model). We work in a non-parametric setting and assume that the components of $\nu$ have sufficiently regular densities with respect to the volume form of ${\mathcal{M}}$. We will primarily work with graph Laplacian operators corresponding to *kernelized* Laplacians (see for the definition and Section \[sec:differentweights\] for some reasons behind this choice, where in particular we discuss that the kernelized Laplacian already covers many other cases of interest). Before describing the geometry of the embedded data set $F_{n} ({\mathcal{M}}_n)$ we study a continuum limit analogue of spectral clustering which we refer to as *measure clustering*. This can be thought as an ideal clustering problem where an infinite amount of data is available. Studying this continuum analogue is motivated by recent results concerning the convergence of graph Laplacian operators to differential operators in the large data limit as $n$, the number of vertices, goes to infinity and ${\varepsilon}$, the [*connectivity length scale*]{} specifying $G$, goes to zero sufficiently slowly. The low-lying spectrum of the limiting differential operator induces an embedding $F: {\mathcal{M}}\rightarrow {\mathbb{R}}^N$ in a manner similar to $F_n$, but now at the continuum level. We characterize the geometry of the measure $F_\sharp \nu$ (i.e. the push-forward of $\nu$ through the continuum 