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Probabilistic Analysis of Large-Scale Urban Traffic Data Set

Explore modeling human count data and fault-tolerant models for urban analysis using sensor data in a large-scale urban traffic study. Learn from over 100 million measurements from 1716 sensors.

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Probabilistic Analysis of Large-Scale Urban Traffic Data Set

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  1. Probabilistic Analysis of a Large-Scale Urban Traffic Sensor Data SetJon Hutchins, Alexander Ihler, and Padhraic SmythDepartment of Computer ScienceUniversity of California, Irvine

  2. Human Activity Sensors Pe MS People Counter – Optical Sensor Car Counter – Loop Detector

  3. Outline • Modeling human count data • Scale-Up challenges • Fault-tolerant model • Urban Analysis

  4. Outline • Modeling human count data • Scale-Up challenges • Fault-tolerant model • Urban Analysis

  5. Outline • Modeling human count data • Scale-Up challenges • Fault-tolerant model • Urban Analysis

  6. Outline • Modeling human count data • Scale-Up challenges • Fault-tolerant model • Urban Analysis

  7. Time Series of Cumulative Counts

  8. One Week of Freeway Observations car count

  9. One Week of Freeway Observations car count

  10. One Week of Freeway Observations car count

  11. One Week of Freeway Observations car count Sensor location

  12. Original Model hidden observed Observed Count

  13. Original Model hidden observed Poisson Rate λ(t) Normal Count Observed Count

  14. Original Model hidden observed Poisson Rate λ(t) Normal Count Observed Count Event Count Event State

  15. Original Model hidden observed Poisson Rate λ(t) Normal Count Observed Count Event Count OBSERVED COUNT NORMAL COUNT (UNOBSERVED) EVENT COUNT (UNOBSERVED) Event State Markov with Poisson counts Time-varying Poisson

  16. Original Model hidden observed Poisson Rate λ(t) Normal Count Observed Count Event Count OBSERVED COUNT NORMAL COUNT (UNOBSERVED) EVENT COUNT (UNOBSERVED) Event State Markov with Poisson counts Time-varying Poisson Markov Modulated Poisson Process (MMPP) e.g., see Scott (1998)

  17. hidden Inference over Time observed Poisson Rate λ(t) Poisson Rate λ(t) Poisson Rate λ(t) Normal Count Normal Count Normal Count Observed Count Observed Count Observed Count Event Count Event Count Event Count Event State Event State Event State Time t-1 Time t Time t+1

  18. Learning and Inference • Bayesian Framework • Gibbs sampling to approximate parameters and hidden variables • Forward-backward algorithm • Complexity • Linear in the number of time slices For Details see Ihler, Hutchins, Smyth ACM TKDD (Dec 2007)

  19. Original Model

  20. Urban Scale-Up Sensor Locations Map of study area 1716 sensors + 7 months = over 100 million measurements

  21. Urban Scale-Up Difficult Sensors to Analyze see Bickel et al. Statistical Science (2007)

  22. Urban Scale-Up – Original Model

  23. Urban Scale-Up – Original Model car count p(E)

  24. Urban Scale-Up - Challenges car count p(E)

  25. Urban Scale-Up - Challenges

  26. Urban Scale-Up - Challenges

  27. Urban Scale-Up - Challenges

  28. Periods of clear periodic behavior missed by our model Long periods of sensor failure

  29. Fault-Tolerant Model hidden Original Model observed Poisson Rate λ(t) Poisson Rate λ(t) Poisson Rate λ(t) Normal Count Normal Count Normal Count Observed Count Observed Count Observed Count Event Count Event Count Event Count Event State Event State Event State Fault State Fault State Fault State Time t-1 Time t Time t+1

  30. Fault-Tolerant Model

  31. Fault-Tolerant Model

  32. Large-Scale Urban Study

  33. Large-Scale Urban Study

  34. Unusual activity detection as a function of day of week and time of day

  35. Spatial Event 16:30

  36. 16:30 16:55 16:40 17:20 17:25 17:05 17:50 18:05 18:20

  37. Model prediction of normal flow Raw flow measurements

  38. Model prediction of normal flow Raw flow measurements

  39. Conclusions • Extended our earlier work to add a fault-tolerant component • Our new model automatically learned normal and anomalous behavior for over 1700 sensors and 100 million measurements • This approach has made possible analysis of a large-scale urban traffic sensor data set that was previously considered beyond analysis

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