Manifold Learning Algorithm DC-ISOMAP of Data Lying on the Well-separated Multi-manifold with Same Intrinsic Dimension

• 1、Key Laboratory of Computation Intelligence and Chinese Information Processing of Ministry of Education, College of Computer and Information Technology, Shanxi University, TaiYuan 030006

Abstract：Manifold learning has become a hot issue in the field of machine learning and data mining. Its algorithms often assume that the data resides on a single manifold. And both the theories and algorithms are lacking when the data is supported on a mixture of manifolds. A new method, which is called DC-ISOMAP method, is proposed for the nonlinear dimensionality reduction of data lying on the separated multi-manifold with same intrinsic dimension. The main idea is first to decompose a given data set into several sub-manifolds by propagating the tangent subspace of the point with maximum sampling density to a separate sub-manifold, and then the low-dimensional embeddings of each sub-manifold is independently calculated. Finally the embeddings of all sub-manifolds are composed into their proper positions and orientations based on their inter-connections. Experimental results on synthetic data as well as real world images demonstrate that our approaches can construct an accurate low-dimensional representation of the data in an efficient manner.

Keywords： Machine Learning Nonlinear Dimensionality reduction Manifold learning Well-separated multi-manifold Tangent space DC-ISOMAP