The document presents a method called iBAT (Isolation-Based Anomalous Trajectory detection) to detect anomalous taxi trajectories from GPS traces. iBAT transforms the problem into an easier isolation-based problem and proposes a novel approach using isolation forests to detect anomalies. It evaluates iBAT on a real-world GPS dataset from over 7,600 taxis in Hangzhou, China, achieving remarkable detection rates of up to 90% for anomalous trajectories with low false alarm rates of only 2%. iBAT provides a computationally efficient way to detect fraud and road network changes from taxi GPS data.

1. iBAT: Detecting Anomalous Taxi
Trajectories from GPS Traces
DAQING ZHANG, NAN LI, ZHI-HUA ZHOU, CHAO
CHEN, LIN SUN, SHIJIAN LI

2. Introduction
• Taxis have been equipped with GPS devices
• Gathering and analyzing large-scale GPS traces reveal the hidden
facts
- City dynamics
- Human behaviors

3. Potential Applications
1. Fraud detection
- Greedy taxi drivers overcharge passenger by taking unnecessary
retours
- Often manually verified upon passenger complain
- In most case frauds are not even noticed by passengers
2. Road network change detection
- Urban road network often change with time. E.g. new road, blocked
road
- Need to update the changes in digital map
- Done manually by digital map providers

4. Example
• Source : S
• Destination : D
• Three clusters of trajectories
• Four trajectories (t0, t1, t2, t3) are considered as anomalies

5. Challenges
• There will be different set of normal trajectories between a pair of
source and destination. E.g. 3 clusters
• Traditional anomaly detection techniques based on distance are not
sufficient. E.g. t3
• Detect an emerging cluster of anomalous trajectories and incorporate
the changes
• Traditional method often requires fixed length feature vectors

6. Solution
• Novel anomalous driving trajectory detection approach
• Contribution
1. Transform the problem into an easy-to-solve problem
2. Propose an Isolation-Based Anomalous Trajectory (iBAT) detection
method
3. Evaluate iBAT with real-world GPS traces
4. Achieves remarkable detection rate with low processing time

7. Related work
• Anomalous trajectory detection
1. Outlier detection using sub-trajectories using distance and density
[1]
2. Outlier detection using direction and density [2]
3. Clustering techniques [3]
4. Discover abnormal traffic change [4]
5. Learning based approaches [5]

8. Related work
• Anomalous detection methods not designed for trajectory data
1. Distance-based approach [6]
2. Density-based approach [7]
3. Isolation-based approach - iForest [8]

9. iForest
• Anomalies are few and different
• No distance or density measures
• State-of-the-art performance for outlier detection
• Lower run time and space complexity
• Fixed-length feature vectors

10. Problem Statement
• GPS Point
- latitude and longitude
- Timestamp
- Estimated speed
- Operation status

11. Problem Statement
• Taxi trajectory
Sequence of GPS points to an occupied taxi ride
t : p1 -> p2 -> …… -> pn
p1 : source
pn : destination
• Problem
Given a set of Trajectories T = {t1, t2,….. , tn} between two locations S
and D, find those in T that are significantly different from the major

12. Proposed approach
• Three-step procedure

13. Augmenting(preprocessing)
• Split the city map into grid-cells of equal size
•Map the taxi trajectory to the cell grid - sequence of traversed
cells
•Augment missing cells by inserting pseudo cells

14. Indexing(preprocessing)
• Given a source-destination cell-pair, find all the related taxi
trajectories
• For given period of time, there may be insufficient trajectories
between a source and destination
• Add all the taxi trajectories which pass through the source-
destination cell pair to solve the issue
• Construct inverted index mechanism for trajectory retrieval

15. Indexing(preprocessing)
• Example:
- Two trajectories
- Create the inverted index as follows
- Source p1 and destination p5: retrieve t1 and t2
- Source p1 and p3: retrieve t1

16. Adapting iForest
• Begin with all the trajectories
• Pick one grid cell at a time
• Partition trajectories based on the grid cell
- Trajectory contains the grid cell : Left
- Otherwise : Right
• Continue until all the instances are isolated
- Either there is only one trajectory to divide
- Or all the trajectories contain same set of grid cells
• Produces short paths for anomalies and long paths for normal
instances

17. Adapting iForest
• Example

18. iBAT
• Lazy learning
- Do not train a model until presented with a test sample
• Keep one trajectory as test t
• Select one grid cell from t randomly and remove trajectories
from train which do not contain the selected cell
• Repeat until no trajectory is left or all the trajectories left
contains cells same as test trajectory
• No of cells required to isolate t, n(t) decides anomalous

