Modern methods in dimensionality reduction are dominated by nonlinear attraction-repulsion force-based methods (this includes t-SNE, UMAP, ForceAtlas2, LargeVis, and many more).
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.
In this paper we modify a popular and well studied method, RankCentrality for rank aggregation to account for few comparisons and that incorporates additional feature information.
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.
Several recent works have empirically observed that Convolutional Neural Nets (CNNs) are (approximately) invertible.