spatial-temporal trajectory simplification for inferring travel paths · spatial-temporal...

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 Melbournehengfeng.li@unimelb.edu.au

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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7Growing Window

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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

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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