Matrix Factorization for Travel Time Estimation in Large Traffic Networks

Matrix factorization techniques have become extremely popular in the recommender systems. We show that this kind of methods can also be applied in the domain of travel time estimation from historical data. We consider a large matrix of travel times in which the rows correspond to short road segments and the columns to 15 minute time slots of a week. Then, by applying matrix factorization technique we obtain a sparse model of latent features in the form of two matrices which product gives a low-rank approximation of the original matrix. Such a model is characterized by several desired properties. We only need to store the two low-rank matrices instead of the entire matrix. The estimation of the travel time for a given segment and time slot is fast as it only demands multiplication of the corresponding row and column of the low-rank matrices. Moreover, the latent features discovered by the matrix factorization may give an interesting insight to the analyzed problem. In this paper, we introduce that kind of the model and design a fast learning algorithm based on alternating least squares. We test this model empirically on a large real-life data set and show its advantage over several standard models for travel estimation.