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Noisy Circles

A circle has one main loop. Persistent homology should see one long H1 bar.

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graph LR
  A["Noisy circle samples"] -- "short edges" --> B["Vietoris-Rips complex"]
  B -- "one persistent loop" --> C["Long H1 bar"]
  B -- "local jitter" --> D["Short bars"]
  C --> E["Rotation-stable feature"]
  D --> F["Noise candidate"]

Use this example to explain:

  • why short bars are often noise;
  • why one long H1 bar is a useful feature;
  • why a classifier can use topology when coordinates rotate or warp.

Claim Boundary

This page demonstrates the interpretation of a loop feature. It does not claim classification improvement unless a benchmark compares topology features against coordinate, PCA, random, and task-specific baselines on the same split.