Signal ensemble classification using low-dimensional embeddings and Earth Mover's Distance (with L. Lieu), in Wavelets and Multiscale Analysis: Theory and Applications (J. Cohen and A. I. Zayed, eds.), Chap.11, pp.227-256, Birkhäuser, 2011.
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
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.
Get the full paper: PDF file.
Get the official version via doi:10.1007/978-0-8176-8095-4_11.
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