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2.1 Introduction
The notion of optimal signal representation is a fundamental problem that the signal
processing community has been addressing from different angles and under multiple
research contexts. The formulation and solution to this problem has provided signifi-cant
contributions in lossy compression, estimation and denoising realms [30, 57]. The
overarching motivation is to find parsimonious representations for a particular family of
signals, where the fact that few coordinates capture most of the target signal energy has
proved to be of significant importance in improving compression and denoising tech-niques
[57, 10].
In the context of pattern recognition, signal representation issues are naturally asso-ciated
with feature extraction (FE). In contrast to compression and denoising scenarios,
where the objective is to design bases that allow optimal representation of the observa-tion
source, for instance in the mean square error sense, in pattern recognition we seek
representations that capture an unobserved finite alphabet phenomena, the class identity,
from the observed signal. Consequently, a suitable optimality criterion is associated with
minimizing the risk of taking the mentioned decision, as considered in Bayes decision
framework [25, 5]. Assuming that we know the observation-class distribution, the min-imum
risk decision can be obtained. However in practice typically this distribution is
unknown, which introduces the learning aspect of the problem. The Bayes framework
proposes to estimate this distribution based on a finite amount of training data [25, 5]. It
is well known that the accuracy of this estimation process is affected by the dimension-ality
of the observation space—the curse of dimensionality—which is proportional to
the disagreement between the real and the estimated distributions, the estimation error
effect of the learning problem. Then, an integral part of the feature extraction (FE) is to
control the estimation error by finding good parsimonious signal transformations, par-ticularly
necessary in scenarios where the original raw observation measurements lie in
5
Object Description
| Title | On optimal signal representation for statistical learning and pattern recognition |
| Author | Silva, Jorge |
| Author email | jorgesil@usc.edu; josilva@ing.uchile.cl |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Electrical Engineering |
| School | Viterbi School of Engineering |
| Date defended/completed | 2008-06-23 |
| Date submitted | 2008 |
| Restricted until | Unrestricted |
| Date published | 2008-10-21 |
| Advisor (committee chair) | Narayanan, Shrikanth S. |
| Advisor (committee member) |
Kuo, C.-C. Jay Ordóñez, Fernando I. |
| Abstract | This work presents contributions on two important aspects of the role of signal representation in statistical learning problems, in the context of deriving new methodologies and representations for speech recognition and the estimation of information theoretic quantities.; The first topic focuses on the problem of optimal filter bank selection using Wavelet Packets (WPs) for speech recognition applications. We propose new results to show an estimation-approximation error tradeoff across sequence of embedded representations. These results were used to formulate the minimum probability of error signal representation (MPE-SR) problem as a complexity regularization criterion. Restricting this criterion to the filter bank selection, algorithmic solutions are provided by exploring the dyadic tree-structure of WPs. These solutions are stipulated in terms of a set of conditional independent assumptions for the acoustic observation process, in particular, a Markov tree property across the indexed structure of WPs. In the technical side, this work presents contributions on the extension of minimum cost tree pruning algorithms and their properties to affine tree functionals. For the experimental validation, a phone classification task ratifies the goodness of Wavelet Packets as an analysis scheme for non-stationary time-series processes, and the effectiveness of the MPE-SR to provide cost effective discriminative filter bank solution for pattern recognition.; The second topic addresses the problem of data-dependent partitions for the estimation of mutual information and Kullback-Leibler divergence (KLD). This work proposes general histogram-based estimates considering non-product data-driven partition schemes. The main contribution is the stipulation of sufficient conditions to make these histogram-based constructions strongly consistent for both problems. The sufficient conditions consider combinatorial complexity indicator for partition families and the use of large deviation type of inequalities (Vapnik-Chervonenkis inequalities). On the application side, two emblematic data-dependent constructions are derived from this result, one based on statistically equivalent blocks and the other, on a tree-structured vector quantization scheme. A range of design values was stipulated to guarantee strongly consistency estimates for both framework. Furthermore, experimental results under controlled settings demonstrate the superiority of these data-driven techniques in terms of a bias-variance analysis when compared to conventional product histogram-based and kernel plug-in estimates. |
| Keyword | signal representation in statistical learning; Bayes decision theory; basis selection; tree-structured bases and Wavelet packet (WP); complexity regularization; minimum cost tree pruning; family pruning problem; mutual information estimation; divergence estimation; data-dependent partitions; statistical learning theory; concentration inequalities; tree-structured vector quantization. |
| Language | English |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Provenance | Electronically uploaded by the author |
| Type | texts |
| Legacy record ID | usctheses-m1684 |
| Contributing entity | University of Southern California |
| Rights | Silva, Jorge |
| Repository name | Libraries, University of Southern California |
| Repository address | Los Angeles, California |
| Repository email | cisadmin@lib.usc.edu |
| Filename | etd-Silva-2450 |
| Archival file | uscthesesreloadpub_Volume32/etd-Silva-2450.pdf |
Description
| Title | Page 18 |
| Contributing entity | University of Southern California |
| Repository email | cisadmin@lib.usc.edu |
| Full text | 2.1 Introduction The notion of optimal signal representation is a fundamental problem that the signal processing community has been addressing from different angles and under multiple research contexts. The formulation and solution to this problem has provided signifi-cant contributions in lossy compression, estimation and denoising realms [30, 57]. The overarching motivation is to find parsimonious representations for a particular family of signals, where the fact that few coordinates capture most of the target signal energy has proved to be of significant importance in improving compression and denoising tech-niques [57, 10]. In the context of pattern recognition, signal representation issues are naturally asso-ciated with feature extraction (FE). In contrast to compression and denoising scenarios, where the objective is to design bases that allow optimal representation of the observa-tion source, for instance in the mean square error sense, in pattern recognition we seek representations that capture an unobserved finite alphabet phenomena, the class identity, from the observed signal. Consequently, a suitable optimality criterion is associated with minimizing the risk of taking the mentioned decision, as considered in Bayes decision framework [25, 5]. Assuming that we know the observation-class distribution, the min-imum risk decision can be obtained. However in practice typically this distribution is unknown, which introduces the learning aspect of the problem. The Bayes framework proposes to estimate this distribution based on a finite amount of training data [25, 5]. It is well known that the accuracy of this estimation process is affected by the dimension-ality of the observation space—the curse of dimensionality—which is proportional to the disagreement between the real and the estimated distributions, the estimation error effect of the learning problem. Then, an integral part of the feature extraction (FE) is to control the estimation error by finding good parsimonious signal transformations, par-ticularly necessary in scenarios where the original raw observation measurements lie in 5 |
