Kernel Feature Extraction in Signal Processing

Kernel‐based feature extraction and dimensionality reduction are becoming increasingly important in advanced signal processing. This is particularly relevant in applications dealing with very high‐dimensional data. Besides changing the data representation space via kernel featu...

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Vydáno v:Digital Signal Processing with Kernel Methods s. 543 - 588
Hlavní autoři: Rojo-Álvarez, José Luis, Martínez-Ramón, Manel, Muñoz-Mar&iacute, Jordi, Camps-Valls, Gustau
Médium: Kapitola
Jazyk:angličtina
Vydáno: Chichester, UK Wiley 2018
John Wiley & Sons, Ltd
Vydání:1
Edice:Wiley - IEEE
Témata:
cross‐covariance operator
Hilbert schmidt independence criterion
kernel based feature extraction
kernel dimensionality reduction methods
signal processing
Dimensionality reduction
Correlation
Signal processing
Feature extraction
Kernel
Covariance matrices
Principal component analysis
ISBN:9781118611791, 1118611799
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Shrnutí:Kernel‐based feature extraction and dimensionality reduction are becoming increasingly important in advanced signal processing. This is particularly relevant in applications dealing with very high‐dimensional data. Besides changing the data representation space via kernel feature extraction, another possibility is to correct for biases in the data distributions operating on the samples. This chapter reviews the main kernel feature extraction and dimensionality reduction methods, dealing with supervised, unsupervised and semi‐supervised settings. It illustrates methods in toy examples, as well as real datasets. The chapter also analyzes the connections between Hilbert‐Schmidt independence criterion (HSIC) and classical feature extraction methods. The HSIC method measures cross‐covariance in an adequate reproducing kernel Hilbert space (RKHS) by using the entire spectrum of the cross‐covariance operator. Kernel dimensionality reduction (KDR) is a supervised feature extraction method that seeks a linear transformation of the data such that it maximizes the conditional HSIC on the labels.
ISBN:9781118611791
1118611799
DOI:10.1002/9781118705810.ch12