19. iBAT
• Example
• Can separately identify loops e.g. t8

20. iBAT
• Real-word example

21. iBAT
• Since the process is completely random, average of n(t) is
considered
• Example: random isolation process for 200 times

22. iBAT
• Calculate the anomaly score for t
s(t, N) = 2-E(n(t))/c(N)
N : Number of trajectories from which we separate t
E(n(t)) : Average number of cells used
c(N): 2H(N-1) - 2(N-1)/N
H(i): Harmonic number, estimated as ln(i) + 0.57721566
• E(n(t)) -> 0, s(t, N) -> 1 : Anomalous trajectory
• s(t, N) < 0.5 : t is categorized as normal trajectory

23. iBAT
• In practice, training set will be large
• Use sub-sample of the training data
• Two additional parameter
m : running trails (100)
ψ : sub-sample size (256)

24. Evaluation
• Real-word taxi GPS dataset collected from the large city of China,
Hangzhou
• More than 7600 taxis
• One record contains:
- latitude
- longitude
- passenger status
- timestamp
• Area is discretized into 100*200 grid cells, each corresponding to
a 250m*250m square

25. Evaluation
• Five source-destination cell-pair is picked
• Trajectories are manually labeled by three volunteers
• If one volunteer thinks a trajectory is anomalous, it is labeled to
be anomalous

26. Evaluation
• Density-based method is taken as the baseline for comparison
- density of a trajectory is average density of all its cells
- density of a cell is the number of trajectories that pass through
it
• Evaluation criteria
- detection rate : The fraction of anomalous trajectories that are
successfully detected
- false alarm rate: The fraction of normal ones that are
wrongly predicted detected as anomalous
- AUC: Area Under ROC Curve
Probability that a randomly chosen anomalous trajectory
is ranked higher than the randomly chosen normal one

27. Evaluation
• Visualization of the results

28. Evaluation
• ROC curve of iBAT
• High detection rate with small false alarm rate
• 90% of anomalous detected at 2% false alarm rate
• For T-4, 100% detection rate with false alarm rate less than 1%

29. Evaluation
• AUC values compared with density-based method
• AUC values are greater than 0.99 for all the datasets
• Density-based method achieves lower AUC values
- less than 0.95 in four datasets
- 0.97 in dataset T-4 as there are less anomalous trajectories
that detour on high-density cells

30. Evaluation
• AUC value and processing time change with m (ψ = 256), and ψ
(m = 100)
• Processing time is about 100 secs, about 0.07 second per
trajectory when m=100

31. Taxi Driving Fraud
• Long-distance detours may correspond to taxi driving frauds
• Detecting anomalous taxi trajectories can help building taxi
driving fraud detection systems
• Challenges
- Some drivers may be truly unfamiliar with the routes
- Some may argue that reason for the detour is due to accident
or traffic

32. Road Network Change
• If more similar anomalous trajectories are accumulating, it may
be an indication of new or blocked road
• 160 trajectories similar to t0

33. Strength
• Simple approach
• Computationally efficient
• Capture the behavior of anomalies, “few and different”

34. Weakness
• Run the algorithm for each trajectory again and again
• Handling temporal trajectories are not explained well
• Only density-based approach is compared in the evaluation

35. Future Work
• Implement the fraud detection system on top of this application
• Use other information associated with a GPS trace such as
driving speed

36. References
[1] J.-G. Lee, J. Han, and X. Li. Trajectory outlier detection: A partition-and-detect framework. In
Proc. ICDE 2008, pages 140–149, 2008.
[2] Y. Ge, H. Xiong, Z.-H. Zhou, H. Ozdemir, J. Yu, and K. C. Lee. Top-Eye: Top-k evolving trajectory
outlier detection. In Proc. CIKM 2010, pages 1733–1736, 2010
[3] Y. Bu, L. Chen, A. W.-C. Fu, and D. Liu. Efficient anomaly monitoring over moving object
trajectory streams. In Proc. KDD 2009, pages 159–168, 2009.
[4] B. Li, D. Zhang, L. Sun, C. Chen, S. Li, G. Qi, and Q. Yang. Hunting or waiting? discovering
passenger-finding strategies from a large-scale real-world taxi dataset. In MUCS’11 in conjunction
with PerCom 2011, pages 63–68, 2011.
[5] Z. Liao, Y. Yu, and B. Chen. Anomaly detection in GPS data based on visual analytics. In Proc.
VAST 2010, pages 51–58, 2010.

37. Thank You