A simple, yet powerful, learning method is presented by combining the famed kernel trick and the least-mean-square (LMS) algorithm, called the KLMS. General properties of the KLMS algorithm are demonstrated regarding its well-posedness in very high dimensional spaces using Tikhonov regularization theory. An experiment is studied to support our conclusion that the KLMS algorithm can be readily u...

In this technical report we analyse the performance of diffusion strategies applied to the Least-Mean-Square adaptive filter. We configure a network of cooperative agents running adaptive filters and discuss their behaviour when compared with a non-cooperative agent which represents the average of the network. The analysis provides conditions under which diversity in the filter parameters is be...

Ensemble of networks has been proven to give better prediction result than a single network. Two commonly used way of determining the ensemble weights are simple average ensemble method and the generalized ensemble method. In the paper, we propose the weighted least square ensemble network. The major difference between this method and the other ensemble methods is that we do not assume that nei...

This paper introduces a novel constraint adaptive filtering algorithm based on a relative logarithmic cost function which is termed as Constrained Least Mean Logarithmic Square (CLMLS). The proposed CLMLS algorithm elegantly adjusts the cost function based on the amount of error thereby achieves better performance compared to the conventional Constrained LMS (CLMS) algorithm. With no assumption...

The recurrent least squares (RLS) learning approach is proposed for controlling the learning rate in parallel principal subspace analysis (PSA) and in a wide class of principal component analysis (PCA) associated algorithms with a quasi{parallel extraction ability. The purpose is to provide a useful tool for applications where the learning process has to be repeated in an on{line self{adaptive ...

In this paper, we present the convergence analysis of proportionate-type least mean square (Pt-LMS) algorithm that identifies the sparse system effectively and more suitable for real time VLSI applications. Both first and second order convergence analysis of Pt-LMS algorithm is studied. Optimum convergence behavior of Pt-LMS algorithm is studied from the second order convergence analysis provid...

The least-squares (or Lomb-Scargle) periodogram is a powerful tool which is used routinely in many branches of astronomy to search for periodicities in observational data. The problem of assessing statistical significance of candidate periodicities for different periodograms is considered. Based on results in extreme value theory, improved analytic estimations of false alarm probabilities are g...

In this work, a new class of stochastic gradient algorithm is developed based on q-calculus. Unlike the existing q-LMS algorithm, the proposed approach fully utilizes the concept of q-calculus by incorporating time-varying q parameter. The proposed enhanced q-LMS (Eq-LMS) algorithm utilizes a novel, parameterless concept of error-correlation energy and normalization of signal to ensure high con...

......................................................................................................................... I Acknowledgments .......................................................................................................... II Author Declaration ........................................................................................................ IV Associated Publicati...