Document detail
ID
oai:arXiv.org:2408.16716
Topic
Mathematics - Algebraic Topology Computer Science - Computational G...Author
Lesnick, Michael McCabe, KennethCategory
Computer Science
Year
2024
listing date
9/4/2024
Keywords
$Abstract
The Vietoris-Rips filtration, the standard filtration on metric data in topological data analysis, is notoriously sensitive to outliers.
Sheehy's subdivision-Rips bifiltration $\mathcal{SR}(-)$ is a density-sensitive refinement that is robust to outliers in a strong sense, but whose 0-skeleton has exponential size.
For $X$ a finite metric space of constant doubling dimension and fixed $\epsilon>0$, we construct a $(1+\epsilon)$-homotopy interleaving approximation of $\mathcal{SR}(X)$ whose $k$-skeleton has size $O(|X|^{k+2})$.
For $k\geq 1$ constant, the $k$-skeleton can be computed in time $O(|X|^{k+3})$.
;Comment: 20 pages
Lesnick, Michael,McCabe, Kenneth, 2024, Sparse Approximation of the Subdivision-Rips Bifiltration for Doubling Metrics
Projection-Specific Heterogeneity of the Axon Initial Segment of Pyramidal Neurons in the Prelimbic Cortex
heterogeneity projection-specific
