Embedding new data points for manifold learning via coordinate propagation

In recent years, a series of manifold learning algorithms have been proposed for nonlinear dimensionality reduction (NLDR). Most of them can run in a batch mode for a set of given data points, but lack a mechanism to deal with new data points. Here we propose an extension approach, i.e., embedding new data points into the previously-learned manifold. The core idea of our approach is to propagate the known coordinates to each of the new data points. We first formulate this task as a quadratic programming, and then develop an iterative algorithm for coordinate propagation. Smoothing splines are used to yield an initial coordinate for each new data point, according to their local geometrical relations. Experimental results illustrate the validity of our approach.