Travel Time Estimation of a Path using Sparse Trajectories

Dr. Yu Zheng yuzheng@microsoft.com

Lead Researcher, Microsoft Research Chair Professor at Shanghai Jiao Tong University

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Goal• Estimate the travel time of any given path

– on road network instantly– using historical and current trajectories generated by a

sample of vehicles

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Challenges• Data sparsity• Trajectory concatenation

– Multiple ways to combine sub-trajectories– Length of a sub-trajectory and its support

• Scalability and efficiency– A citywide estimation– E.g. Beijing has over 100,000 road segments

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Methodology

• Framework– Context-Aware Tensor Decomposition (CATD)– Optimal Concatenation (OC)

Map-Matching

Tensor Construction

Tensor Decomposition

Road Networks

Trajectory Database

Frequent Trajectory Pattern Mining

Optimal Concatenation

Features

Path

Context Feature Extraction

Trajectories

Patterns cost

Arec

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Methodology• Supplementing missing values

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Methodology• Supplementing missing values

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Methodology

• Framework

Map-Matching

Tensor Construction

Tensor Decomposition

Road Networks

Trajectory Database

Frequent Trajectory Pattern Mining

Optimal Concatenation

Features

Path

Context Feature Extraction

Trajectories

Patterns cost

Arec

Ar

Methodology

,

estimated travel time:true travel time: .

Suppose is decomposed as

• Optimal Concatenation

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𝑃1 𝑃2 𝑃𝑘

𝑡𝑃1𝑡𝑃2

𝑡𝑃𝑘

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Methodology• Optimal Concatenation

assuming and are independent

=0

Methodology

• Support vs. Variance – The bigger the support is, the smaller the error is– The bigger the variance the bigger the error

• Solved by dynamic programming– Denote

.

𝑜𝑝𝑡𝑛=min1≤𝑖<𝑛

(𝑜𝑝𝑡 𝑖+𝑔(𝑃𝑟 𝑖+1∨¿ 𝑟𝑖 +2⋯ ¿∨𝑟𝑛))

Methodology

• Make optimal concatenation more efficient• Frequent trajectory pattern mining

– Not necessary to check every combination– Using suffix-tree-based method

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A) An example of suffix-tree B) Filling in the missing time for a pattern

Patterns:

Methodology• Combining the suffix tree with tensors

– Searching for frequent trajectory pattern from the suffix tree– Find the travel time of a particular user from the tensor

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A) An example of suffix-tree B) Filling in the missing time for a pattern

Patterns:

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Methodology• Deal with efficiency and scalability

– data-driven space partition – an element-wise optimization algorithm– Use trajectory patterns as concatenation candidates– Indexing recent trajectories for a fast online retrieval

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Experiments• Datasets

– Taxi Trajectories: • Generated by 32,670 taxicabs in Beijing • From Sept. 1 to Oct. 31, 2013. • 673+ million GPS points • Total length: over 26 million km. • Sampling rate: 96 seconds per point.

– Road networks: • 148,110 nodes and 196,307 edges. • Covers a 4050km spatial range• Total length of road segments: 21,985km.

– POIs: • Th273,165 POIs of Beijing• 195 tier two categories. • Chose the top 10 categories that occur around road

segments

Download data here

Experiments

MAE (min) RMSE

0.747 1.646

0.732 1.629 0.714 1.613

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Metrics

• Performance of CATD– /(5×5): 4,736×12,674×4– 0.09%

Experiments• Query paths

– From taxi trajectories • 12,384 queries, 50 paths per hour/day• Traveled by at least two drivers• Total length 76,412.6km • Effective time span: 2,734 hours

A) Geographical distribution

B) Distribution of the length

C) Distribution of time length

– In the field study • 114 queries • from Sept. 1 to Oct. 30, 2013• Total length 999km • Effective time span: 62 hours

Experiments• Baselines

– Speed-Constraint-based (SC) method– Trajectory-based Simple Concatenation (TSC) method. – Optimal Concatenation with Historical Travel Time (OC+H) method.– Optimal Concatenation with Nonnegative Matrix Factorization (OC+MF)

MAE (min) MRE MAE/L (min/km)8.808 0.665 1.4285.244 0.396 0.8503.245 0.245 0.5263.061 0.231 0.4962.545 0.192 0.412

MAE (min) MRE MAE/L (min/km)

18.193 0.561 2.07511.300 0.349 1.2894.990 0.154 0.5694.052 0.125 0.4623.771 0.116 0.430

In-the-field study

Query paths from taxi data

Experiments

Components Time Memory (MB)

Deal with missing values ()

Building matrix 34ms 9

Tensor construction

44ms 4.4233ms 14.6

Decomposition 5×5 6.31min 116Total 6.4min 144

Optimal Concatenation (OC)

Best OC 2.3ms 995

w/o trajectory patterns 8.6ms 877

w/o index 12.2s 714

• Efficiency

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A) An example of suffix-tree B) Filling in the missing time for a pattern

Patterns:

Conclusion

• A very fundamental but challenging task– Data sparsity– Trade off between length of a path and support of trajectories– Efficiency and scalability

• Our method– Context-Aware Tensor Decomposition– Optimal Concatenation

• Results– Effectiveness

• 12,384 query paths and 114 in the field study• Relative error ratio: 19% and 11.6%

– Efficiency• Partition a city into grids• Suffix-tree-based pattern mining and index• Infer the travel time of a path in 2.3ms

Download data and codes

Search for “Urban Computing”

Thanks!

Yu Zhengyuzheng@microsoft.com

Homepage

Experiments• Datasets

– Taxi Trajectories: • Generated by 32,670 taxicabs in Beijing • From Sept. 1 to Oct. 31, 2013. • 673+ million GPS points • Total length: over 26 million km. • Sampling rate: 96 seconds per point.

– Road networks: • 148,110 nodes and 196,307 edges. • Covers a 4050km spatial range• Total length of road segments: 21,985km.

– POIs: • Th273,165 POIs of Beijing• 195 tier two categories. • Chose the top 10 categories that occur around road

segments

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Download data here