LDME of the embedding found.

To be closer to the actual biophysical application and real-world data, we actually use the *root mean square deviation* ([RMSD]{}) to *evaluate* our solutions. The [RMSD]{}compares the embedding against a reference structure: $$\label{eq:rmsd}
\textnormal{{RMSD\xspace}}(x, x') = \min \sqrt{\frac{1}{|V|} \sum_{v \in V} \lVert x_v - x'_v \rVert^2},$$ with $x_v$ and $x_v'$ being the coordinates of the embedding and the reference structure, respectively. The minimum value is over all possible spatial translations and rotations of both superimposed structures. [RMSD]{}values $<1.5$Å  approach the structure resolution limit of experimental wet-lab techniques (NMR and X-ray) [@voet2010biochemistry]. While error functions that test the capability of the algorithm to match the constraints can be useful from an optimization point of view, a good value does not necessarily mean that the embedding reproduces the molecular structure. In particular, the algorithm must be able to handle noisy and erroneous data. In the end, the structure must also be physically meaningful. The [RMSD]{}addresses this challenge and is a standard measure of (dis)similarity in structural molecular biology by directly assessing the usefulness in a real-life scenario[@voet2010biochemistry]. We will therefore rely on the [RMSD]{}to compare algorithms.

Related Work {#sub:rel-work}
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There exist many algorithms for solving the 