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

Definition of “Latent” https://en.oxforddictionaries.com/definition/latent

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

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

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

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?

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

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

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

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

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

Latent Space Model

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:

Latent Space Model

Latent Space Model

Latent Space Model

Latent Space Model

Latent Space Model

Experimental Results

Experimental Results Experiments on loop sensor network (15,000 sensors, 3420 miles) From March and April 2014 - 60 million records “LARGE” and “SMALL” subgraphs of Los Angeles SMALL LARGE Vertices 5984 8242 Edges 12538 19986 Sensors 1642 4048

Experimental Results

Experimental Results

Experimental Results

Experimental Results Scalability

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