Article
Complex-Valued Kernel Methods for Regression
Author/s | Boloix Tortosa, Rafael
Murillo Fuentes, Juan José Santos, Irene Pérez Cruz, Fernando |
Department | Universidad de Sevilla. Departamento de Teoría de la Señal y Comunicaciones |
Publication Date | 2017-10 |
Deposit Date | 2024-09-23 |
Abstract | In this paper, we propose a widely linear reproducing kernel Hilbert space (WL-RKHS) for nonlinear regression with complex-valued signals. Our approach is a nonlinear extension of WL signal processing that has been proven ... In this paper, we propose a widely linear reproducing kernel Hilbert space (WL-RKHS) for nonlinear regression with complex-valued signals. Our approach is a nonlinear extension of WL signal processing that has been proven to be more versatile than linear systems for dealing with complex-value signals. To be able to use the WL concept in kernel methods, we need to introduce a pseudo-kernel to complement the standard kernel in RKHS, which is not defined in previous RKHS approaches in the existing literature. In this paper, we present WL-RKHS, its properties, and the kernel and pseudo-kernel designs. We illustrate the need of the pseudo-kernel with simply verifiable examples that allow understanding the intuitions behind this kernel. We conclude this paper, showing that in the all-relevant nonlinear equalization problem the pseudo-kernel plays a significant role and previous approaches that do not rely on this kernel clearly underperform. |
Funding agencies | Ministerio de Educación y Ciencia (MEC). España |
Project ID. | TEC2016-78434-C03-02) |
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Widely Linear Complex-Valued ... | 2.048Mb | [PDF] | View/ | |