An Improved Manifold Learning Algorithm for Data Visualization

Recently, a series of methods called manifold learning have been developed to visualize the convex but intrinsically flat manifolds such as Swiss roll. Isomap is a representative of them, which can easily discover low dimensional manifolds from high dimensional data but its computation complexity is quadratic. To speed up Isomap, L-Isomap was proposed to reduce the complexity by using landmark points. But how to select landmarks is an open problem. In this paper, we present an extension of Isomap focusing on the suitable selection of landmarks even the number of landmarks is quite small. In our method, each data point is assigned a weight according to the distance between it and its neighbors and point with a higher weight has a larger probability to be selected as a landmark point. The selection of landmarks falls into two phases. In 1st phase, n´ candidate landmarks are selected only by the weights of data points. And in 2nd phase, n landmarks are refined from the candidates by maximizing the sum of distances between all pairwise landmarks. Experimental results showed that our method was more stable than L-Isomap and outperformed L-Isomap especially when the number of landmark points is quite small