Regularization of Mixture Models for Robust Principal Graph Learning
- URL: http://arxiv.org/abs/2106.09035v2
- Date: Mon, 10 Jul 2023 13:14:18 GMT
- Title: Regularization of Mixture Models for Robust Principal Graph Learning
- Authors: Tony Bonnaire, Aur\'elien Decelle, Nabila Aghanim
- Abstract summary: A regularized version of Mixture Models is proposed to learn a principal graph from a distribution of $D$-dimensional data points.
Parameters of the model are iteratively estimated through an Expectation-Maximization procedure.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: 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.
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