Extended Manifold Learning Algorithm Based on Riemannian Normal Coordinates

LOGMAP is a Riemannian manifold learning algorithm proposed recently.It is efficient for many nonlinear dimension reduction problems.However,the algorithm is only fit for single class problem,when applied to multi-class data,it can't get desirable embedding.In this paper,an extended LOGMAP algorithm is proposed for the multi-class manifold learning.In the algorithm,the local base points are found through the shortest distance from the class of global base point to other classes.Then the local Riemannian normal coordinates of each class are calculated based on the local base point of the class.At last,the global low-dimensional coordinates are obtained by the relationship of extended geodesic distance between the global base point and the local base points.Experimental results demonstrate the validity of the algorithm.