A kernel-based RLS algorithm for nonlinear adaptive filtering using.pdf

A kernel-based RLS algorithm for nonlinear adaptive filtering using.pdf

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A kernel-based RLS algorithm for nonlinear adaptive filtering using

A kernel-based RLS algorithm for nonlinear adaptive filtering using sparse approximation theory Ce?dric Richard Institut Charles Delaunay (ICD, FRE CNRS 2848), Laboratoire LM2S Universite? de Technologie de Troyes, BP 2060, 10010 Troyes cedex - France tel.: +33.3.25.71.58.47 fax.: +33.3.25.71.56.99 cedric.richard@utt.fr 1 Short abstract In the last ten years, there has been an explosion of activity in the field of learning algorithms utilizing reproducing kernels, most notably for classification and regression. A common characteristic in kernel- based methods is that they deal with models whose order equals the number of input data, making them unsuitable for online applications. In this paper, we investigate a new kernel-based RLS algorithm that makes unnecessary the use of any computationally demanding sparsification procedure. The increase in the model order is controlled by the coherence parameter, a fundamental quantity that is used to characterize the behavior of dictionaries in sparse approximation problems. 2 Extended abstract Adaptive filtering has become a topic of keen interest over the past three decades to help cope with time variations of system parameters and lack of a priori statistical information [11, 15]. Linear models are still routinely used because of their inherent simplicity from conceptual and implementational point of view. In many practical situations, however, nonlinear signal processing is needed. It includes items such as nonlinear system identification, prediction and control, e.g., in communications and biomedical engineering, see [9]. Following the pioneering works [1, 2, 13], there has been recent progress in function approximation methods based on reproducing kernel Hilbert spaces (RKHS) [12, 16], including, for example, support vector regression [18]. A common characteristic in kernel-based methods is that they deal with models whose order is the size of the training set, making them unsuitable for online applications. Several alg

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