Discrete Time Signal Processing Framework with Support Vector Machines

Discrete Time Signal Processing Framework with Support Vector Machines

José Luis Rojo-Álvarez (Universidad Rey Juan Carlos, Spain), Manel Martínez-Ramón (Universidad Carlos III de Madrid, Spain), Gustavo Camps-Valls (Universitat de València, Spain), Carlos E. Martínez-Cruz (Universidad Carlos III de Madrid, Spain) and Carlos Figuera (Universidad Rey Juan Carlos, Spain)
Copyright: © 2007 |Pages: 29
DOI: 10.4018/978-1-59904-042-4.ch006
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Digital signal processing (DSP) of time series using SVM has been addressed in the literature with a straightforward application of the SVM kernel regression, but the assumption of independently distributed samples in regression models is not fulfilled by a time-series problem. Therefore, a new branch of SVM algorithms has to be developed for the advantageous application of SVM concepts when we process data with underlying time-series structure. In this chapter, we summarize our past, present, and future proposal for the SVM-DSP frame-work, which consists of several principles for creating linear and nonlinear SVM algorithms devoted to DSP problems. First, the statement of linear signal models in the primal problem (primal signal models) allows us to obtain robust estimators of the model coefficients in classical DSP problems. Next, nonlinear SVM-DSP algorithms can be addressed from two different approaches: (a) reproducing kernel Hilbert spaces (RKHS) signal models, which state the signal model equation in the feature space, and (b) dual signal models, which are based on the nonlinear regression of the time instants with appropriate Mercer’s kernels. This way, concepts like filtering, time interpolation, and convolution are considered and analyzed, and they open the field for future development on signal processing algorithms following this SVM-DSP framework.

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Table of Contents
Bernhard Schölkopf
Gustavo Camps-Valls, José Luis Rojo-Álvarez, Manel Martínez-Ramón
Gustavo Camps-Valls, José Luis Rojo-Álvarez, Manel Martínez-Ramón
List of Reviewers
Chapter 1
Nello Cristianini, John Shawe-Taylor, Craig Saunders
During the past decade, a major revolution has taken place in pattern-recognition technology with the introduction of rigorous and powerful... Sample PDF
Kernel Methods: A Paradigm for Pattern Analysis
Chapter 2
Jean-Philippe Vert
Support vector machines and kernel methods are increasingly popular in genomics and computational biology due to their good performance in... Sample PDF
Kernel Methods in Genomics and Computational Biology
Chapter 3
Nathalie L.M.M. Pochet, Fabian Ojeda, Frank De Smet, Tijl De Bie, Johan A.K. Suykens
Clustering techniques like k-means and hierarchical clustering have shown to be useful when applied to microarray data for the identification of... Sample PDF
Kernel Clustering for Knowledge Discovery in Clinical Microarray Data Analysis
Chapter 4
Stanislaw Osowski, Tomasz Markiewicz
This chapter presents an automatic system for white blood cell recognition in myelogenous leukaemia on the basis of the image of a bone-marrow... Sample PDF
Support Vector Machine for Recognition of White Blood Cells of Leukaemia
Chapter 5
Manel Martínez-Ramón, Vladimir Koltchinskii, Gregory L. Heileman, Stefan Posse
Pattern recognition in functional magnetic resource imaging (fMRI) is a novel technique that may lead to a quantity of discovery tools in... Sample PDF
Classification of Multiple Interleaved Human Brain Tasks in Functional Magnetic Resonance Imaging
Chapter 6
José Luis Rojo-Álvarez, Manel Martínez-Ramón, Gustavo Camps-Valls, Carlos E. Martínez-Cruz, Carlos Figuera
Digital signal processing (DSP) of time series using SVM has been addressed in the literature with a straightforward application of the SVM kernel... Sample PDF
Discrete Time Signal Processing Framework with Support Vector Machines
Chapter 7
M. Julia Fernández-Getino García, José Luis Rojo-Álvarez, Víctor P. Gil-Jiménez, Felipe Alonso-Atienza, Ana García-Armada
Most of the approaches to digital communication applications using support vector machines (SVMs) rely on the conventional classification and... Sample PDF
A Complex Support Vector Machine Approach to OFDM Coherent Demodulation
Chapter 8
Christos Christodoulou, Manel Martínez-Ramón
Support vector machines (SVMs) are a good candidate for the solution of antenna array processing problems such as beamforming, detection of the... Sample PDF
Comparison of Kernel Methods Applied to Smart Antenna Array Processing
Chapter 9
Joseph Picone, Aravind Ganapathiraju, Jon Hamaker
Automated speech recognition is traditionally defined as the process of converting an audio signal into a sequence of words. Over the past 30 years... Sample PDF
Applications of Kernel Theory to Speech Recognition
Chapter 10
Vincent Wan
This chapter describes the adaptation and application of kernel methods for speech processing. It is divided into two sections dealing with speaker... Sample PDF
Building Sequence Kernels for Speaker Verification and Word Recognition
Chapter 11
Blaž Fortuna, Nello Cristianini, John Shawe-Taylor
We present a general method using kernel canonical correlation analysis (KCCA) to learn a semantic of text from an aligned multilingual collection... Sample PDF
A Kernel Canonical Correlation Analysis for Learning the Semantics of Text
Chapter 12
Gökhan Bakir, Bernhard Schölkopf, Jason Weston
In this chapter, we are concerned with the problem of reconstructing patterns from their representation in feature space, known as the pre-image... Sample PDF
On the Pre-Image Problem in Kernel Methods
Chapter 13
Juan Gutiérrez, Gabriel Gómez-Perez, Jesús Malo, Gustavo Camps-Valls
Support vector machine (SVM) image coding relies on the ability of SVMs for function approximation. The size and the profile of the e-insensitivity... Sample PDF
Perceptual Image Representations for Support Vector Machine Image Coding
Chapter 14
Francesca Odone, Alessandro Verri
In this chapter we review some kernel methods useful for image classification and retrieval applications. Starting from the problem of constructing... Sample PDF
Image Classification and Retrieval with Kernel Methods
Chapter 15
Daniel Cremers, Timo Kohlberger
We present a method of density estimation that is based on an extension of kernel PCA to a probabilistic framework. Given a set of sample data, we... Sample PDF
Probabilistic Kernel PCA and its Application to Statistical Modeling and Inference
Chapter 16
Lorenzo Bruzzone, Luis Gomez-Chova, Mattia Marconcini, Gustavo Camps-Valls
The information contained in hyperspectral images allows the characterization, identification, and classification of land covers with improved... Sample PDF
Hyperspectral Image Classification with Kernels
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