F-Geometry and Amari’s α-Geometry on a Statistical Manifold

F-Geometry and Amari's α-Geometry on a Statistical Manifold

An Information Geometry of Statistical Manifold Learning

Manifold learning seeks low-dimensional representations of high-dimensional data. The main tactics have been exploring the geometry in an input data space and an output embedding space. We develop a manifold learning theory in a hypothesis space consisting of models. A model means a specific instance of a collection of points, e.g., the input data collectively or the output embedding collective...

Proofs of “An Information Geometry of Statistical Manifold Learning”

Manifold Alignment Preserving Global Geometry

This paper proposes a novel algorithm for manifold alignment preserving global geometry. This approach constructs mapping functions that project data instances from different input domains to a new lower-dimensional space, simultaneously matching the instances in correspondence and preserving global distances between instances within the original domains. In contrast to previous approaches, whi...

Interactive Learning Using Manifold Geometry

We present an interactive learning method that enables a user to iteratively refine a regression model. The user examines the output of the model, visualized as the vertical axis of a 2D scatterplot, and provides corrections by repositioning individual data instances to the correct output level. Each repositioned data instance acts as a control point for altering the learned model, using the ge...