103 research outputs found
Adaptive Random Fourier Features Kernel LMS
We propose the adaptive random Fourier features Gaussian kernel LMS
(ARFF-GKLMS). Like most kernel adaptive filters based on stochastic gradient
descent, this algorithm uses a preset number of random Fourier features to save
computation cost. However, as an extra flexibility, it can adapt the inherent
kernel bandwidth in the random Fourier features in an online manner. This
adaptation mechanism allows to alleviate the problem of selecting the kernel
bandwidth beforehand for the benefit of an improved tracking in non-stationary
circumstances. Simulation results confirm that the proposed algorithm achieves
a performance improvement in terms of convergence rate, error at steady-state
and tracking ability over other kernel adaptive filters with preset kernel
bandwidth.Comment: 5 pages, 2 figure
Extension of Wirtinger's Calculus to Reproducing Kernel Hilbert Spaces and the Complex Kernel LMS
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. However, so far, the emphasis has been on batch
techniques. It is only recently, that online techniques have been considered in
the context of adaptive signal processing tasks. Moreover, these efforts have
only been focussed on real valued data sequences. To the best of our knowledge,
no adaptive kernel-based strategy has been developed, so far, for complex
valued signals. Furthermore, 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 that deal
with complex signals, with Communications being a typical example. In this
paper, we present a general framework to attack the problem of adaptive
filtering of complex signals, using either real reproducing kernels, taking
advantage of a technique called \textit{complexification} of real RKHSs, or
complex reproducing kernels, highlighting the use of the complex gaussian
kernel. In order to derive gradients of operators that need to be defined on
the associated complex RKHSs, we employ the powerful tool of Wirtinger's
Calculus, which has recently attracted attention in the signal processing
community. To this end, in this paper, the notion of Wirtinger's calculus is
extended, for the first time, to include complex RKHSs and use it to derive
several realizations of the Complex Kernel Least-Mean-Square (CKLMS) algorithm.
Experiments verify that the CKLMS offers significant performance improvements
over several linear and nonlinear algorithms, when dealing with nonlinearities.Comment: 15 pages (double column), preprint of article accepted in IEEE Trans.
Sig. Pro
Εφαρμογές των Reproducing Kernel Hilbert Spaces στη Μηχανική Μάθηση και Υλοποίηση Αλγορίθμων
Σύντομη αναφορά ιδιοτήτων των Reproducing Kernel Hilbert Spaces. Εφαρμογή της
θεωρίας αυτής σε αλγορίθμους (Kernel LMS, Kernel RLS) με τη βοήθεια του kernel
τεχνάσματος. Παρουσίαση αποτελεσμάτων από την υλοποίηση ορισμένων αλγορίθμων.Brief reference of the characteristics of Reproducing Kernel Hilbert Spaces.
Application of this theory in various algorithms (Kernel LMS, Kernel RLS) using
the kernel trick. Presentation of the results of several experiments
Adaptation and learning over networks for nonlinear system modeling
In this chapter, we analyze nonlinear filtering problems in distributed
environments, e.g., sensor networks or peer-to-peer protocols. In these
scenarios, the agents in the environment receive measurements in a streaming
fashion, and they are required to estimate a common (nonlinear) model by
alternating local computations and communications with their neighbors. We
focus on the important distinction between single-task problems, where the
underlying model is common to all agents, and multitask problems, where each
agent might converge to a different model due to, e.g., spatial dependencies or
other factors. Currently, most of the literature on distributed learning in the
nonlinear case has focused on the single-task case, which may be a strong
limitation in real-world scenarios. After introducing the problem and reviewing
the existing approaches, we describe a simple kernel-based algorithm tailored
for the multitask case. We evaluate the proposal on a simulated benchmark task,
and we conclude by detailing currently open problems and lines of research.Comment: To be published as a chapter in `Adaptive Learning Methods for
Nonlinear System Modeling', Elsevier Publishing, Eds. D. Comminiello and J.C.
Principe (2018
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