Parallel Projections for Manifold Learning

Abstract

Manifold learning is a widely used statistical tool which reduces the dimensionality of a data set while aiming to maintain both local and global properties of the data. We present a novel manifold learning technique which aligns local hyperplanes to build a global representation of the data. A Minimum Spanning Tree provides the skeleton needed to traverse the manifold so that the local hyperplanes can be merged using parallel projections to build a global hyperplane of the data. We show state of the art results when compared against existing manifold learning algorithm on both artificial and real world image data.