This document summarizes statistical analysis of taxi mobility data in San Francisco using complex network analysis. It analyzes GPS data from 537 taxis over 106 trips to build a directed weighted network and study its structure. Key findings include taxis operating mainly within the city with short typical trips but fat tails in trip distances and durations. The network shows truncated power law degree and strength distributions and disassortative mixing by degree and strength. Long trips are correlated between consecutive empty and full taxi states, influenced by customer movement habits. The network structure is robust with assortative tendency for middle nodes but disassortative for small/top nodes.

1. STATISTICAL ANALYSIS OF TAXI
MOBILITY IN SAN FRANCISCO
Oleguer Sagarra Pascual
Master in Computational Physics. UB-UPC 2011
PhD Supervisor: Dr. Albert Diaz Guilera

2. Motivation
Human Mobility Research
GPS data applications
Complex Network Science
Directed Weighted network metric
Big dataset visualisation

3. Structure
The data
Statistical review
Building the net
Net structure
Open questions and some answers

4. The Data
GPS high frequency* mobility traces from CRAWDAD
UNIX time, GPS latitude & longitude, occupancy
537 Taxis**
106 Trips
* <ti+1-ti> ∼90 s
** Considered independent

5. Statistical Analysis: Overview
Constant regime
ending with fat tails
Initial Noise
Similar shapes for Δr
Bump on the tails
Typical Δt, Δr

6. Efficiency & Location
Do taxis perform different?
Efficiency parameters
Do taxis move different?
Centre of Masses
Radius of Gyration

7. Spread
Radius of Gyration: Mean
spread over taxi reference
frame.
Taxis wander when empty,
not when full.
Taxis mainly operate
inside the city: Short
Trips*.
* But the tails are fat... what about long trips?

8. Long Trips: Ranges & Correlation
Overlap in Δr not present in Δt
Length correlation for consecutive (full-empty) trip pairs in two groups:
Short (Δr<5 km)
Long (Δr>20 km)
The similude between tails is explained by legal issues
Movement habits of customers determine the tails of both statistics

9. Building the net
Discretized grid of San Fracisco area (100 x 100 m)*
Nodes: Locations (∼17000)
Edges: Trips between locations (weighted and directed)
Excluded self-loops (∼5000) and isolated nodes (∼100)
* Using the cartesian coordinates UTM system

10. Net structure
Truncated power law
k,s,ω distribution*
Full net less dense, faster
decay in trips**
*Locations in San Francisco are
limited, amount of trips is not.
**Behavioural differences

11. Weighted net: Correlations
Strength and degree provide similar information
The more connected a node is, the more usual it is
visited, it becomes more important and better
connected with important nodes.

12. Assortativity: r values
We want to study behavioral patterns: Linking tendency
Pearson r values on strengths (quantitative measurement)
Directed net : 4 possible pairs
Full: All disassortative, Empty: Mixed behavior

13. Top connected nodes greatly influence the statistics
Net is robust
Assortative tendency for middle ranged nodes
Dissassortative tendency for small/top nodes

14. Assortativity:neighbor degree
We compute the mean (weighted) neighbor degree: Qualitative
measure for linking tendency of equivalent* nodes P(k|k’).
If the network is uncorrelated, <knn>=ctt.
*Taking a mean field approach, i.e. nodes are equivalent if they are equally connected/preferred (degree/strength).

15. Net representations
Empty Net (video)

16. Some answers
So, how do customers move?
Limited minimum range of usage of taxi (but non-negligible long trips)
Heterogeneous destinations (mostly inside the city) and heterogeneous lengths
Move between hot spots, move from/to hubs and scattered locations
So, how do drivers move?
They are strongly influenced by customers (long trips)
They do not seem to perform very differently*
Searching strategy after each run: Nearest local hot spot (clustering) or global
hub (assortativity)**
Obvious? Maybe, but allows for comparison with other data sets and is a proof that
the methodology is correct.
* Although no scaling relation was found...
** Reminiscent of Lévy Flight...

17. Open questions and further research
Mobility:
GPS mobility traces can be studied through a consistent* complex metric
Set the basis for a simple mechanistic (agent based) model to be simulated and
optimitzed
Compare with other datasets (other transportation means, other cities...)
Complex Networks:
Refine assortativity measures (r/neighbor degree)
Further statistical characterization of the network (correlations, clustering, disparity...)
Introduction of time measures: Net growth, dynamical weighted net, coupling
transport/social networks...
* Fat tailed degree distributions, similar features shared with other studied systems.

18. Thanks for your attention...

19. STATISTICAL ANALYSIS OF TAXI
MOBILITY IN SAN FRANCISCO:
Complementary Material
Oleguer Sagarra Pascual
Master in Computational Physics. UB-UPC 2011

20. Trimming and fitting the data

21. Distributions for Δr,Δt

22. Building the net: Isolated and Selfloops

23. Complex Networks: Definitions
E : Number of edges, N: Number of nodes
Density
Degree k (in-out): Number of edges entering (leaving) a node.
Degree (strength) assortativity: r, <kwnn>,<swnn>
Betweenness centrality: Rel. number of (weighted) shortest path
passing through a node.
Strongly (Weakly) connected component: Complete subgraph
containing the nodes connected among themselves via pairs of
directed edges (undirected).

24. Betweenness/Strength and Assortativity