Enhancing Both Efficiency and Representational Capability of Isomap by Extensive Landmark Selection

Figure 1

(a) is a D manifold combined by two crossed S-curve manifolds; (b) is a data set with vertices sampled from the manifold of (a), superimposed with 5-NN neighborhood graph; A, B, and C are three vertices lying on the manifold; the real curves are estimated geodesic curves between A and B and A and C, respectively; (c) is the unwrapped 2D corresponding points of (b); the broken lines are Euclidean lines between A and B and A and C, respectively; the big grey points are the preferred landmarks with faithful geodesic distances to other points.

(a)

(b)

(c)