Related papers: The Generalized Complex Kernel Least-Mean-Square A…
Usually, complex-valued RKHS are presented as an straightforward application of the real-valued case. In this paper we prove that this procedure yields a limited solution for regression. We show that another kernel, here denoted as pseudo…
Over the last decade, kernel methods for nonlinear processing have successfully been used in the machine learning community. The primary mathematical tool employed in these methods is the notion of the Reproducing Kernel Hilbert Space.…
The kernel least mean squares (KLMS) algorithm is a computationally efficient nonlinear adaptive filtering method that "kernelizes" the celebrated (linear) least mean squares algorithm. We demonstrate that the least mean squares algorithm…
In this paper we propose a novel Bayesian solution for nonlinear regression in complex fields. Previous solutions for kernels methods usually assume a complexification approach, where the real-valued kernel is replaced by a complex-valued…
Kernel Regularized Least Squares (KRLS) is a popular method for flexibly estimating models that may have complex relationships between variables. However, its usefulness to many researchers is limited for two reasons. First, existing…
In most adaptive signal processing applications, system linearity is assumed and adaptive linear filters are thus used. The traditional class of supervised adaptive filters rely on error-correction learning for their adaptive capability.…
In the last decade, a considerable research effort has been devoted to developing adaptive algorithms based on kernel functions. One of the main features of these algorithms is that they form a family of universal approximation techniques,…
In this research, a novel adaptive filtering algorithm is proposed for complex domain signal processing. The proposed algorithm is based on Wirtinger calculus and is called as q-Complex Least Mean Square (q-CLMS) algorithm. The proposed…
Complex-valued signals are used in the modeling of many systems in engineering and science, hence being of fundamental interest. Often, random complex-valued signals are considered to be proper. A proper complex random variable or process…
Kernel adaptive filters (KAF) are a class of powerful nonlinear filters developed in Reproducing Kernel Hilbert Space (RKHS). The Gaussian kernel is usually the default kernel in KAF algorithms, but selecting the proper kernel size…
The robustness of the kernel recursive least square (KRLS) algorithm has recently been improved by combining them with more robust information-theoretic learning criteria, such as minimum error entropy (MEE) and generalized MEE (GMEE),…
Multiple kernel methods less consider the intrinsic manifold structure of multiple kernel data and estimate the consensus kernel matrix with quadratic number of variables, which makes it vulnerable to the noise and outliers within multiple…
We study the relationship between online Gaussian process (GP) regression and kernel least mean squares (KLMS) algorithms. While the latter have no capacity of storing the entire posterior distribution during online learning, we discover…
This work presents a distributed algorithm for nonlinear adaptive learning. In particular, a set of nodes obtain measurements, sequentially one per time step, which are related via a nonlinear function; their goal is to collectively…
Although the real reproducing kernels are used in an increasing number of machine learning problems, complex kernels have not, yet, been used, in spite of their potential interest in applications such as communications. In this work, we…
Partial Least-Squares (PLS) Regression is a widely used tool in chemometrics for performing multivariate regression. PLS is a bi-linear method that has a limited capacity of modelling non-linear relations between the predictor variables and…
Least squares kernel based methods have been widely used in regression problems due to the simple implementation and good generalization performance. Among them, least squares support vector regression (LS-SVR) and extreme learning machine…
In this paper, we consider the nonparametric least square regression in a Reproducing Kernel Hilbert Space (RKHS). We propose a new randomized algorithm that has optimal generalization error bounds with respect to the square loss, closing a…
Functional regression is very crucial in functional data analysis and a linear relationship between scalar response and functional predictor is often assumed. However, the linear assumption may not hold in practice, which makes the methods…
Kernel methods have been extensively utilized in machine learning for classification and prediction tasks due to their ability to capture complex non-linear data patterns. However, single kernel approaches are inherently limited, as they…