spatial-temporal trajectory simplification for inferring travel paths · spatial-temporal...
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F1 Score Error Rate:
Spatial-Temporal Trajectory Simplification for Inferring Travel PathsHengfeng Li, Lars Kulik, Kotagiri Ramamohanarao Department of Computing and Information SystemsThe University of [email protected]
METHOD
CONTRIBUTIONS
PROBLEM & CHALLENGES
RESULTS(a) Ground truth (b) Simplified trace
Noisy GPS points - Noise in GPS measurement causes the uncertainty of recorded locations; Stop points - If vehicles get stuck in traffic jams or have to stop at intersections, GPS points are still recorded; Variable road density - In some regions, roads are fairly well distributed. However, in urban areas, roads are densely placed due to the space limitations.
Challenges:
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3 4
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7Growing Window
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2
3 4
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7Growing Window
pi−1
pi
pi+1
sh
sb
pi−1
pi
pi+1
αs1
s2
We propose three simplification algorithms - Incremental Simplification (IS), Sliding Window Simplification (SWS), and Global Simplification (GS); We use different weighting functions that incorporate spatial knowledge into the trajectory simplification process. We evaluate our algorithms on two real datasets – Seattle and Melbourne.
Problem:
Noisy GPS Data
Ground Truth Nosie
Trajectory Simplification Map Matching Footprint
Evaluation
+
Algorithms
Input Output
Experimental Procedure
How to map GPS traces to a road network accurately under noisy conditions?
We proposed three simplification algorithms to enhance map matching:
We use following evaluation methods (ground truth P and predicted path P’):
Incremental Simplification (IS) simplifies a trajectory point-by-point by maintaining an incremental window; Sliding Window Simplification (SWS) keeps a fixed size of window moving forward with an increasing number of points; Global Simplification (GS) considers the entire trajectory while reducing the number of GPS points.
We use geometric property to determine the importance of a GPS point:
Angular biased: L2 error norm: Normalised linear:
f(s1, s2,↵) 7! s1 · s2 · ↵3
f(sh, sb) 7!1
2· sh · sb
f(s1, s2,↵) 7! (s1 · s2 · ↵)/(s1 + s2)
Precision =length(P \ P
0)
length(P 0)Recall =
length(P \ P 0)
length(P )
HMM Error: F1 Error Rate = 1� 2 · Precision ·Recall
Precision+Recall
d� = length(P )� length(P \ P 0)
d+ = length(P 0)� length(P \ P 0)
HMM Error = (d� + d+)/length(P )
(a) IS (b) Geometric property
Raw: Raw Data SS: Spatial Sampling GS: Global Simplification
Ground TruthGPS Point
Road Network Simplified TracePoint in Simplified Trace