An Ab Initio Local Principal Path Algorithm

We introduce an improved version of the principal path method, an algorithm conceived to find smooth paths between objects in space. Some key steps of the algorithm have been changed, making the solution intrinsically local and preventing it from being attracted by a global manifold. Judiciously performing the initialization step with the Dijkstra algorithm and a proper metric, the functional now only performs a final refinement of the initial solution. Hence the algorithm is stabler as the space of possible solutions has been considerably reduced with respect to the original method. We tested the proposed algorithm in 2D toy data sets (to understand the behaviour) and in high-dimensional data sets. Compared to the previous version of the algorithm, we obtained significantly stabler and more realistic generated samples.