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The LASSO is a widely used shrinkage method for linear regression. We propose an online homotopy algorithm to solve a generalization of the LASSO in which the regularization is applied on a linear transformation of the solution, allowing to input prior information on the structure of the problem and to improve interpretability of the results. The algorithm takes advantage of the sparsity of...
The development and update of reliable Geographic Information Systems (GIS) greatly benefits Intelligent Transportation Systems developments including real-time traffic management platforms and assisted driving technologies. The collection and processing of the data required for the development and update of GIS is a long and expensive process which is prone to errors and inaccuracies, making its...
This article presents a method for reconstructing downstream boundary conditions to a HamiltonJacobi partial differential equation for which initial and upstream boundary conditions are prescribed as piecewise affine functions and an internal condition is prescribed as an affine function. Based on viability theory, we reconstruct the downstream boundary condition such that the solution of the Hamilton-Jacobi...
Using least-squares with an l1-norm penalty is well-known to encourage sparse solutions. In this article, we propose an algorithm that performs online least-squares estimation of a time varying system with a l1-norm penalty on the variations of the state estimate, leading to state estimates that exhibit few “jumps” over time. The algorithm analytically computes a path to update the state estimate...
Sparse location measurements of probe vehicles are a promising data source for arterial traffic monitoring. One common challenge in processing this source of data is that vehicles are sampled infrequently (on the order of once per minute), which means that many vehicles will travel several links of the network between consecutive measurements. In this article, we propose an optimal decomposition of...
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