Regularization of Mixture Models for Robust Principal Graph Learning

Comparison of several algorithms to identify a principal graph in point-cloud datasets.


A regularized version of Mixture Models is proposed to learn a principal graph from a distribution of D-dimensional data points. In the particular case of manifold learning for ridge detection, we assume that the underlying manifold can be modeled as a graph structure acting like a topological prior for the Gaussian clusters turning the problem into a maximum a posteriori estimation. Parameters of the model are iteratively estimated through an Expectation-Maximization procedure making the learning of the structure computationally efficient with guaranteed convergence for any graph prior in a polynomial time. We also embed in the formalism a natural way to make the algorithm robust to outliers of the pattern and heteroscedasticity of the manifold sampling coherently with the graph structure. The method uses a graph prior given by the minimum spanning tree that we extend using random sub-samplings of the dataset to take into account cycles that can be observed in the spatial distribution.

In IEEE Transactions on Pattern Analysis and Machine Intelligence
Tony Bonnaire
Tony Bonnaire
Postdoctoral researcher