Reconstructing Latent Orderings by Spectral Clustering

Antoine Recanati 1, 2 Thomas Kerdreux 1, 2 Alexandre D'Aspremont 3
3 SIERRA - Statistical Machine Learning and Parsimony
DI-ENS - Département d'informatique de l'École normale supérieure, CNRS - Centre National de la Recherche Scientifique, Inria de Paris
Abstract : Spectral clustering uses a graph Laplacian spectral embedding to enhance the cluster structure of some data sets. When the embedding is one dimensional, it can be used to sort the items (spectral ordering). A number of empirical results also suggests that a multidimensional Laplacian embedding enhances the latent ordering of the data, if any. This also extends to circular orderings, a case where unidimensional embeddings fail. We tackle the task of retrieving linear and circular orderings in a unifying framework, and show how a latent ordering on the data translates into a filamentary structure on the Laplacian embedding. We propose a method to recover it, illustrated with numerical experiments on synthetic data and real DNA sequencing data. The code and experiments are available at https://github.com/antrec/mdso.
Type de document :
Pré-publication, Document de travail
2018
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https://hal.archives-ouvertes.fr/hal-01846269
Contributeur : Antoine Recanati <>
Soumis le : samedi 21 juillet 2018 - 14:47:05
Dernière modification le : mercredi 30 janvier 2019 - 11:07:50

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  • HAL Id : hal-01846269, version 1
  • ARXIV : 1807.07122

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Antoine Recanati, Thomas Kerdreux, Alexandre D'Aspremont. Reconstructing Latent Orderings by Spectral Clustering. 2018. 〈hal-01846269〉

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