isomap-pipeline-floyd-warshall-then-mds

IN premise — summaries/2026/08/24/wiki-Nonlinear_dimensionality_reduction.md

Created 2026-08-24T17:11:20+00:00

Isomap constructs a k-NN neighborhood graph, computes pairwise geodesic distances via Floyd-Warshall shortest-path algorithm on that graph, then applies classical MDS on the resulting geodesic distance matrix

Summary

Isomap works in three stages: it first connects each point to its nearest neighbors, then finds the shortest path between every pair of points by walking that network, and finally projects the result into a lower-dimensional space using standard scaling. This matters because it means the method's behavior and cost are fully determined by those three steps, and any error or bottleneck (like the cubic-time shortest-path computation) can be traced back to a specific stage.