1. Incremental Frequent Route Based Trajectory Prediction Karlsruhe Institute of Technology European Centre for Soft Computing KTH – Royal Institute of Technology Anja Bachmann Christian Borgelt Gyözö Gidofalvi

2. Outline  Introduction  Related work  IncCCFR  Trajectory representation  Stream processing model  Incremental mining of Closed Contiguous Frequent Routes (CCFR)  CCFR-based trajectory prediction  Empirical evaluations 2013-11-05IWCTS 2013, Orlando, FL2

3. Introduction  Congestion is a serious problem  Economic losses and quality of life degradation that result from increased and unpredictable travel times  Increased level of carbon footprint that idling vehicles leave behind  Increased number of traffic accidents that are direct results of stress and fatigue of drivers that are stuck in congestion 2013-11-05IWCTS 2013, Orlando, FL3  Road network expansion is not a sustainable solution  Instead: monitor  understand  control movement and congestion

4. Modern Traffic Prediction and Managemnt System (TPMS)  Motivated by:  Widespread adoption of online GPS-based on-board navigation systems and location-aware mobile devices  Movement of an individual contains a high degree of regularity  Use vehicle movement data as follows:  Vehicles periodically send their location (and speed) to TPMS  TPMS extracts traffic / mobility patterns from the submitted information  TPMS uses traffic / mobility patterns + current / recent historical locations (and speeds) of the vehicles for:  Short-term traffic prediction and management:  Predict near-future locations of vehicles and near-future traffic conditions  Inform the relevant vehicles in case of an (actual / predicted) event  Suggest how and which vehicles to re-route in case of an event  Long-term traffic and transport planning 2013-11-05IWCTS 2013, Orlando, FL4

5. Remaining Challenges  Sequential pattern based trajectory prediction is difficult to adopt to capture the temporal and periodic variations  Trajectory prediction systems model and provide knowledge about the movement of the objects at a fixed level of detail, while different applications (real-time management vs. long-term planning) need different levels of detail.  Predictions tend to be based on either historical or current information while both types of information are relevant.  No end-to-end system for management, incremental mining and accurate prediction of continuously evolving trajectories of moving objects. 2013-11-05IWCTS 2013, Orlando, FL5

6. Outline  Introduction  Related work  IncCCFR  Trajectory representation  Stream processing model  Incremental mining of Closed Contiguous Frequent Routes (CCFR)  CCFR-based trajectory prediction  Empirical evaluations 2013-11-05IWCTS 2013, Orlando, FL6

7. Related Work: Frequent Pattern Mining  20 years of research  Frequent pattern types: itemsets  sequences  graphs  Exponential search space is pruned based on the anti-monotonicity of the pattern support measure given a minimum support threshold min_sup  Pattern constraints:  Maximal (lossy): Pattern X is a maximal if X is frequent and there does not exist another pattern Y that is a proper superset of X that is frequent.  lossy  Closed (lossless): Pattern X is closed if X is frequent and there does not exist another pattern Y that is a proper superset of X that has the same support as X.  Processing models: batch  online / stream  incremental 2013-11-05IWCTS 2013, Orlando, FL7

8. Related Work: Trajectory Prediction  Prediction model  Markov model  Sequential rule / trajectory pattern  Model basis / generality  General model for all objects  Type-base model for similar (type of) objects  Specific model for each individual object  Definition of Regions Of Interest (ROI) for prediction  Application specific ROIs (road segments, network cells, sensors, etc.)  Density-based ROIs  Grid-based ROIs  Prediction provision  Sequential spatial prediction (loc. of next ROI)  Spatio-temporal prediction  Additional movement assumptions or models: YES / NO 2013-11-05IWCTS 2013, Orlando, FL8

9. Outline  Introduction  Related work  IncCCFR  Trajectory representation  Stream processing model  Incremental mining of Closed Contiguous Frequent Routes (CCFR)  CCFR-based trajectory prediction  Empirical evaluations 2013-11-05IWCTS 2013, Orlando, FL9

