Persistent Homology
The first Betti number counts independent one-dimensional cycles. Ripser was run on two-dimensional embeddings with maxdim = 1 for the stress tests. Reference Betti curves for the arXiv experiment were computed on the original 384-dimensio…
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The first Betti number counts independent one-dimensional cycles. Ripser was run on two-dimensional embeddings with maxdim = 1 for the stress tests. Reference Betti curves for the arXiv experiment were computed on the original 384-dimensional point cloud using stratified samples. Persistent-homology cost limited topology-error evaluation to beta0 and beta1 on 1000-point stress samples. The study did not scale topology objectives to higher-dimensional homology or larger sample sizes.