9 articles in this category
So you've got a point cloud, a distance matrix, maybe a graph. You want to find loops, holes, clusters that persist across scales—the usual persistenc...
You've got a point cloud that looks like a Swiss cheese—lots of holes, maybe a tunnel or two. Persistent homology is supposed to find those features. ...
Persistence landscapes are a staple in topological data analysis. But when a landscape looks too jagged or too flat, the first instinct is to tweak ei...
Witness complexes promised a cure for the curse of dimensionality. Instead of building a simplicial complex on every point, you pick a few landmarks a...
Persistent homology is a gift to data scientists who think topologically. It takes a point cloud, builds a simplicial complex at multiple scales, and ...
You compute persistent homology on a 3D point cloud from a LiDAR scan. The persistence diagram looks plausible, but the bottleneck distance between tw...
Reeb graph are everywhere in computational topology—from shape analysis to sensor networks. But if you have ever run one on real data, you know the si...
I watched a staff burn two months chasing a false signal. They had computed persistence landscape from lone-cell RNA data, then used Wasserstein dista...
Persistent homology is a beautiful lens for data—but only if the filtra you choose doesn't crush the very structure you're after. Pick off, and your p...