Great amount of data under varying intrinsic features is thought of as high dimensional nonlinear manifold in the observation space. How to analyze the mapping relationship between the high dimensional manifold and the corresponding intrinsic low dimensional one quantitatively is important to machine learning and cognitive science. In this paper, we propose SVD (singular value decomposition) ba...

The present article serves the purpose of pursuing Geometrization of heat flow on volumetrically isothermal manifold by means of RF approach. In this article, we have analyzed the evolution of heat equation in a 3-dimensional smooth isothermal manifold bearing characteristics of Riemannian manifold and fundamental properties of thermodynamic systems. By making use of the notions of various curva...

In this paper we study geometrical structures on the manifold of FIR lters and their application to multichannel blind deconvolution First we introduce the Lie group and Riemannian metric to the manifold of FIR lters Then we derive the natu ral gradient on the manifold using the isometry of the Riemannian metric Using the natural gradient we present a novel learning algorithm for blind deconvol...

In this paper, we propose Wasserstein Isometric Mapping (Wassmap), a nonlinear dimensionality reduction technique that provides solutions to some drawbacks in existing global algorithms imaging applications. Wassmap represents images via probability measures space, then uses pairwise distances between the associated produce low-dimensional, approximately isometric embedding. We show algorithm i...

Graph-oriented methods have been widely adopted in multi-view clustering because of their efficiency learning heterogeneous relationships and complex structures hidden data. However, existing are typically investigated based on a Euclidean structure instead more suitable manifold topological structure. Hence, it is expected that will be to carry out intrinsic similarity learning. In this paper,...