# Regularization of Mixture Models for Robust Principal Graph Learning

arXiv: https://arxiv.org/abs/2106.09035 · HTML: https://mlsanity.com/paper/2106.09035/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 40 references that are in the map.
- First posted on arXiv 16 Jun 2021.

## Builds on (most cited first, 5 of 5)

- [Robust Topological Inference: Distance To a Measure and Kernel Distance](https://mlsanity.com/paper/1412.7197/) (2014)
- [A Comparison and Evaluation of Map Construction Algorithms](https://mlsanity.com/paper/1402.5138/) (2014)
- [Cascade of Phase Transitions for Multi-Scale Clustering](https://mlsanity.com/paper/2010.07955/) (2020)
- [Generalized Mode and Ridge Estimation](https://mlsanity.com/paper/1406.1803/) (2014)
- [Robust principal graphs for data approximation](https://mlsanity.com/paper/1603.06828/) (2016)

## Built on by (most cited first, 1 of 1)

- [FLASC: A Flare-Sensitive Clustering Algorithm](https://mlsanity.com/paper/2311.15887/) (2023)

## Abstract (arXiv)

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.