Iterative Hyperplane Merging: A Framework for Manfiold Learning

We present a framework for the reduction of dimensionality of a data set via manifold learning. Using the building blocks of local hyperplanes we show how a global manifold can be reconstructed by iteratively merging these hyperplanes. A Minimum Spanning Tree provides the skeleton needed to traverse the manifold so that the local hyperplanes can be used to build a global, locally stable, embedding. We show state of the art results when compared against existing manifold learning approaches using benchmark synthetic data. We also show how our technique can be used on real world image data.