Algorithmic applications of low-distortion geometric embeddings

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Unsupervised state representation learning with robotic priors: a robustness benchmark (2017, neutral): “it considers the preservation of the geodesic distance between those points in the state space. We refer the reader to [20] for more detail on its implementation. We also experimented with distortion [21], but this measure was found to bring no more information and we therefore omit these results. I”
Scalable Fair Clustering (2019, background): “For a proof of its properties refer to Indyk (2001) and the references therein.”
State Representation Learning for Control: An Overview (2018, methodology): “Distortion [Indyk, 2001] Measures the preservation of local and global geometry coherence in unsupervised representation learning.”
Approximate clustering via core-sets (2002, methodology): “No algorithm for this problem has been previously known, although (as pointed out in [12]) by using the techniques of [15] one could achieve a much slower algorithm with running time nO(k 2=ε2).”
Distance geometry and data science (2019, background): “2010), k-nearest neighbors (k-NN) (Indyk and Naor 2007), robust learning (Arriaga and Vempala 2006) and more (Indyk 2001), and approximating large MP formulations (e.g., LP, QP, see Sect.”