10. Trajectory Representation  Grid G with side length glen uniformly partitions the 2D space  Representation is without limitations, easily scalable to different level of details  Grid based trajectory:  start time  temporally annotated sequence: sequence of traversed grid cells and associated traversal times  Modeling the stopping of objects: append a pseudo grid cell (‘stop’) after the last (real) grid cell of each completed trip trajectory 2013-11-05IWCTS 2013, Orlando, FL10

11. Stream Processing Model  Temporal sliding window model: window size and window stride 2013-11-05IWCTS 2013, Orlando, FL11 completed tripspartial trips stridesize

12. Mining of Closed Contiguous Frequent Routes  Grow CCFRs (or patterns) in a depth-first fashion  Start with single grid cells  Recursively extend by adding one grid cell in each recursion  Data structure:  Simple flat array representation of the trajectories is used  References are kept to the current ends of the pattern occurrences in order to be able to quickly find and group possible extensions.  Simple and fast closedness checking of contiguous patterns: direct check of possible superpatterns and their support by generating and testing all possible extensions of a given pattern  Without limitations, annotate CCFRs with global traversal times of grid cells 2013-11-05IWCTS 2013, Orlando, FL12

13. Increamental CCFR Mining  General idea from Bifet et al. for incremental closed subgraph mining  Weight closed patterns by their ”relative support” and mine the weighted patterns to reproduce the original pattern set, i.e., the combined operation of weighting and mining is an idempotent operation: f(x)=f(f(x))  Idempotent pattern weight (ipw) of a pattern is its support minus the support of all of its super-patterns in the pattern set  Incremental mining: combine and mine patterns of patterns sets from non-overlapping windows to reproduce and approximation of results 2013-11-05IWCTS 2013, Orlando, FL13 stride mine wiwi w i-1 w i-2 ipw i CCFR i ipw i-1 CCFR i-1 ipw i-2 CCFR i-2 mine ++ Approx. CCFR (i-2..i) CCFR (i-2..i)

14. Capture Temporal and Periodic Variations  Use the same pattern weighting methodology to combine patterns from temporally relevant historical windows  Temporal domain projections to capture periodic variations at different levels 2013-11-05IWCTS 2013, Orlando, FL14 ipw Monday@9am CCFR Monday@9am mine Approx. CCFR weekdays@9am + CCFR Tuesday@9am CCFR Friday@9am + + … ipw Tuesday@9am ipw Friday@9am

15. Faulty Support Definition and the Fix  Example database of two sequences: ABC and ABDBC  min_sup = 2  Original support def: # of sequences that contain the pattern  Closed patterns and their support: AB:2 and BC:2  NOTE: A, B, or C alone are not closed!  ipw of patterns: ipw(AB)=2 and ipw(BC)=2  Mining after ipw-weigting yields patterns: AB:2, BC:2 and B:4  cannot be!  New support def: # of times the pattern occurs in the sequences  Closed patterns and their support: B:3, AB:2 and BC:2  ipw of patterns: ipw(B)=3-2-2=- 1, ipw(AB)=2 and ipw(BC)=2  Mining after ipw-weigting yields patterns: AB:2, BC:2 and B:3 (idempotency)  Fix only works for directed sequences and contiguous patterns! 2013-11-05IWCTS 2013, Orlando, FL15

16. CCFR Based Prediction  Given a set of CCFRs R, iteratively extend the query vector q (partial trajectory) that ends in an anchor a as follows: 1.Find the set of best matching patterns R* that contain the longest contiguous suffix s of q starting from a 2.Calculate the successor probability of the cell grid cells that occur in the patterns in R* directly after an occurrence of s 3.Retrieve the neighboring cell probability of every grid cell that occurs in the trips after the anchor a 4.Complete the successor probability distribution over the neighbors of a using the neighboring cell probabilities 5.Extend q with the most likely successor grid cell c* and reduce the prediction horizon by the gobal average of the traversal time of c* 6.Stop and return c* if the remaining prediction horizon<=0; otherwise go to step 1. 2013-11-05IWCTS 2013, Orlando, FL16

