An Automatic and Adaptive Multi-manifolds Learning Algorithm

Isomap is a classic and representative manifold learning algorithm for nonlinear dimensionality reduction, which aims to circumvent the problem of “the curse of dimensionality” and attempts to recover the intrinsic structure hidden in high-dimensional data based on the assumption that data lie in or near a single manifold. However, Isomap fails to work when data set consists of multi-clusters or multiple sub-manifolds due to the requirement of preserving global geometric structure within data points. Several extended Isomap algorithms have been proposed to handle this issue, such as D-C Isoamp, M-Isomap, etc.. Here, we describe a new multi-manifolds learning algorithm by using a universal concept of neighbor: natural nearest neighbor (3N neighbor), which can be utilized automatically to construct a single or multiple adaptive neighborhood graphs that roughly coincide with the corresponding real multi-manifolds. The new algorithm preserves local adaptive neighborhood graph structure in terms of multi-manifolds as good as possible, in contrast to the previous algorithms, no category information about multi-manifolds are required. So it is a natural extension to the original Isomap, and also an adaptive multi-manifolds learning algorithm without the use of free parameter.