A geometric viewpoint of manifold learning

Manifold Regularization: A Geometric Framework for Learning from Examples

We propose a family of learning algorithms based on a new form of regularization that allows us to exploit the geometry of the marginal distribution. We focus on a semi-supervised framework that incorporates labeled and unlabeled data in a general-purpose learner. Some transductive graph learning algorithms and standard methods including Support Vector Machines and Regularized Least Squares can...

Geometric Manifold Energy and Manifold Clustering

A general nonparametric technique is proposed for the description of geometric manifold energy of unorganized data. Minimizing the energy leads to an optimal cycle, from which underlying manifolds are easily distinguished. We design a new framework for manifold clustering based on energy minimization. In addition, we propose the active tabu search method to approximately solve for the optimal s...

investigating the feasibility of a proposed model for geometric design of deployable arch structures

deployable scissor type structures are composed of the so-called scissor-like elements (sles), which are connected to each other at an intermediate point through a pivotal connection and allow them to be folded into a compact bundle for storage or transport. several sles are connected to each other in order to form units with regular polygonal plan views. the sides and radii of the polygons are...

Dedekind sums: a combinatorial-geometric viewpoint

Spectral Clustering from a Geometric Viewpoint

Spectral methods have received attention as powerful theoretical and practical approaches to a number of machine learning problems. The methods are based on the solution of the eigenproblem of a similarity matrix formed from distance kernels. In this article we discuss three problems that are endemic in current implementations of spectral clustering: (1) the need to use another clustering metho...