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Grant support

This work was supported in part by the funding for the ByoPiC Project from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program under Grant ERC-2015-AdG 695561. The work of A.Decelle was supported by the Comunidad de Madrid and the Complutense University of Madrid (Spain) through the Atraccion de Talento Program under Grant 2019-T1/TIC-13298.

Analysis of institutional authors

Decelle, AurelienAuthor
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Article

Regularization of Mixture Models for Robust Principal Graph Learning

Publicated to:Ieee Transactions On Pattern Analysis And Machine Intelligence. 44 (12): 9119-9130 - 2022-12-01 44(12), DOI: 10.1109/TPAMI.2021.3124973

Authors: Bonnaire, Tony; Decelle, Aurelien; Aghanim, Nabila

Affiliations

CNRS, Inst Astrophys Spatiale, F-91405 Bures Sur Yvette, France - Author
CNRS, Lab Rech Informat, F-91190 Gif Sur Yvette, France - Author
Univ Complutense, Dept Fis Teor 1, Madrid 28040, Spain - Author
Univ Paris Saclay, F-91190 Gif Sur Yvette, France - Author

Abstract

A regularized version of Mixture Models is proposed to learn a principal graph from a distribution of D-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 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.

Keywords
Dimensionality reductionExpectation-maximizationGaussian mixture modelsGraph regularizationLaplacian eigenmapManifold learninPrincipal graph

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal Ieee Transactions On Pattern Analysis And Machine Intelligence due to its progression and the good impact it has achieved in recent years, according to the agency WoS (JCR), it has become a reference in its field. In the year of publication of the work, 2022, it was in position 2/145, thus managing to position itself as a Q1 (Primer Cuartil), in the category Computer Science, Artificial Intelligence. Notably, the journal is positioned above the 90th percentile.

From a relative perspective, and based on the normalized impact indicator calculated from the Field Citation Ratio (FCR) of the Dimensions source, it yields a value of: 2.88, which indicates that, compared to works in the same discipline and in the same year of publication, it ranks as a work cited above average. (source consulted: Dimensions May 2025)

Specifically, and according to different indexing agencies, this work has accumulated citations as of 2025-05-25, the following number of citations:

  • WoS: 3
  • Scopus: 6
  • OpenCitations: 4
Impact and social visibility

From the perspective of influence or social adoption, and based on metrics associated with mentions and interactions provided by agencies specializing in calculating the so-called "Alternative or Social Metrics," we can highlight as of 2025-05-25:

  • The use, from an academic perspective evidenced by the Altmetric agency indicator referring to aggregations made by the personal bibliographic manager Mendeley, gives us a total of: 9.
  • The use of this contribution in bookmarks, code forks, additions to favorite lists for recurrent reading, as well as general views, indicates that someone is using the publication as a basis for their current work. This may be a notable indicator of future more formal and academic citations. This claim is supported by the result of the "Capture" indicator, which yields a total of: 6 (PlumX).

With a more dissemination-oriented intent and targeting more general audiences, we can observe other more global scores such as:

  • The Total Score from Altmetric: 4.75.
  • The number of mentions on the social network X (formerly Twitter): 9 (Altmetric).
Leadership analysis of institutional authors

This work has been carried out with international collaboration, specifically with researchers from: France.