17. Illustrative Example: Trajectories and Mining 2013-11-05IWCTS 2013, Orlando, FL17

18. Illustrative Example: Prediction 2013-11-05IWCTS 2013, Orlando, FL18

19. When Patterns Make a Difference  Neighboring cell probabilities predict (4.1) with confidence 57%, but the patterns predict (5.2) with confidence 100%. 2013-11-05IWCTS 2013, Orlando, FL19

20. When Neighboring Probabilities Fail: Avoid cycles and u-turns!  Cases when predictions with patterns differ from predictions with neighboring cell probabilities 2013-11-05IWCTS 2013, Orlando, FL20  Explicitly rule out u-turns (as well as cycles) in the prediction

21. Outline  Introduction  Related work  IncCCFR  Trajectory representation  Stream processing model  Incremental mining of Closed Contiguous Frequent Routes (CCFR)  CCFR-based trajectory prediction  Empirical evaluations 2013-11-05IWCTS 2013, Orlando, FL21

22. Empirical Evaluation  Hardware: 64bit Ubuntu 12.10 on Intel Core 2 Quad Q8400 2.66GHz processor and 4GB memory  Data set: 6 day sample of 11K taxis in Wuhan, China (85M records) 2013-11-05IWCTS 2013, Orlando, FL22  Outlier removal  Sampling gaps of more the 120 seconds delimit trips  Linear interpolation of trips between samples using 100- meter grid cells  Eliminate short trips (less than 300 seconds or 10 grid cells)  2 million trips that have an average length of 1390 seconds and 94 grid cells and refer to 2 billion grid cells Raw sample vs. interpolated trips

23. Evaluation Measure 2013-11-05IWCTS 2013, Orlando, FL23

24. Prediction Tests  Sliding window model: t_wsize = 60 minutes, t_wstride = 5 minutes  Prediction horizon: upto 5 minutes  Methods:  global: neighboring probabilities only, based on all trips (even future ones!)  g ¬o: global + cycle prevention  g ¬ou: global + cycle and u-turn prevention  g best: best prediction of global  local: neighboring probabilities only, based on completed trips in the window  l ¬o: local + cycle prevention  l ¬ou: local + cycle and u-turn prevention  l best: best prediction of local  60: patterns with min_sup=60 + neighboring probabilities, based on completed trips in the window  60, 6d: same as 60 but with hour-of-day projection  60, 4d: same as 60 but with hour-of-day and weekday-weekend projections 2013-11-05IWCTS 2013, Orlando, FL24

25. Absolute Prediction Error Absolute prediction error (i.e., average grid cell distance to the predicted and to ‘best’ grid cell) of different methods. 2013-11-05IWCTS 2013, Orlando, FL25

26. Relative Prediction Error  Relative prediction error (i.e., percentage improvement) of different methods w.r.t. the baseline predictor ‘global’. 2013-11-05IWCTS 2013, Orlando, FL26

27. Effects of Incremental Mining  Using 20 minute subwindows the average prediction errors virtually unchanged compared to method ’60’. 2013-11-05IWCTS 2013, Orlando, FL27 Trips during 1 hourDirectly mined CCFRsIncrementally mined CCFRs

28. Conclusions and Future Work  IncCCFR: a novel, incremental approach for managing, mining, and predicting the incrementally evolving trajectories of moving object  Essentially a varying order, deterministic Markov model that is based on closed contiguous frequent routes and neighboring cell probabilities  Advantages:  Reduced mining and storage costs  Ability to combine multiple temporally relevant mining results from the past to capture temporal and periodic regularities in movement  Future work:  Use pattern combination approach to parallelize mining  Use current speed + historical CCFRs to be able to react to rare, unpredictable, sudden changes 2013-11-05IWCTS 2013, Orlando, FL28

29. Thank you for your attention! Q/A? 2013-11-05IWCTS 2013, Orlando, FL29