Theoretical Guarantees for Isomap

[POST IN PROGRESS]. In machine learning, where empirical studies rule and explainability is literally an entire subfield, provable theoretical guarantees don’t come around often. When I first learned about dimensionality reduction methods, I was impressed by Isomap for various reasons, not least its “[guarantee] asymptotically to recover the true dimensionality and geometric structure of a strictly larger class of nonlinear manifolds.” There are plenty of casual articles describing how Isomap works, but the proof of said guarantee is usually glossed over (and omitted from the main body of the original paper), so I wanted to write the proof down for myself here.