  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.
