A Fast Manifold Learning Algorithm

A Curvature-based Manifold Learning Algorithm

Manifold learning aims to find a low dimensional parameterization for data sets which lie on nonlinear manifolds in a high-dimensional space. Applications of manifold learning include face recognition, image retrieval, machine learning, classification, visualization, and so on. By studying the existing manifold learning algorithms and geometric properties of local tangent space of a manifold, w...

A Fast Algorithm for Computing Reeb Graph of 2-Manifold

The notion of Reeb graph is part of the Morse theory which provides an analysis of the relationship between the topology and the geometrical information of a space given by a suitable function, a Morse function. Until recently, the main drawback for using Reeb graph analysis was the incapacity of constructing adequate Morse functions. Before the work of Ni et al. [2004], the used Morse function...

A Domain Decomposition Method for Fast Manifold Learning

We propose a fast manifold learning algorithm based on the methodology of domain decomposition. Starting with the set of sample points partitioned into two subdomains, we develop the solution of the interface problem that can glue the embeddings on the two subdomains into an embedding on the whole domain. We provide a detailed analysis to assess the errors produced by the gluing process using m...

A New Fast Data Encryption Algorithm (FDE)

A New Fast Data Encryption Algorithm (FDE)