REVIEW 1 cited by
Metric Space Spread, Intrinsic Dimension and the Manifold Hypothesis
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
read the original abstract
The concepts of spread and spread dimension of a metric space were introduced by Willerton in the context of quantifying biodiversity of ecosystems. This paper develops practical applications of spread dimension in the context of machine learning and manifold learning; we show that the topological dimension of a Riemannian manifold can be accurately estimated by computing the spread dimension of a finite subset. These results are presented as the theoretical basis for a novel method of estimating the intrinsic dimension of data. The practical applications of this method are demonstrated with empirical computations using real and synthetic data.
Forward citations
Cited by 1 Pith paper
-
A Survey of Dimension Estimation Methods
A broad benchmark of intrinsic dimension estimators shows that no single method or set of hyperparameters works across datasets, and tuned benchmark scores frequently indicate overfitting rather than transferable accuracy.
Discussion (0). Continue with ORCID to comment.