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Bouboulis P.,National and Kapodistrian University of Athens | Theodoridis S.,National and Kapodistrian University of Athens | Theodoridis S.,Research Academic Computer Technology Institute
IEEE Transactions on Signal Processing | Year: 2011

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 (RKHS). 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 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. Wirtinger's calculus simplifies computations and offers an elegant tool for treating complex signals. 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. © 2010 IEEE. Source

Garofalakis J.,University of Patras | Garofalakis J.,Research Academic Computer Technology Institute | Stergiou E.,ATEI of Epirus
Future Generation Computer Systems | Year: 2013

The aim of this paper is to develop an analytical method for performance evaluation of double prioritized Multistage Interconnected Networks (MINs) with single or multilayers and backpressure operation which provide service differentiation and QoS guarantee to an end application running over next generation Internet or Grid systems. Specifically, a new architecture of switching elements is used for the construction of MINs. This switch element uses two parallel queues in order to serve dual priority traffic. Besides this, uniform traffic conditions are presupposed and the bulk of packet arrivals in each cycle to the network inputs follow a Bernoulli distribution. A new analytical model for evaluating single buffered MIN's with 2×2 special switching elements supporting internally two classes' priority traffic is presented. Equations for the steady state are derived. These equations are then used in finding the most important multistage network performance metrics, such as throughput, and packet latency. The results are also validated using simulation and compared with previous related work in marginal cases. This proposed analytical model is accurate for various network sizes and various values of offered traffic to the multistage network inputs. © 2012 Published by Elsevier B.V. All rights reserved. Source

Bouboulis P.,National and Kapodistrian University of Athens | Slavakis K.,University of Peloponnese | Theodoridis S.,Research Academic Computer Technology Institute
IEEE Transactions on Neural Networks and Learning Systems | Year: 2012

This paper presents a wide framework for non-linear online supervised learning tasks in the context of complex valued signal processing. The (complex) input data are mapped into a complex reproducing kernel Hilbert space (RKHS), where the learning phase is taking place. Both pure complex kernels and real kernels (via the complexification trick) can be employed. Moreover, any convex, continuous and not necessarily differentiable function can be used to measure the loss between the output of the specific system and the desired response. The only requirement is the subgradient of the adopted loss function to be available in an analytic form. In order to derive analytically the subgradients, the principles of the (recently developed) Wirtinger's calculus in complex RKHS are exploited. Furthermore, both linear and widely linear (in RKHS) estimation filters are considered. To cope with the problem of increasing memory requirements, which is present in almost all online schemes in RKHS, the sparsification scheme, based on projection onto closed balls, has been adopted. We demonstrate the effectiveness of the proposed framework in a non-linear channel identification task, a non-linear channel equalization problem and a quadrature phase shift keying equalization scheme, using both circular and non circular synthetic signal sources. © 2012 IEEE. Source

Bouboulis P.,National and Kapodistrian University of Athens | Theodoridis S.,National and Kapodistrian University of Athens | Theodoridis S.,Research Academic Computer Technology Institute | Mavroforakis M.,University of Houston
IEEE Transactions on Signal Processing | Year: 2012

Recently, a unified framework for adaptive kernel based signal processing of complex data was presented by the authors, which, besides offering techniques to map the input data to complex reproducing kernel Hilbert spaces, developed a suitable Wirtinger-like calculus for general Hilbert spaces. In this short paper, the extended Wirtinger's calculus is adopted to derive complex kernel-based widely linear estimation filters suitable for applications involving noncircular data. Furthermore, we illuminate several important characteristics of the widely linear filters. We show that, although in many cases the gains from adopting widely linear estimation filters, as alternatives to ordinary linear ones, are rudimentary, for the case of kernel based widely linear filters significant performance improvements can be obtained. © 1991-2012 IEEE. Source

Agency: Cordis | Branch: FP7 | Program: CP | Phase: ICT-2007.8.2 | Award Amount: 3.09M | Year: 2008

In the near future, it is reasonable to expect that new types of systems will appear, designed or emerged, of massive scale, expansive and permeating their environment, of very heterogeneous nature, and operating in a constantly changing networked environment. We expect that most such systems will have the form of a large society of networked artifacts that are small, have limited sensing, signal processing, and communication capabilities, and are usually of limited energy. Yet by cooperation, they will be organized in large societies to accomplish tasks that are difficult or beyond the capabilities of todays conventional centralized systems. The scale and nature of these systems requires naturally that they are pervasive and are expected to operate beyond the complete understanding and control of their designers, developers, and users. These systems or societies should have particular ways to achieve an appropriate level of organization and integration that is achieved seamlessly and with appropriate levels of flexibility. The aim of this project is to establish the foundations of adaptive networked societies of small or tiny heterogeneous artifacts. We indent to develop an understanding of such societies that will enable us to establish their fundamental properties and laws, as well as, their inherent trade-offs. We will approach our goal by working on a usable quantitative theory of networked adaptation based on rigorous and measurable gains. We also indent to apply our models, methods, and results to the scrutiny of large-scale simulations and experiments, from which we expect to obtain valuable feedback. The foundational results and the feedback from simulations and experiments will form a unifying framework for adaptive nets of artifacts that hopefully will enable us to come up with a coherent working set of design rules for such systems. In a nutshell, we will work towards a science of adaptive organization of pervasive networks of small or tiny artifacts.

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