The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Tokunbo Ogunfunmi - One of the best experts on this subject based on the ideXlab platform.
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Study of the Convergence Behavior of the complex kernel least mean square algorithm
IEEE Transactions on Neural Networks and Learning Systems, 2013Co-Authors: Thomas K. Paul, Tokunbo OgunfunmiAbstract:The complex kernel least mean square (CKLMS) algorithm is recently derived and allows for online kernel adaptive learning for complex data. Kernel adaptive methods can be used in finding solutions for neural network and machine learning applications. The derivation of CKLMS involved the development of a modified Wirtinger calculus for Hilbert spaces to obtain the cost function gradient. We analyze the Convergence of the CKLMS with different kernel forms for complex data. The expressions obtained enable us to generate theory-predicted mean-square error curves considering the circularity of the complex input signals and their effect on nonlinear learning. Simulations are used for verifying the analysis results.
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analysis of the Convergence Behavior of the complex gaussian kernel lms algorithm
International Symposium on Circuits and Systems, 2012Co-Authors: Thomas Paul, Tokunbo OgunfunmiAbstract:Kernel-based adaptive filters present a new opportunity to re-cast nonlinear optimization problems over a Reproducing Kernel Hilbert Space (RKHS), transforming the nonlinear task to linear, where easier and well-known methods may be used. The approach can be seen to yield solutions suitable for sparse adaptive filtering. The new Complex Kernel Least Mean Square algorithm (CKLMS), derived by Bouboulis and Theodoridis, allows kernel-based online adaptive filtering for complex data. Here we report our results on the Convergence of CKLMS with the complexified form of the Gaussian kernel. The analysis performed is based on a recent study of the Kernel LMS from Parreira et al. The analysis is used to generate theory-predicted MSE curves which consider the circularity/non-circularity of complex input which to our knowledge has not been considered previously for online nonlinear learning. Simulations are used to verify the theoretical analysis results.
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on the Convergence Behavior of the affine projection algorithm for adaptive filters
IEEE Transactions on Circuits and Systems, 2011Co-Authors: Thomas Paul, Tokunbo OgunfunmiAbstract:The affine projection class of algorithms (APA) provides faster Convergence than LMS-based adaptive filters. Its Convergence analysis is not as extensively studied as Normalized LMS (NLMS), and remains an active area of research. For tractability, most works on APA make many assumptions on the statistics of the input, as well as correlation between signals. Here we consider the effect of the correlation between filter coefficients and past measurement noise on MSE error. The effect of this correlation was found to be dependent on step-size mu, increasing or decreasing the predicted MSE depending on whether mu is less than or greater than 1, irrespective of the input statistics. Simulations are used to verify the analysis results presented.
Behrouz Farhangboroujeny - One of the best experts on this subject based on the ideXlab platform.
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analysis of the stereophonic lms newton algorithm and impact of signal nonlinearity on its Convergence Behavior
IEEE Transactions on Signal Processing, 2010Co-Authors: Harsha Inna Kedage Rao, Behrouz FarhangboroujenyAbstract:The strong cross-correlation that exists between the two input audio channels makes the problem of stereophonic acoustic echo cancellation (AEC) complex and challenging to solve. Recently, two new implementations of the LMS/Newton algorithm that uses a linear decorrelation technique were proposed. This method helps to mitigate the effect of the ill-conditioned problem on the Convergence rate of the LMS/Newton adaptive algorithm. The complexity of these algorithms is significantly lower than the recursive least-squares (RLS) algorithm, which is known to provide excellent echo cancellation. Furthermore, unlike the various versions of the RLS algorithm, the LMS/Newton algorithm is more robust to numerical errors. It has also been suggested that applying nonlinearities to signals at the two audio channels will help to alleviate the misalignment problem of stereophonic AEC systems. Simulation studies reveal that application of certain classes of nonlinearities to the two-channel LMS/Newton algorithms helps to further reduce the misalignment but it also leads to an unexpected and significant reduction in the rate of Convergence of the mean-square error. The contributions of this paper are twofold. First, we provide an analysis of the two-channel LMS/Newton algorithm that was proposed in our earlier work. Second, we provide a theoretical understanding for the appearance of the slow modes of Convergence in the presence of nonlinearities and show that they can be resolved through a preprocessing step.
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analysis of the frequency domain block lms algorithm
IEEE Transactions on Signal Processing, 2000Co-Authors: Behrouz Farhangboroujeny, Kheong Sann ChanAbstract:We present a new analysis of the frequency-domain block least-mean-square (FBLMS) algorithm. An earlier analysis uses a mapping of the frequency-domain information to the time-domain before proceeding with the analysis of the algorithm. We present a direct analysis of the FBLMS algorithm in the frequency domain. As compared with the previous analysis, the new analysis is easier to follow. It is also more rigorous than the previous works and gives a better insight to the effect of various processing components in the algorithm structure on its Convergence Behavior. In particular, we show how the transformation of input samples to the frequency domain, combined with the effect of the involved windowing matrices, and step-normalization affect the Convergence Behavior of both constrained and unconstrained versions of the FBLMS algorithm. We also report a procedure for derivation of misadjustment equations of various versions of the FBLMS algorithm.
