Loading skill
Install any skill in seconds. Free to start, no credit card required.
Get Started Free →brycewang-stanford/topology-data-analysis
Topological data analysis: persistent homology, Mapper, and TDA tools
Passed 18 of 22 test cases with the skill, and 17 of 22 without it.
2 fixed16 passed either way3 still failing1 broke
Tokens, turns and time describe resource use, not a dollar price.
One of 2 test cases the skill fixed. Same model, same prompt, with and without the skill.
In persistence diagram feature extraction, what statistical metric serves as a proxy for persistence entropy when converting persistence lifetimes into tabular features?
| Checked | Without skill | With skill |
|---|---|---|
| Uses the sum of squared persistence lifetimes as the entropy proxy | Missed | Passed |
The instructions your model reads when the skill loads.
A skill for applying topological data analysis (TDA) methods to research data. Covers persistent homology, Vietoris-Rips complexes, persistence diagrams, the Mapper algorithm, and vectorization methods for integrating topological features into machine learning pipelines.
TDA extracts topological features (connected components, loops, voids) from data by building simplicial complexes at multiple scales:
| Complex | Construction | Computational Cost |
|---|---|---|
| Vietoris-Rips | Edge if distance < epsilon | O(n^d) for d-simplices |
| Cech | Ball intersection (exact) | Computationally expensive |
| Alpha | Delaunay-based (exact in low dim) | Efficient in R^2, R^3 |
| Cubical | Grid-based (for images) | Linear in pixels |
Scale epsilon: 0.1 0.3 0.5 0.7 1.0
|------|------|------|------|------|
Components: 10 6 3 2 1
(H0 features born at 0, die at merging scale)
Loops: 0 0 1 2 0
(H1 features born when loop forms, die when filled)
A feature that persists across many scales is a genuine topological signal; short-lived features are noise.
import numpy as np
from ripser import ripser
from persim import plot_diagrams
test cases passed, vs 17 / 22 without
More skills from the same source and nearby in the registry, with their headline benchmark lift.