that the empirical measure of $F_n({\mathcal{M}}_n)$ and the measure $F_{\sharp} \nu$ get closer in the Wasserstein sense as $n$ grows. In turn, this convergence guarantees that if $F_{\sharp} \nu$ has an orthogonal cone structure, then $F_n({\mathcal{M}}_n)$ will have one as well (i.e., orthogonal cone structures are stable under Wasserstein perturbations). In Theorem \[PropMuMun\] we make the previous discussion mathematically precise. For the moment we provide an informal statement of that result.

\[thm:discrete-is-consistent-with-continuum\] Under suitable conditions, if $F_\sharp \nu$ has an orthogonal cone structure then, with very high-probability, the empirical measure of the embedded cloud $F_n({\mathcal{M}}_n)$ also has an orthogonal cone structure.

Related work {#sec:Literature}
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In recent years, graph-based methods have been used extensively in machine learning literature, due to their ability to capture the intrinsic geometry of a data set with relatively simple algorithms. Operators and functionals defined on graphs often induce sensible approaches to address fundamental data analysis tasks such as semi-supervised learning and clustering.

In this paper we focus on clustering. More specifically, clustering by means of appropriate embeddings using the spectrum of a graph Laplacian operator. In the context of stochastic block models, large sample properties of the spectra of graph Laplacians have been studied in 