Asymptotic data analysis on manifolds

Asymptotic data analysis on manifolds

Given an m-dimensional compact submanifold M of Euclidean space R, the concept of mean location of a distribution, related to mean or expected vector, is generalized to more general R-valued functionals including median location, which is derived from the spatial median. The asymptotic statistical inference for general functionals of distributions on such submanifolds is elaborated. Convergence...

Ranking on Data Manifolds

The Google search engine has enjoyed huge success with its web page ranking algorithm, which exploits global, rather than local, hyperlink structure of the web using random walks. Here we propose a simple universal ranking algorithm for data lying in the Euclidean space, such as text or image data. The core idea of our method is to rank the data with respect to the intrinsic manifold structure ...

Implications of Dynamical Data on Manifolds to Empirical KL Analysis

Abstract We explore the approximation of attracting manifolds of complex systems using dimension reducing methods. Complex systems having high dimensional dynamics typically are initially analyzed by exploring techniques to reduce the dimension. Linear techniques, such as Galerkin projection methods, and nonlinear techniques, such as center manifold reduction are just some of the examples used ...

New Strategies for Data Analysis and Optimization on Riemannian Manifolds

How can video clips be analyzed to describe organic human actions automatically? How can the long-wave infrared spectrum of an underwater object be identified when the water is distorting the signature of the target? If you had the reflection of an image from a fun-house mirror, could you recognize the original image? My research focuses on geometric analysis of high dimensional data, and inclu...

Parabolic Equations: Asymptotic Behavior and Dynamics on Invariant Manifolds