A Sliding-Window Kernel RLS Algorithm and Its Application to Nonlinear Channel Identification

Vaerenbergh, Steven Van; Vía, Javier; Santamarı́a, Ignacio

doi:10.1109/icassp.2006.1661394

Cited by 124 publications

(109 citation statements)

References 9 publications

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“…which uses the same block definition as in (20). Again, note that R D (i, j) in the above equation reduces to δ ij R uu in the regular case (L = M ) considered in [29].…”

Section: ) Mean Weight Behaviormentioning

confidence: 99%

Online Dictionary Learning for Kernel LMS

Wei

Chen

Richard

et al. 2014

IEEE Trans. Signal Process.

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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 of strategies based on dictionary learning have been proposed to overcome this severe drawback. In the literature, there is no theoretical work that strictly analyzes the problem of updating the dictionary in a time-varying environment. In this paper, we present an analytical study of the convergence behavior of the Gaussian least-mean-square algorithm in the case where the statistics of the dictionary elements only partially match the statistics of the input data. This theoretical analysis highlights the need for updating the dictionary in an online way, by discarding the obsolete elements and adding appropriate ones. We introduce a kernel least-mean-square algorithm with 1-norm regularization to automatically perform this task. The stability in the mean of this method is analyzed, and the improvement of performance due to this dictionary adaptation is confirmed by simulations.

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“…which uses the same block definition as in (20). Again, note that R D (i, j) in the above equation reduces to δ ij R uu in the regular case (L = M ) considered in [29].…”

Section: ) Mean Weight Behaviormentioning

confidence: 99%

Online Dictionary Learning for Kernel LMS

Wei

Chen

Richard

et al. 2014

IEEE Trans. Signal Process.

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“…reg can also be computed quickly, given the inverse of K (n−1) reg [10]. We then iteratively update our parameter estimates for ω Λ and α x as new data arrives using eq.…”

Section: Adaptive Algorithmmentioning

confidence: 99%

Adaptive kernel canonical correlation analysis for estimation of task dynamics from acoustics

Rudzicz¹

2010

2010 IEEE International Conference on Acoustics, Speech and Signal Processing

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We present a method for acoustic-articulatory inversion whose targets are the abstract tract variables from task dynamic theory. Towards this end we construct a non-linear Hammerstein system whose parameters are updated with adaptive kernel canonical correlation analysis. This approach is notably semi-analytical and applicable to large sets of data. Training behaviour is compared across four kernel functions and prediction of tract variables is shown to be significantly more accurate than state-of-the-art mixture density networks.

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“…An exponentially weighted version of KRLS (EW-KRLS) algorithm was introduced in (Liu et al 2010) which includes a forgetting factor for incoming data. A more radical approach was the sliding window KRLS which obtained solution based only on recent data while discarded older data (Van Vaerenbergh et al 2006). From another perspective, to improve tracking capability of the KRLS, Extended KRLS (EX-KRLS) was proposed in (Liu et al 2009) which included a state-space model within the KRLS framework.…”

Section: Introductionmentioning

confidence: 99%