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In this paper, an adaptive adjustment method for the kernel parameter used in the kernel adaptive filters (KAFs) is proposed. The KAF is one of the linear-in-the-parameters (LIP) nonlinear filters, and is based on the kernel method used in machine learning. Typically, the Gaussian kernel function is used, but there is no effective method for automatically adjusting its parameter that influences the...
This paper introduces a novel framework for the study of adaptive or online estimation problems for a common class of nonlinear systems governed by ordinary differential equations (ODEs) on ℝd. In contrast to most conventional strategies for ODEs, the approach here embeds the estimate of the unknown nonlinear function appearing in the plant in a reproducing kernel Hilbert space (RKHS), H. The nonlinear...
Dynamic Movement Primitives (DMPs) are a generic approach for trajectory modeling in an attractor land-scape based on differential dynamical systems. DMPs guarantee stability and convergence properties of learned trajectories, and scale well to high dimensional data. In this paper, we propose DMP+, a modified formulation of DMPs which, while preserving the desirable properties of the original, 1)...
Domain adaptation (DA) algorithms address the problem of distribution shift between training and testing data. Recent approaches transform data into a shared subspace by minimizing the shift between their marginal distributions. We propose a method to learn a common subspace that will leverage the class conditional distributions of training samples along with reducing the marginal distribution shift...
Volterra models can be used to represent a nonlinear systems with vanishing memory. The main drawback of these models is their huge number of parameters to be estimated. To reduce this parametric complexity, we can consider Volterra kernels of order (p > 2) as symmetric tensors and we use a parallel factor (PARAFAC) decomposition of the kernels to derive Volterra-PARAFAC models. In this paper,...
The nonlinear spline adaptive filtering under least mean square (SAF-LMS) uses the mean square error (MSE) based cost function to identify the Wiener-type nonlinear systems, which is rational under the assumption of Gaussian distributions. However, the mere second-order statistics are often not suitable for nonlinear and/or non-Gaussian systems. To address this issue, a new nonlinear adaptive filter,...
In this paper, the optimization of Laguerre-Volterra filters (LVFs) is carried out adaptively. Each kernel is expanded on an independent Laguerre basis. An analytical solution to Laguerre poles optimization is provided using the knowledge of the expansion coefficients, also called Fourier coefficients, associated with an arbitrary Laguerre basis. These coefficients are estimated by means of the Normalized...
In this paper, we highlight a design of Gaussian kernels for online model selection by the multikernel adaptive filtering approach. In the typical multikernel adaptive filtering, the maximum value that each kernel function can take is one. This means that, if one employs multiple Gaussian kernels with multiple variances, the one with the largest variance would become dominant in the kernelized input...
In this paper, we consider the characteristics of the kernel adaptive filters for the mixture of linear and non-linear environments. We first consider employing a linear kernel as one of the kernels in multi-kernel adaptive filters. It is pointed out that the convergence characteristics of the filter corresponding to the linear kernel is affected by the selection of the other kernels. Then, we propose...
Adaptive filtering algorithms operating in reproducing kernel Hilbert spaces have demonstrated superiority over their linear counterpart for nonlinear system identification. Unfortunately, an undesirable characteristic of these methods is that the order of the filters grows linearly with the number of input data. This dramatically increases the computational burden and memory requirement. A variety...
Nonlinear adaptive filters are getting more common and are useful especially where performance of linear adaptive filters may be unacceptable. Such areas include communications, image processing and biological systems. Quaternion valued data has also been drawing recent interest in various areas of statistical signal processing, including adaptive filtering, image pattern recognition, and modeling...
Modeling background and segmenting moving objects are significant techniques for video segmentation and other video processing applications. Many different methods about background modeling and video extraction have been proposed over the recent years. In this paper, we present a novel recursive Kernel Density Estimation based video segmentation method. In the algorithm, local maximum in the density...
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