Reconstructing Latent Orderings by Spectral Clustering

TITLE: Reconstructing Latent Orderings by Spectral Clustering.

AUTHORS: A. Recanati, T. Kerdreux, A. d'Aspremont

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.

STATUS: Submitted

CODE: The code and experiments are available here.

ArXiv PREPRINT: 1807.07122