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

  • Linh Lieu
  • Naoki Saito
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


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.


Principal Component Analysis Dimensionality Reduction Video Frame Hausdorff Distance Spectral Cluster 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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This work was partially supported by the ONR grants N00014-06-1-0615, N00014-07-1-0166, N00014-09-1-0041, N00014-09-1-0318, the NSF grant DMS-0410406, and the NSF VIGRE grants DMS-0135345, DMS-0636297. A preliminary version of a subset of the material in this article was presented at the SPIE Wavelets XII Conference, in San Diego, in August 2007 [ 22]. We thank Dr. Quyen Huynh and Dr. Joe Lopes of NSWC-PC for providing the experimental sonar data. We have used the SPECTRAL Toolbox version 0.1 distributed on the web by Dr. Guido Sanguinetti and Dr. Jonathan Laidler to compute Elongated Kmeans. Finally, we would like to thank Dr. Bradley Marchand for his help in processing the sonar data used in the numerical experiments and Mr. Julien van Hout for his help in numerical experiments on underwater object classification.


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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaDavisUSA

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