Incremental Frequent Route Based Trajectory Prediction

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

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

• 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

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.

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

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

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

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

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

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Stream Processing Model

• Temporal sliding window model window size and
  window stride

stride
size
completed trips
partial trips
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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

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

CCFR(i-2..i)
wi
wi-1
wi-2
stride
mine
mine
ipwi-2
Approx. CCFR(i-2..i)


CCFRi-2
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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

ipwMonday_at_9am
CCFRMonday_at_9am

ipwTuesday_at_9am
mine
CCFRTuesday_at_9am



ipwFriday_at_9am
CCFRFriday_at_9am
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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 AB2 and BC2
• 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 AB2,
  BC2 and B4 ? cannot be!
• New support def of times the pattern occurs in
  the sequences
• Closed patterns and their support B3, AB2 and
  BC2
• ipw of patterns ipw(B)3-2-2-1, ipw(AB)2 and
  ipw(BC)2
• Mining after ipw-weigting yields patterns AB2,
  BC2 and B3 (idempotency)
• Fix only works for directed sequences and
  contiguous patterns!

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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
• Find the set of best matching patterns R that
  contain the longest contiguous suffix s of q
  starting from a
• Calculate the successor probability of the cell
  grid cells that occur in the patterns in R
  directly after an occurrence of s
• Retrieve the neighboring cell probability of
  every grid cell that occurs in the trips after
  the anchor a
• Complete the successor probability distribution
  over the neighbors of a using the neighboring
  cell probabilities
• 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
• Stop and return c if the remaining prediction
  horizonlt0 otherwise go to step 1.

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Illustrative Example Trajectories and Mining
18
Illustrative Example Prediction
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When Patterns Make a Difference

• Neighboring cell probabilities predict (4.1) with
  confidence 57, but the patterns predict (5.2)
  with confidence 100.

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When Neighboring Probabilities Fail Avoid
cycles and u-turns!

• Cases when predictions with patterns differ from
  predictions with neighboring cell probabilities

• Explicitly rule out u-turns (as well as cycles)
  in the prediction

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Outline

• Introduction
• Related work
• IncCCFR
• Trajectory representation
• Stream processing model
• Incremental mining of Closed Contiguous Frequent
  Routes (CCFR)
• CCFR-based trajectory prediction
• Empirical evaluations

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)

• 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
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Evaluation Measure
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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_sup60 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

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Absolute Prediction Error

• Absolute prediction error (i.e., average grid
  cell distance to the predicted and to best grid
  cell) of different methods.

26
Relative Prediction Error

• Relative prediction error (i.e., percentage
  improvement) of different methods w.r.t. the
  baseline predictor global.

27
Effects of Incremental Mining

• Using 20 minute subwindows the average prediction
  errors virtually unchanged compared to method
  60.

Trips during 1 hour
Directly mined CCFRs
Incrementally mined CCFRs
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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

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• Thank you for your attention!
• Q/A?