Topology Error
The study defines topology error as the absolute deviation between embedding beta1 and known beta1 over a fixed stress-test set. Persistent-homology outputs were converted into Betti curves, and beta1 was estimated by counting significant…
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The study defines topology error as the absolute deviation between embedding beta1 and known beta1 over a fixed stress-test set. Persistent-homology outputs were converted into Betti curves, and beta1 was estimated by counting significant bars. The stress tests used noisy figure-8 and torus samples, both with true beta1 equal to 2. Topology error is proposed as a replacement or complement for local-only evaluation of dimensionality reduction. Topology error can distinguish manifold preservation from noise reproduction when used with task metrics.