While $D_l$ is not metric, when given as input to cMDS instead of $D$, it empirically results in solutions whose distance to $D$ does not increase when we increase the dimension and the classification accuracy degrades less than the cMDS solution.
The construction and application of knowledge graphs have seen a rapid increase across many disciplines in recent years.
In fact the generalization error versus number of of training data points is a double descent curve.
Given data, finding a faithful low-dimensional hyperbolic embedding of the data is a key method by which we can extract hierarchical information or learn representative geometric features of the data.
Given a set of dissimilarity measurements amongst data points, determining what metric representation is most "consistent" with the input measurements or the metric that best captures the relevant geometric features of the data is a key step in many machine learning algorithms.
Given a set of distances amongst points, determining what metric representation is most “consistent” with the input distances or the metric that captures the relevant geometric features of the data is a key step in many machine learning algorithms.
Here, we present a new algorithm MR-MISSING that extends these previous algorithms and can be used to compute low dimensional representation on data sets with missing entries.