流形学习概述

流形学习是一种新的非监督学习方法，近年来引起越来越多机器学习和认知科学工作者的重视．为了加深对流形学习的认识和理解，该文由流形学习的拓扑学概念入手，追溯它的发展过程．在明确流形学习的不同表示方法后，针对几种主要的流形算法，分析它们各自的优势和不足，然后分别引用Isomap和LLE的应用示例．结果表明，流形学习较之于传统的线性降维方法，能够有效地发现非线性高维数据的本质维数。利于进行维数约简和数据分析．最后对流形学习未来的研究方向做出展望，以期进一步拓展流形学习的应用领域．

Overview of manifold learning

As a new unsupervised learning method, manifold learning is capturing increasing interests of researchers in the field of machine learning and cognitive sciences. To understand manifold learning better, the topology concept of manifold learning was presented firstly, and then its development history was traced. Based on different representations of manifold, several major algorithms were introduced, whose advantages and defects were pointed out respectively. After thal, two kinds of typical applications of Isomap and LLE were indicated. The results show that compared with traditional linear method, manifold learning can discover the intrinsic dimensions of nonlinear high-dlmensional data effectively, helping researchers to reduce dimensionality and analyze data better. Finally the prospect of manifold learning was discussed, so as to extend the application area of manifold learning.