In this work we address the challenge of inferring the road network of a city from crowd-sourced GPS traces. While the problem has been addressed before, our solution has the following unique characteristics: (i) we formulate the road network inference problem as a network alignment optimization problem where both the nodes and edges of the network have to be inferred, (ii) we propose both an offline (\kha) and an online (\khastar) algorithm which are intuitive and capture the key aspects of the optimization formulation but are scalable and accurate. The \khastar in particular is, to the best of our knowledge, the first known online algorithm for map inference, (iii) we test our approach on two real data sets and both our code and data sets have been made available for research reproducibility.

1. Robust Road Map Inference Through
Network Alignment of Trajectories
May 3rd, 2018
Rade Stanojevic, Sofiane Abbar, Saravanan Thirumuruganathan, Sanjay Chawla
@ Qatar Computing Research Institute, HBKU
Fethi Filali @ Qatar Mobility Innovations Center
Ahid Aleima @ Land Transport Planning Department, MoTC, Qatar

2. Map Inference from GPS Traces
GPS Traces Road Network

3. ● Increasing frequency of map updates
○ OSM: ~ 1.5 million new nodes/day
● Map-making is
○ Very expensive
○ Tedious and manual
● Map data is
○ Valuable
○ Becoming proprietary
[Source: http://wiki.openstreetmap.org/wiki/File:Osmdbstats7A.png]
Maps are not static… and are not cheap!

4. High industrial value, autonomous vehicles

5. Why work on this problem? Why Qatar?
● Despite massive investment, maps
have errors: fundamental
challenges to overcome
● Fast Growing Cities (Doha)
○ Extensive construction: frequent diversions,
new roads, road blocks, etc.
○ Commercial maps (e.g., Google) often out of
date
○ Working with local stakeholders to update
maps (e.g., MoTC, QMIC, Karwa)

6. Why work on this problem? Why Qatar?

7. GPS-only: Prior work
● Clustering Schemes (Edelkamp et al.)
● Trace merging from Microsoft (Cao et al.)
● KDE schemes from U. Chicago (Biagioni et al.)

8. Problem Definition
Given a collection of GPS Trajectories <T>, infer a directed and
weighted graph <G> representing the underlying road network.
● T = {tr1,... trn}
● tri = {x1, … xmi}
● xi = <latitude, longitude, timestamp, angle, speed>

9. Kharita Overview
● Kharita infers the topology (directed graph) of the underlying
road network based solely on GPS data
● Kharita models the problem as a “multi network alignment
problem - MNAP” where each GPS trace is one network
● MNAP is modeled as a nonlinear extension of the Facility
Location Problem

10. MNAP for Map Inference
Directed Graph
● Nodes:
intersections/junctions
● Edges: road segmens.

11. Kharita: Non linear extension of FLP
Standard Facility Location Objective Term to infer the edges Sparsification
S.T:
i
j
k
l
O_ik
S_jl

12. Kharita: Non linear extension of FLP
For “small size” problems we can solve the optimization problem using a
Lagrangian relaxation heuristic
Standard Facility Location Objective Term to infer the edges Sparsification
S1. K-means clustering S2. Edge Inference S3. Spanners

13. Kharita: Offline Algorithm
● Distance Metric
○ Combine lat, lon, and angle into one distance metric (penalize angles
difference.)
○ L_i: (lat, lon); 𝛼_i: angle, 𝜃: heading penalty
○ E.g., An angle difference of 180 should be equivalent to a geometric
distance of 50 meters

14. Kharita: Offline Algorithm
● Densification
○ Create fictional points to deal
with varying sampling rates
● Clustering
○ One cluster every x meters
● Edge Inference
○ Geometry of clusters
○ Trajectories
● Graph Sparsification
○ Remove spurious edges
GPS Traces Clustering
Edge Inference Graph spanner

15. Kharita*: Online Algorithm
● Streaming
○ Process trajectory edges
one at a time
● Trace merging
○ Combine clustering and
edge inference into one step
● Adapt a variant of
streaming graph spanner

16. Kharita*: Online Algorithm
● Streaming
○ Process trajectory edges
one at a time
● Trace merging
○ Combine clustering and
edge inference into one step
● Adapt a variant of
streaming graph spanner

17. Evaluation
● Data
○ QMIC data from Doha (lat, lon, ts, angle, speed)
○ UIC data from Chicago (lat, lon, ts)
● SOTA
○ Edelkamp et al. ’03 (k-means)
○ Cao et al. SIGSPATIAL’09 (Trace merging)
○ Biagioni et al. KDD’12 (KDE /Hybrid)
○ Chen et al. KDD’16 (Meanshift / Hybrid)
● Evaluation metric
○ Holes and marbles
○ GEO and TOPO
Ground Truth Map Inferred Map

18. Evaluation: Quantitative
F1_GEO F1_TOPO
Doha
Chicago

19. Evaluation: Qualitative
GPS Data Kharita

20. Evaluation: Performance

21. Concluding Remarks
● Keep it simple
● Always check the quality of your data
○ Good data collection rules can lead to very accurate maps. E.g.,
■ Generate points every x seconds, or
■ Every time the angle changes significantly, or
■ Every time the speed changes significantly, etc.
○ Use as much data as you can
■ If you don’t have angle (or/and speed) information, infer them.
● Online map update is not easy
○ Revisit the network to fix errors
● Code on github: https://github.com/vipyoung/kharita

22. QCRI is hiring for its new Center for Artificial
Intelligence (Q-CAI).
Come and talk to us!
FYI
Sofiane Abbar
(sabbar@qf.org.qa)
Sanjay Chawla
(schawla@qf.org.qa)

23. Thank You!