topological-data-analysis

What problem does it solve?

This Skill helps you identify meaningful “shape” and multi-scale structure in complex datasets that standard statistics and distance-based methods often miss.

Core Features & Use Cases

• Persistent homology & Betti numbers: Compute topological features across a filtration and summarize them using persistence diagrams, barcodes, and Betti numbers.
• Topology-aware feature engineering: Convert persistence outputs into vector representations (e.g., persistence landscapes, Betti curves, persistence images, silhouettes) suitable for ML pipelines.
• Practical analysis tools: Use Wasserstein or bottleneck distances to compare persistence diagrams, and apply Mapper to build a topological network from point clouds.
• Use Case: Analyze a 3D sensor point cloud (or a noisy image-derived point cloud) to detect loops, cavities, and connected components that indicate underlying physical or biological structure.

Quick Start

Use the topological-data-analysis skill to compute persistent homology for your point cloud and output Betti numbers plus persistence diagrams so you can interpret the dataset’s topology.