1. Latent Space Model for Road Networks to Predict Time-Varying Traffic
Presented by: Rob Fitzgerald
Spring 2017

3. Definition of “Latent”

4. Latent Space Model?
Is this what they were referring to?

5. Introduction
The traffic prediction problem aims to find the future link flows based on historical flow data and some observations of the current network state
Applications include traffic warning systems, route guidance systems, emergency planning systems, and network design
Online applications require fast and correct solutions

6. Introduction
Traffic prediction solutions require many iterations over massive networks
Flows are not independent
Driver behavior is very difficult to model

7. Introduction
Can we take a predictive technique which has been successfully applied to social media, and apply it to the traffic prediction problem?
Can we produce a solution to traffic prediction which is less computationally demanding than leading techniques such as HMM and SGD?

8. Latent Space Model
Latent Models find emergent “topics” that associate observations
Social networks
Find consumer trends
Track disease transmission
Sentiment analysis

9. Latent Space Model
Paper proposes Latent Space Modeling for Road Networks (LSM-RN)
Group vertices of a road network graph
Match pairs of vertices which are similar
Traffic behavior
Road network topology
Embed matched pair in a latent space
Use these latent spaces to make traffic prediction

10. Latent Space Model
Differences between social networks and road networks
Spatial and temporal correlations between neighbors on road networks are not present in social networks
Road networks are fast to evolve as traffic conditions vary on a short time scale; people in social networks tend to evolve smoothly
Road networks require dynamic updates to the network links, whereas social network links are relatively static
We have relatively instantaneous validation of our prediction in road networks - short time between prediction and the ground truth

11. Latent Space Model LSM-RN avoids pure “global learning”
Iterative multiplicative methods for model convergence
“Not practical” for real-time traffic prediction
LSM-RN has “incremental online learning” approach
Feedback-based
Instead of a single vertex update per round, multiple vertices can be predicted
… and leverages both global and incremental
Balance between accuracy and efficiency
Long-term global learning batches
Short-term incremental learning

12. Latent Space Model Road Networks have Sparse data
Strongly correlated vertices - temporal and spatial
The need to model time variance
LSM-RN uses Non-negative Matrix Factorization (NMF) for latent space learning
Traditional global multiplicative algorithm
Topology-aware incremental algorithm
Updates vertices with topology constraints
Based on adjacency matrix graph representation

13. Latent Space Model

14. Latent Space Model
Loss function only defined on edges with observed readings
Sparse network data results in missing values
LSM-RN applies a graph Laplacian constraint for “smoothing”
Defined as L = D - W where
W is a graph proximity matrix
D is a diagonal matrix
Traffic model with Laplacian constraint:

15. Latent Space Model

16. Latent Space Model

17. Latent Space Model

18. Latent Space Model

19. Latent Space Model

20. Experimental Results

21. Experimental Results
Experiments on loop sensor network (15,000 sensors, 3420 miles)
From March and April million records
“LARGE” and “SMALL” subgraphs of Los Angeles
SMALL
LARGE
Vertices
5984
8242
Edges
12538
19986
Sensors
1642
4048

22. Experimental Results

23. Experimental Results

24. Experimental Results

25. Experimental Results
Scalability

26. Experimental Results Additional Experiments
Effect of varying algorithm parameters and discussion
Convergence rate