An Approach Of Hierarchical Manifold Learning Algorithm

Manifold learning methods are recognized as effective methods by academia in recent decades. In this paper, an approach of hierarchical manifold learning Algorithm based on selecting landmark points from the given samples is proposed for representing data on manifold, which include:1) we construct a land mark point set which preserve the topological properties of manifold ;2) we propose a hierarchical manifold learning Algorithm based on selecting landmark points, which includes: adaptive neighbor selection algorithm, the optimization of land mark point set ,the layering of manifold, topological characteristics testing ,and noisy hierarchical manifold learning. From a above, the characteristics and innovations of this paper is as follow:1) It is a general framework that can fit any manifold learning algorithm as long as its result of an input can be predicted by the results of the neighbor inputs.2) Compared to the existing techniques of organizing data based on spatial partitioning, our method preserves the topology of the latent space of the data.Different from manifold learning algorithms that use landmark points to reduce complexity, our approach is designed for fast retrieval of samples. It may find its way in high dimensional data analysis such as indexing, clustering, and progressive compression. The experiments prove that the method preserves the topological features of manifold, and can help inquire the manifold data efficiently.