Cascade of Phase Transitions for Multi-Scale Clustering
This addresses clustering challenges in spatially structured datasets with multiple scales, though it appears incremental as it builds on existing methods like Expectation-Maximization and simulated annealing.
The authors tackled the problem of clustering datasets with multi-scale structures by exploiting phase transitions during simulated annealing of the Expectation-Maximization algorithm, enabling extraction of cluster numbers and sizes at different scales without prior knowledge.
We present a novel framework exploiting the cascade of phase transitions occurring during a simulated annealing of the Expectation-Maximisation algorithm to cluster datasets with multi-scale structures. Using the weighted local covariance, we can extract, a posteriori and without any prior knowledge, information on the number of clusters at different scales together with their size. We also study the linear stability of the iterative scheme to derive the threshold at which the first transition occurs and show how to approximate the next ones. Finally, we combine simulated annealing together with recent developments of regularised Gaussian mixture models to learn a principal graph from spatially structured datasets that can also exhibit many scales.