Concept and Context Bi-Hierarchical Learning

Synthesizing a variety of ideas and algorithms from Machine Learning, Kernel methods, Spectral Graph Theory, Diffusion Geometries, Harmonic Analysis and Signal Processing into a single mathematical framework, we propose a data driven processing toolbox capable of generating bi-hierarchical information organization and prediction (models) essential for analytical data organization. The associated empirical models are also complemented by natural extensions of all quantities measured on the known data to new data. This extension methodology leads to automatic invariant feature or language definitions and to regression and analysis of empirical functions on and off the data. These resulting algorithms yield a powerful system for automatic learning and classification that is essentially data agnostic and requires no specific ab initio knowledge.