High-Dimensional Pattern Recognition using Low-Dimensional Embedding and Earth Mover's Distance

TL;DR: An algorithm is proposed that combines existing techniques in a novel way to do classification of datasets consisting of high-dimension data (e.g., sets of signals or images) and sets up a framework for application of the Earth Mover’s Distance as a discriminant between datasets.

Abstract: We propose an algorithm that combines existing techniques in a novel way to do classification of datasets consisting of high-dimension al data (e.g., sets of signals or images). Furthermore, our algorithm sets up a framework for application of the Earth Mover’s Distance (EMD) [1, 2] as a discriminant m easure between datasets. We show how to prepare a compact representation ‐ a signature ‐ for each dataset so that computation of EMD between datasets can be done efficiently. This signature-construction step requires the tasks of dim ension reduction, automatic determination of the data’s intrinsic dimensionalit y, out-of-sample extension, and point clustering. We will show how to apply some existing methods (which include Laplacian eigenmaps [3, 4, 5], diffusion maps framework [6, 7, 8], and elongated K-means [9]) to perform these tasks successfully. We will also provide two examples of applications of our proposed algorithm.