Signal Ensemble Classification Using Low-Dimensional Embeddings and Earth Mover’s Distance

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Instead of classifying individual signals, we address classification of objects characterized by signal ensembles (i.e., collections of signals). Such necessity arises frequently in real situations: e.g., classification of video clips or object classification using acoustic scattering experiments to name a few. In particular, we propose an algorithm for classifying signal ensembles by bringing together well-known techniques from various disciplines in a novel way. Our algorithm first performs the dimensionality reduction on training ensembles using either the linear embeddings (e.g., Principal Component Analysis (PCA), Multidimensional Scaling (MDS)) or the nonlinear embeddings (e.g., the Laplacian eigenmap (LE), the diffusion map (DM)). After embedding training ensembles into a lower-dimensional space, our algorithm extends a given test ensemble into the trained embedding space, and then measures the “distance” between the test ensemble and each training ensemble in that space, and classify it using the nearest neighbor method. It turns out that the choice of this ensemble distance measure is critical, and our algorithm adopts the so-called Earth Mover’s Distance (EMD), a robust distance measure successfully used in image retrieval and image registration. We will demonstrate the performance of our algorithm using two real examples: classification of underwater objects using multiple sonar waveforms; and classification of video clips of digit-speaking lips. This article also provides a concise review on the several key concepts in statistical learning such as PCA, MDS, LE, DM, and EMD as well as the practical issues including how to tune parameters, which will be useful for the readers interested in numerical experiments.