Interactive Learning Using Manifold Geometry

A Geometry Preserving Kernel over Riemannian Manifolds

Abstract- Kernel trick and projection to tangent spaces are two choices for linearizing the data points lying on Riemannian manifolds. These approaches are used to provide the prerequisites for applying standard machine learning methods on Riemannian manifolds. Classical kernels implicitly project data to high dimensional feature space without considering the intrinsic geometry of data points. ...

Sensor Map Discovery for Developing Robots

Modern mobile robots navigate uncertain environments using complex compositions of camera, laser, and sonar sensor data. Manual calibration of these sensors is a tedious process that involves determining sensor behavior, geometry and location through model specification and system identification. Instead, we seek to automate the construction of sensor model geometry by mining uninterpreted sens...

Composition of Local Normal Coordinates and Polyhedral Geometry in Riemannian Manifold Learning

The Local Riemannian Manifold Learning (LRML) recovers the manifold topology and geometry behind database samples through normal coordinate neighborhoods computed by the exponential map. Besides, LRML uses barycentric coordinates to go from the parameter space to the Riemannian manifold in order to perform the manifold synthesis. Despite of the advantages of LRML, the obtained parameterization ...

Proofs of “An Information Geometry of Statistical Manifold Learning”

Linear Subspace and Manifold Learning via Extrinsic Geometry

Linear Subspace and Manifold Learning via Extrinsic Geometry by Brian St. Thomas Department of Statistical Science Duke University Date: Approved: Sayan Mukherjee, Supervisor