Incremental Frequent Route
Based Trajectory Prediction
Anja Bachmann
Christian Borgelt
Gyözö Gidofalvi
Karlsruhe Institute of Technology
European Centre for Soft Computing
KTH – Royal Institute of Technology
Outline
 Introduction
 Related work
 IncCCFR




Trajectory representation
Stream processing model
Incremental mining of Closed Contiguous Frequent Routes (CCFR)
CCFR-based trajectory prediction
 Empirical evaluations
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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
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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
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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.
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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
2013-11-05
IWCTS 2013, Orlando, FL
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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
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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
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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
2013-11-05
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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
size
completed trips
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stride
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
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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
wi-1
mine
ipwi-2
ipwi-1
CCFR(i-2..i)
wi
stride
mine
wi-2
ipwi
CCFRi-2 + CCFRi-1 + CCFRi
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Approx. CCFR(i-2..i)
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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@9am
CCFRMonday@9am
ipwTuesday@9am
CCFRTuesday@9am
+
…
+
ipwFriday@9am
mine
+
Approx. CCFRweekdays@9am
CCFRFriday@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: 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!
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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:
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.
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Illustrative Example: Trajectories and Mining
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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
2013-11-05
IWCTS 2013, Orlando, FL
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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 100meter 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
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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:
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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
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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.
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Relative Prediction Error
 Relative prediction error (i.e., percentage improvement) of different
methods w.r.t. the baseline predictor ‘global’.
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Effects of Incremental Mining
 Using 20 minute subwindows the average prediction errors virtually
unchanged compared to method ’60’.
Trips during 1 hour
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Directly mined CCFRs
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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?
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