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Topologically Regularized Data Embeddings
In some cases, users may have prior topological knowledge about the data, such as a known cluster structure or the fact that the data is known to lie along a tree- or graph-structured topology.
Topologically Regularized Data Embeddings
For tasks for which prior expert topological knowledge is available, incorporating this into the learned representation may lead to higher quality embeddings.
The Curse Revisited: When are Distances Informative for the Ground Truth in Noisy High-Dimensional Data?
Previously, it has been argued that neighborhood queries become meaningless and unstable when distance concentration occurs, which means that there is a poor relative discrimination between the furthest and closest neighbors in the data.
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