Kheong Sann Chan - One of the best experts on this subject based on the ideXlab platform.
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analysis of the frequency domain block lms algorithm
IEEE Transactions on Signal Processing, 2000Co-Authors: Behrouz Farhangboroujeny, Kheong Sann ChanAbstract:We present a new analysis of the frequency-domain block least-mean-square (FBLMS) algorithm. An earlier analysis uses a mapping of the frequency-domain information to the time-domain before proceeding with the analysis of the algorithm. We present a direct analysis of the FBLMS algorithm in the frequency domain. As compared with the previous analysis, the new analysis is easier to follow. It is also more rigorous than the previous works and gives a better insight to the effect of various processing components in the algorithm structure on its Convergence Behavior. In particular, we show how the transformation of input samples to the frequency domain, combined with the effect of the involved windowing matrices, and step-normalization affect the Convergence Behavior of both constrained and unconstrained versions of the FBLMS algorithm. We also report a procedure for derivation of misadjustment equations of various versions of the FBLMS algorithm.
Thom H Dunning - One of the best experts on this subject based on the ideXlab platform.
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the effect of basis set superposition error bsse on the Convergence of molecular properties calculated with the correlation consistent basis sets
Advances in Quantum Chemistry, 1998Co-Authors: Tanja Van Mourik, David E Woon, Angela K Wilson, Kirk A Peterson, Thom H DunningAbstract:It is shown that, in many cases, the Convergence Behavior of molecular properties computed with the correlation consistent basis sets (both standard and augmented sets) is significantly improved if basis set superposition error (BSSE) is taken into account. The effects are most pronounced for pure van der Waals systems like the helium or argon dimers. For these systems the uncorrected D e , r e , and ω e behave very irregularly with increasing basis set size, with the Convergence Behavior being dramatically improved by use of the counterpoise procedure. Even for strongly bound diatomics like N 2 , HF, and HCl, the counterpoise correction often significantly improves the Convergence Behavior of r e and ω e . Similar Behavior is observed in the weakly bound molecular complexes, ArHF, HCO − , and (HF) 2 , as well as for the more strongly bound HCO molecule. For HCO − , because of the pronounced lengthening of the CO bond upon molecular formation, the deformation energy must also be taken into account.
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the effect of basis set superposition error bsse on the Convergence of molecular properties calculated with the correlation consistent basis sets
Advances in Quantum Chemistry, 1998Co-Authors: Tanja Van Mourik, David E Woon, Angela K Wilson, Kirk A Peterson, Thom H DunningAbstract:It is shown that, in many cases, the Convergence Behavior of molecular properties computed with the correlation consistent basis sets (both standard and augmented sets) is significantly improved if basis set superposition error (BSSE) is taken into account. The effects are most pronounced for pure van der Waals systems like the helium or argon dimers. For these systems the uncorrected D e , r e , and ω e behave very irregularly with increasing basis set size, with the Convergence Behavior being dramatically improved by use of the counterpoise procedure. Even for strongly bound diatomics like N 2 , HF, and HCl, the counterpoise correction often significantly improves the Convergence Behavior of r e and ω e . Similar Behavior is observed in the weakly bound molecular complexes, ArHF, HCO − , and (HF) 2 , as well as for the more strongly bound HCO molecule. For HCO − , because of the pronounced lengthening of the CO bond upon molecular formation, the deformation energy must also be taken into account.
Woojin Song - One of the best experts on this subject based on the ideXlab platform.
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a theory on the Convergence Behavior of the affine projection algorithm
IEEE Transactions on Signal Processing, 2011Co-Authors: Seongeun Kim, Jaewoo Lee, Woojin SongAbstract:In this paper, we present a theoretical Convergence analysis of the affine projection algorithm (APA) based on the arguments of energy conservation. Although the APA and its Convergence analysis have been widely studied, the dependency of weight-error vector on past noise is usually neglected for simplicity. To obtain accurate theoretical results for the APA, we here consider the dependency between the weight-error vector and past noise in the mean-square analysis presented by Shin and Sayed in [“Mean-square performance of a family of affine projection algorithms,” IEEE Transactions on Signal Processing, vol. 52, no. 1, pp. 90-102, January 2004]. Through this work, we can also theoretically analyze the Behavior of the periodic APA, which updates its weights periodically. Simulation results show that our theoretical results coincide closely with simulations.