A Probabilistic Model for Road Selection in Mobile Maps Thomas C. van Dijk Jan-Henrik Haunert W2GIS,...
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A Probabilistic Model for Road Selection in Mobile Maps Thomas C. van Dijk Jan-Henrik Haunert W2GIS, 5 April 2013
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Transcript of A Probabilistic Model for Road Selection in Mobile Maps Thomas C. van Dijk Jan-Henrik Haunert W2GIS,...
- Slide 1
- A Probabilistic Model for Road Selection in Mobile Maps Thomas C. van Dijk Jan-Henrik Haunert W2GIS, 5 April 2013
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- Overview: a little bit of modelling, interpretation, algorithms, evaluation, outlook,
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- Road selection focus -and- context map route map Depends on user task
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- Road selection destination map Kopf et al. focus maps Yamamoto et al.
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- Motivating example Pedestrian with a smartphone Current location available Wayfinding to a destination Interest in surroundings Freedom of movement Contrast: in-car sat nav
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- From scoring to selection Maximise score using given number of road segments Minimise number of road segments selecting at least a given amount of score Additional constraints?
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- Betweenness centrality Consider all shortest paths between all pairs of nodes; count how often each edge is used Folklore interpretation: People are likely to travel shortest paths Heavily traveled edges are important
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- Betweenness centrality Consider all shortest paths between all pairs of nodes; count how often each edge is used Probabilistic interpretation: Start at a uniformly random node, uniformly random destination, take a uniformly random shortest path Probability that you visit a certain edge
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- PageRank primer Origin in web page ranking (Page, Brinn, Motwani, Winograd Google) Previous application in predicting human movement (Jiang) Usually stated as eigenvector calculation Also: interpretation in terms of random walks
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- Random Surfer model Hypothetical user is at a web page Transitions along a uniformly random link All transitions take equal time Sometimes jumps to a uniformly random page on road segment turn Traveler road segment
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- Non-uniform transition probability Walking along a road segment Coming up to a crossing Where to go? Shortest path? Straight on? Anywhere? Whats the network? Web pages, hyperlinks?
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- Whats the network? Web pages? Links? Modelling user behaviour: routing decisions Road network -> bidirectional line graph linear dual graph (Winter)
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- Bidirected line graph
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- Non-uniform transition probability At a node of the line graph Follow an arc Where to go? Straight on? Constant given road network Shortest path? Constant given road network and destination
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- Non-uniform damping PageRank jumps to uniformly random node Instead, jump to the current user location! Probabilistic interpretation: Consider random walk starting at user location Exponential distribution of walk length Score of node = probability of going to node
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- Data set OpenStreetMap City of Wrzburg and surroundings Lower Franconia, Germany Approx 10 5 nodes Examples here: crop to the city itself 3786 nodes, 4987 road segments
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- Demo
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- Shortest-path bonus
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- Non-turning bonus
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- Runtime of simple implementation Calculate PageRank Loop over nodes Distribute score to neighbours Repeat Select nodes with high score Runtime: ~100 ms
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- Direct selection Select all nodes with high rank Select no nodes with tiny rank O( log n ) time Correctness holds almost surely Almost immediately from Borgs et als algorithm for Significant PageRanks.
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- Really big maps? 1.Just calculate, then select 2.Approximation algorithm: Runtime O( log(n) log( -1 ) -1 -2 ) # nodes Calculate + Select Direct selection (reasonable , ) 3786~100ms~200ms 10 5 ~10.000 ms~300ms
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- Gaps Selection is not necessarily connected Simplified example:
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- Gaps
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- Strokes
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- Overview: a little bit of modelling, interpretation, algorithms, evaluation, outlook,
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- Q?
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- A!