building a visual summary of multiple trajectories natalia andrienko & gennady andrienko

Building a Visual Summary of Multiple Trajectories

Natalia Andrienko & Gennady Andrienko

http://geoanalytics.net

2Natalia Andrienko & Gennady Andrienko

Joint visual analytics research group

of Fraunhofer IAIS and Univ.Bonn http://visual-analytics.info and http://geoanalytics.net

DFG SPP Visual AnalyticsViAMoD:Visual Spatiotemporal Pattern Analysis of Movement and Event Data

Hamburg, March 2009

Introduction





Hamburg, March 2009

Problem statement

Given: data about movement of multiple objects {<o, t, x, y>}.o { o1, o2, …, oN }; t0 ≤ t ≤ tmax

Trajectory: {<o, tk, x, y>} where o = const, tk > tk-1 for k>1

Example: movement of vehicles and/or pedestrians in a city

Problem: represent groups of spatially similar trajectories in a summarised form.

- E.g. trajectories with close starts and/or close ends and/or similar routes

- Such groups may be found e.g. by means of clustering

Purposes:

- Promote abstraction, understanding of common spatial features

- Reduce display clutter and overlapping of symbols





Hamburg, March 2009

Example: trajectories of cars in Milan

Trajectories on Wednesday morning (6591 trajectories, shown with 20% opacity)

Result of density-based clustering by route similarity (noise excluded)





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Some of the 45 clusters

How can we see several (all) clusters at once? How can we compare the clusters?





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An overview of the clusters (“small multiples”)





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A summarised representation (graphical spatial model) of a cluster





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How is it done?

1. Divide the territory using a suitable mesh*2. Transform each trajectory into a sequence of

moves between areas (cells of the mesh)3. Count the moves between pairs of areas4. Represent by arrows with varying thickness

* Voronoi polygons built around characteristic points





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Sensitivity to generalisation parameters

Radius 1000m: Radius 2000m: Radius 3000m:





Hamburg, March 2009

Groups of trajectories with close ends (or close starts)

47 clusters (noise excluded)





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Summarised representation, variant 1





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Summarised representation, variant 2





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Two summarisations





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Further work

Numeric estimation of displacement

Minimization of displacement

User evaluation

Application to trajectories stored in a database

Extending the method to spatio-temporal summarisation

building a visual summary of multiple trajectories natalia andrienko & gennady andrienko

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