An Adaptive Manifold Learning Algorithm Based on ISOMAP

Manifold learning algorithms, such as ISOMAP, LLE, Laplacian Eigenmaps, LTSA and so on, are designed to map nonlinear high dimensional data into the low dimensional space. The key of their success is to select a suitable neighborhood parameter. However, it is difficult to determine a proper neighborhood size for most of manifold learning methods, in particular for non-uniform data sets. An adaptive manifold learning algorithm based on ISOMAP is presented to solve the problem by combining two methods of building the neighborhoods. In the method, all points within a fixed radius are taken as the neighborhood candidate points. The data point number contained in the neighborhood is constricted to a more proper range by setting a minimum value and a maximum value containing points in the neighborhood. Experiments show that the proposed algorithm is effective for the uniform data sets as well as the non-uniform data sets. Moreover, the difficulty of selecting the neighborhood parameter is greatly degraded.