IsoMap: Local MDS without local optima

• Instead of only modeling local distances, we can try to measure the distances along the manifold and then model these intrinsic distances. – The main problem is to find a robust way of measuring distances along the manifold. – If we can measure manifold distances, the global optimisation is easy: It’s just global MDS (i.e. PCA)

If we measure distances along the manifold, d(1,6) > d(1,4)

2-D

1

4

6

1-D