Electrical and Computer Engineering Commons^™

Adaptive Graph Construction For Isomap Manifold Learning, Loc Tran, Zezhong Zheng, Guoquing Zhou, Jiang Li, Karen O. Egiazarian (Ed.), Sos S. Agaian (Ed.), Atanas P. Gotchev (Ed.)

Electrical & Computer Engineering Faculty Publications

Isomap is a classical manifold learning approach that preserves geodesic distance of nonlinear data sets. One of the main drawbacks of this method is that it is susceptible to leaking, where a shortcut appears between normally separated portions of a manifold. We propose an adaptive graph construction approach that is based upon the sparsity property of the ℓ₁ norm. The ℓ₁ enhanced graph construction method replaces k-nearest neighbors in the classical approach. The proposed algorithm is first tested on the data sets from the UCI data base repository which showed that the proposed approach performs better than …