Persistent Homology Visualizations
Interactive exploration of persistent homology concepts. Click to place nodes in the network canvas, then drag the filtration radius slider to watch the simplicial complex grow. The barcode and persistence diagrams update in real-time, showing how topological features (connected components and loops) appear and disappear as the filtration progresses.
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Persistent homology extracts topological features from point cloud data at multiple scales. The filtration process shown here is foundational to topological data analysis (TDA), revealing structure that clustering algorithms miss.
Persistence barcodes and diagrams provide statistical summaries of topological features. Long bars indicate robust features; points far from the diagonal represent significant structure. This is shape statistics.