sensor among 400 Regularity of the human activity generating traffic
10
SeCoGIS 200810 Schema of Data Base for Analysis sensor-id Sensors day-id Days hour-id Hours annotation-id Annotation weather-id Weather sensor-id day-id hour-id annotation-id weather-id Traffic flow rate occupancy rate traffic state
11
SeCoGIS 200811 Symbolic representation of sets of temporal series Symbol = label associated to a class reduction of size and intelligibility Class identification of typical behavior, detection of atypical behaviors Episod partition Symbol Alphabet Symbolic Representation
12
SeCoGIS 200812 Plan Received Data Exploratory studies Deeper Analysis STPCA Continuous Traffic State Variable Concluding remarks
13
SeCoGIS 200813 STPCA Spatio-Temporal Principal Component Analysis Goal : data representation in a reduced number of spatial dimensions => sensors temporal dimensions => 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
SeCoGIS 200814 Spatial Reduction X d (complete) matrix of daily realizations element x i,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 X d : Y = col (X 1, X 2,......,X N )
15
SeCoGIS 200815 Sensors Number Number of Measure Instants Daily Data Matrix Y for spatial reduction
16
SeCoGIS 200816 Spatial Reduction Y assembles horizontally N matrices X d : Y = col (X 1, X 2,...,X N ) Each line is a temporal serie for 1 sensor Singular value decomposition of Y Spatial correlation matrix: M S = YY T Eigenvalues l 1 >= l 2 >=... l KM Eigenvectors (F k ) for k = 1…K M
17
SeCoGIS 200817 Spatial Reduction Spatial correlation matrix M s = YY T Eigenvalues: λ 1 ≥ λ 2 ≥... λ KM Eigenvectors: Ψ k for k = 1…K M P matrix of the K first eigenvectors Ψ k P = col (Ψ 1, Ψ 2,... Ψ K ) for K<< K M
18
SeCoGIS 200818 Spatial Reduction Estimate X’ d of each realization X d : X’ d = P P T X d K reduced spatial order Reduced order matrix : X r = P T 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
SeCoGIS 200819 Temporal Reduction Z assembles vertically N day realizations X d : Z = row (X 1, X 2,...,X N ) 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
SeCoGIS 200820 Sensors Number Number of Measure Instants Daily Data Matrix Z for temporal reduction
21
SeCoGIS 200821 Temporal Reduction Z assembles vertically N day realizations X d : Z = row (X 1, X 2,...,X N ) Singular value decomposition of Z Temporal correlation matrix M t = Z T Z Eigenvalues μ 1 ≥ μ 2 ≥... μ LM Eigenvectors (Φ l ) for l = 1, 2…L M Q matrix of the L first eigenvectors Φ l Q = col (Φ 1, Φ 2,...Φ L ) for L << L M
22
SeCoGIS 200822 Temporal Reduction Estimate X’ for each realization X: X’ = X Q Q T Reduced order matrix: X r = 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
SeCoGIS 200823 Results of temporal component analysis The 6 first temporal modes (ACP-t) -order :colon- define the matrix Q (J r =6)
24
SeCoGIS 200824 Reduction: projection on the first temporal mode Flow rates, 1 work day, 6 sensors - Observed flow rate - Projection on the 1rst temporal mode temps Capteur 1 Capteur 3 Capteur 5 Capteur 2 Capteur 4 Capteur 6 Time Sensor 1 Sensor 2 Sensor 3 Sensor 4 Sensor 5 Sensor 6
25
SeCoGIS 200825 Spatio-Temporal Reduction Combines spatial and temporal analysis new estimate of each realization X X’ = PP T XQQ T Reduced order matrix: X r =P T XQ contains the latent variables of X size K*L
26
SeCoGIS 200826 Cumulative Energy Spatial correlation matrix Eigenvalue Index Cumulative Energy Temporal correlation matrix
27
SeCoGIS 200827 Sensor 1Sensor 2 Sensor 3 Sensor 4 Sensor 5 Sensor 6Sensor 7 Sensor 8 Sensor 9 Sensor 10Sensor 11 Sensor 12 Sensor 13 Sensor 14Sensor 15 Sensor 16 Work days K=3, L=3
28
SeCoGIS 200828 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
SeCoGIS 200829 g Sensor 1Sensor 2Sensor 3Sensor 4 Sensor 5 Sensor 9 Sensor 13 Sensor 6 Sensor 10 Sensor 14 Sensor 7 Sensor 11 Sensor 15 Sensor 8 Sensor 12 Sensor 16 Chrismas Day K=3, L=3
30
SeCoGIS 200830 Error Distribution Function Sensors Number of Sensors
31
SeCoGIS 200831 Error Distribution Function Days Number of days
32
SeCoGIS 200832 Plan Received Data Exploratory studies Deeper Analysis STPCA Continuous Traffic State Variable Concluding remarks
33
SeCoGIS 200833 Generation of 7 new traffic states using analysis in phase space Saturé Fluide Grande circulation Occupancy Rate Flow Rate
34
SeCoGIS 200834 Continuous traffic state variable Occupancy rate Throughput
35
SeCoGIS 200835 Sensor 1 Time (hour) Flow Rate (nb vehicles) Occupancy Rate (%) Circulation State (%)
36
SeCoGIS 200836 State NameSymb. StateNum. SymbolE value at tDeriv. Sign in t Calm Negative Very high level circ. Saturation level 1 High level circul. Saturation level 2 Saturation level 3 Positive Back to Calm New circulation states
37
SeCoGIS 200837 Dynamic Visualization of the Traffic State Fluid Congestion Animation : spatio-temporal patterns appear
38
SeCoGIS 200838 Other results Missing Data STPCA for state variables Spatio-temporal patterns See Marc Joliveau ‘s PhD Thesis
39
SeCoGIS 200839 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
SeCoGIS 200840 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
SeCoGIS 200841 Future Prospects Data coming from embarked sensors Go farther in spatio-temporal reduction
Similar presentations
© 2024 SlidePlayer.com Inc.
All rights reserved.