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   -> Volume 5, Issue 10

Preprint: Preprints from Naoki Saito available
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Naoki Saito (

PostPosted: Wed Nov 20, 1996 4:44 pm    
Subject: Preprint: Preprints from Naoki Saito available
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#4 Preprint: Preprints from Naoki Saito available

The following two preprints are available via ftp or www:

Title: Improved Local Discriminant Bases Using Empirical Probability Density

Authors: Naoki Saito and Ronald R. Coifman

Abstract: The authors developed the so-called Local Discriminant Bases
(LDB) method for signal and image classification problems a few years
back. The original LDB method relies on the difference in
time-frequency energy distributions of the signal classes: from a
time-frequency dictionary (a large collection of localized basis
functions including wavelet packets and local trigonometric
functions), it selects a basis which maximizes "distances" among
energy distributions of signal classes. Through our experience and
experiments on various datasets, however, we realized that the
time-frequency energy distribution is not always the best quantity to
analyze for classification. In this paper, we propose to use
empirical probability densities of coordinates for discrimination
instead of the time-frequency energy distributions. That is, we first
estimate the probability density function of projection of signals
onto each basis vector in the time-frequency dictionary using the
available training signals. Then, we measure the "distances" among
the corresponding densities using the Kullback-Leibler divergence or
the Hellinger distance for each coordinate and use them as the
discriminant power of that coordinate. Finally, we select a basis
which maximizes the sum of these discriminant powers. Compared to the
original LDB, our new LDB should be able to carry subtler discriminant
information including phase information of signals. Using this
probability setting, the meaning of the original LDB is clarified. We
also compare the performances of the original and new methods using
both synthetic and real datasets.

Note: To appear in Amer. Stat. Assoc. 1996 Proceeding on Statistical


Title: Classification of Geophysical Acoustic Waveforms Using
Time-Frequency Atoms

Author: Naoki Saito

Abstract: Acoustic waveforms recorded in boreholes carry important
information for oil and gas exploration and development. For example,
classifying such waveforms to the ones propagated through sandstone
layers and the ones through shale layers is helpful for identifying
the reservoir region. We apply the Local Discriminant Basis (LDB)
method recently developed by Saito and Coifman to this classification
problem. In this paper, we compare the performance of a variety of
discriminant measures on the time-frequency energy distributions
including the Kullback-Leibler divergence, the Hellinger distance, and
the l^2 distance. We also examine the dependence of classification
accuracy on the number of time-frequency features (or coordinates)
supplied to the final classifiers (LDA or CART). It turned out that
in this dataset the classification accuracy was rather sensitive to
the number of features fed to the classifiers whereas the choice of
the distance measure did not make much difference.

Note: To appear in Amer. Stat. Assoc. 1996 Proceeding on Statistical


Naoki Saito, Ph.D. Schlumberger-Doll Research
Email: Old Quarry Road
Voice: (203) 431-5209 Fax: (203) 438-3819 Ridgefield, CT 06877 USA
All times are GMT + 1 Hour
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