Constructing Popular Constructing Popular Routes from Uncertain Routes from Uncertain TrajectoriesTrajectoriesAuthors of Paper:Authors of Paper:

Ling-Yin WeiLing-Yin Wei(National Chiao Tung University, Hsinchu)(National Chiao Tung University, Hsinchu)

Yu ZhengYu Zheng(Microsoft Research Asia)(Microsoft Research Asia)

Wen-Chih PengWen-Chih Peng(National Chiao Tung University, Hsinchu)(National Chiao Tung University, Hsinchu)

Paper reviewed by:Paper reviewed by:

Aniruddha DesaiAniruddha Desai(University of Washington, Tacoma)(University of Washington, Tacoma)

ApplicationsApplicationsScope: Infer popular routes from a set of uncertain trajectoriesTrip Planning (Travel / Tourism)Traffic Management (Transportation)Animal Movement studies

Spatial TrajectoriesSpatial TrajectoriesWhat is a trajectory?

Sequence of points: Location (Latt, Long) & Time-stamp

What are the moving objects?Humans, Vehicles, Animals etc.

How are the trajectories collected?Ubiquitous location acquisition technologies / devices using GPS

Uncertainty and InferenceUncertainty and InferenceTrajectories generated at low or

irregular frequencies.

Routes between consecutive points on trajectories are uncertain.

To infer a popular route we need to find similarity between two uncertain trajectories – this is hard to measure.

““RICK”RICK”Route Inference framework based onCollective Knowledge

Approach: aggregate uncertain trajectories in a mutually reinforcing way: uncertain + uncertain => certain

Datasets:Datasets:◦Real datasets used for conducting

extensive experiments

◦Check-in dataset from Foursquare – 6,600 trajectories from Manhattan (3 check-ins min)

◦15,000 taxi trajectories in Beijing.

How does it work?How does it work?Rick Overview: user specified query consists of a location sequence & a time span; RICK infers the top-k popular routes that pass through these locations within given time span

Region ConstructionRegion ConstructionHistorical uncertain trajectories used to

construct a routable graph in a gridded space based on spatio-temporal characteristics

Grid cell size (“l”) represents granularity of inferences

Data points (or grid “cells”) “spatially close” if: |x - x’| <= 1 and |y - y’| <= 1

Region Construction Region Construction (cont’d…)(cont’d…)Data points “st-correlated” (spatio-

temporally correlated) if they are spatially close (Rule 1 or Rule 2) and they mutually satisfy a temporal constraint

Connection support C is of a cell pair is a threshold for connectivity in the graph.

Neighbor: If the connection support of a cell pair is >= C then they are neighbors.

Region Construction Region Construction (cont’d…)(cont’d…)

Region: Based on the connection support (above a specified threshold value ‘C’) between individual cell pairs regions are constructed.Cell pairs are merged into regions using an efficient recursive algorithm; Time complexity: O(cnm2)

Where c = minimum loop iterationsn = size (cardinality) of the set of cells in the grid spacem = size (cardinality) of the dataset

Edge InferenceEdge InferenceAfter the regions are constructed we infer

edges.

Two types of Edges:◦ Edges within each region

◦ Edges among regions

Edge Inference (cont’d…)Edge Inference (cont’d…)Each vertex represents a cell and each edge

indicates a transition relationship and has two attributes:◦ Transition support◦ Travel time

Virtual bidirected edges between cells (vertices) are generated if cells are neighbors in a region.

Shortest path inference approach is used. The direction, transition supports and travel time information for edge on shortest path is stored.

Redundant edges and edges whose transition support is 0 are eliminated

Route InferenceRoute InferenceTwo phases:

◦ Route generation◦ Route refinement

Route generation:◦ Top-k coarse routes are discovered with the

routable graph

Route Inference (cont’d…)Route Inference (cont’d…) If query location can not be mapped to a graph

vertex we use MINDIST (nearest neighbor algorithm) to find the cells close to the query location.

Local Routes: the top-k local routes between any two consecutive cells are searched in the cell sequence by an A*-like algorithm.

Route score is computed based on the range of time interval between the two query locations.

Based on top-k local routes top-k global routes are searched by a branch-and-bound search approach

Route Inference (cont’d…)Route Inference (cont’d…)Two-Layer Routing AlgorithmBefore searching for local routes region sequences are generated to reduce the search space by using a lower bound of the transition times between the regions with respect to two given cells.

Thus, multiple region sequences are possible

Route Inference (cont’d…)Route Inference (cont’d…)Route Refinement:Use historical data points (of trajectories that traverse the cells on the rough route) that locate in the cells on the route generated.

Adopt linear regression for set of points of each cell to derive a line segment.

Concatenate line segments in the order of the inferred route

Performance EvaluationPerformance Evaluation Inferred routes are compared against ground-

truth from raw-trajectories.Two metrics used:

◦ NDTW – normalized dynamic time warping distance◦ MD - maximum distance between inferred route and

the raw-trajectory of the ground truth.Compared RICK with existing approach MPR

(Most Popular Route) as a baselineTime Efficiency is tested (avg. query time 0.5

secs).RICK outperforms the baseline by generating

routes 300-700m closer to the ground-truth (than the those of the baseline).

Visualization of ResultsVisualization of ResultsVisualization of the query: “Central Park - > The Museum of Modern Art - > Times Square - > Empire State Building - > SoHo”, for top-1 (most popular) route inferred by RICK

Note: The route does not just connect the query locations, but passes through other attractions along the “inferred” most popular route.

StrengthsStrengthsThorough / Credible

The authors have conducted extensive experiments on real data. Their results show that the route inference framework is effective, efficient and measurably accurate.

Organized / Easy to understandThe content of the paper is very well organized and can be easily understood even by a naïve reader.

Illustrations: (where provided) are very effective in describing spatial concepts.

WeaknessesWeaknessesConnection Support: Not explained

sufficiently, diagrams would have been helpful explain key concept

Route generated using A*-like algorithm: Not explained the role of A*-like algorithm adequately in the context of inferred route generated.

NDTW: “Normalized dynamic time warping” distance is not explained adequately; diagrams would have helped explain this key performance metric better.

Thank you!

Q&A