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- W3211494064 abstract "A regularized version of Mixture Models is proposed to learn a principal graph from a distribution of <inline-formula><tex-math notation=LaTeX>$D$</tex-math></inline-formula> -dimensional datapoints. In the particular case of manifold learning for ridge detection, we assume that the underlying structure can be modeled as a graph acting like a topological prior for the Gaussian clusters turning the problem into a maximum <i>a posteriori</i> 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." @default.
- W3211494064 created "2021-11-22" @default.
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- W3211494064 date "2022-12-01" @default.
- W3211494064 modified "2023-10-06" @default.
- W3211494064 title "Regularization of Mixture Models for Robust Principal Graph Learning" @default.
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- W3211494064 doi "https://doi.org/10.1109/tpami.2021.3124973" @default.
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