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Building a Visual Summary of Multiple Trajectories. Natalia Andrienko & Gennady Andrienko http://geoanalytics.net. Introduction. Problem statement.

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Building a Visual Summary of Multiple Trajectories

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Building a visual summary of multiple trajectories l.jpg

Building a Visual Summary of Multiple Trajectories

Natalia Andrienko & Gennady Andrienko

http://geoanalytics.net


Introduction l.jpg

Introduction


Problem statement l.jpg

Problem statement

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


Example trajectories of cars in milan l.jpg

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)


Some of the 45 clusters l.jpg

Some of the 45 clusters

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


An overview of the clusters small multiples l.jpg

An overview of the clusters (“small multiples”)


A summarised representation graphical spatial model of a cluster l.jpg

A summarised representation (graphical spatial model) of a cluster


How is it done l.jpg

How is it done?

Divide the territory using a suitable mesh*

Transform each trajectory into a sequence of moves between areas (cells of the mesh)

Count the moves between pairs of areas

Represent by arrows with varying thickness

* Voronoi polygons built around characteristic points


Sensitivity to generalisation parameters l.jpg

Sensitivity to generalisation parameters

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


Groups of trajectories with close ends or close starts l.jpg

Groups of trajectories with close ends (or close starts)

47 clusters (noise excluded)


Summarised representation variant 1 l.jpg

Summarised representation, variant 1


Summarised representation variant 2 l.jpg

Summarised representation, variant 2


Two summarisations l.jpg

Two summarisations


Further work l.jpg

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


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