Numerical Complexity

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O. Caspary - One of the best experts on this subject based on the ideXlab platform.

  • Enhanced high resolution spectral analysis of sleep spindles
    Proceedings of 16th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 1
    Co-Authors: O. Caspary, M. Tomczak, N. Di Renzo, Marc Mouze-amady, D. Henry
    Abstract:

    A method to extract the spectral components from spindles of sleep electroencephalograms (EEG) is proposed. High resolution (HR) spectral methods are used which yield better results than Fourier transform (FT) or parametric estimators. A zoom function is produced to reduce their Numerical Complexity and increase their resolution. The method allows to clearly separate the different spectral components (spindles, K complexes, background activity), and should be considered for spectral analysis of various short EEG transients.

  • Adaptive spectral analysis of sleep spindles based on subspace tracking
    Proceedings of 18th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 1
    Co-Authors: O. Caspary, P. Nus
    Abstract:

    A method to track the spectra of human sleep electroencephalogram (EEG) spindles is presented. This method uses a low-rank approximation of the covariance matrix and offers a compromise between Numerical Complexity and convergence. In the first part of the article, the authors describe the method briefly. In the second part, they apply it to filtered spindles to find an adequate agreement with a model of spindles that they put forward. Finally, it is concluded that there are different sorts of spindles according to frequency variation.

Amrane Houacine - One of the best experts on this subject based on the ideXlab platform.

  • Regularized fast recursive least squares algorithms for finite memory filtering
    IEEE Transactions on Signal Processing, 1992
    Co-Authors: Amrane Houacine
    Abstract:

    Novel fast recursive least squares algorithms are developed for finite memory filtering, by using a sliding data window. These algorithms allow the use of statistical priors about the solution, and they maintain a balance between a priori and data information. They are well suited for computing a regularized solution, which has better Numerical stability properties than the conventional least squares solution. The algorithms have a general matrix formulation, such that the same equations are suitable for the prewindowed as well as the covariance case, regardless of the a priori information used. Only the initialization step and the Numerical Complexity change through the dimensions of the intervening matrix variables. The lower bound of O(16m) is achieved in the prewindowed case when the estimated coefficients are assumed to be uncorrelated, m being the order of the estimated model. It is shown that a saving of 2m multiplications per recursion can always be obtained. The lower bound of the resulting Numerical Complexity becomes O(14m), but then the general matrix formulation is lost. >

  • Regularized fast recursive least squares algorithms for adaptive filtering
    IEEE Transactions on Signal Processing, 1991
    Co-Authors: Amrane Houacine
    Abstract:

    Fast recursive least squares (FRLS) algorithms are developed by using factorization techniques which represent an alternative way to the geometrical projections approach or the matrix-partitioning-based derivations. The estimation problem is formulated within a regularization approach, and priors are used to achieve a regularized solution which presents better Numerical stability properties than the conventional least squares one. The Numerical Complexity of the presented algorithms is explicitly related to the displacement rank of the a priori covariance matrix of the solution. It then varies between O(5m) and that of the slow RLS algorithms to update the Kalman gain vector, m being the order of the solution. An important advantage of the algorithms is that they admit a unified formulation such that the same equations may equally treat the prewindowed and the covariance cases independently from the used priors. The difference lies only in the involved Numerical Complexity, which is modified through a change of the dimensions of the intervening variables. Simulation results are given to illustrate the performances of these algorithms. >

  • ICASSP - Regularized fast recursive least squares algorithms
    International Conference on Acoustics Speech and Signal Processing, 1
    Co-Authors: Amrane Houacine
    Abstract:

    Chandrasekhar type factorization is used to develop new fast recursive least squares (FRLS) algorithms for finite memory filtering. Statistical priors are used to get a regularized solution which presents better Numerical stability properties than that of the conventional least squares one. The algorithms presented have a unified matrix formulation, and their Numerical Complexity is related to the factorization rank and then depends on the a priori solution covariance matrix used. Simulation results are presented to illustrate the approach. >

P. Nus - One of the best experts on this subject based on the ideXlab platform.

  • Adaptive spectral analysis of sleep spindles based on subspace tracking
    Proceedings of 18th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 1
    Co-Authors: O. Caspary, P. Nus
    Abstract:

    A method to track the spectra of human sleep electroencephalogram (EEG) spindles is presented. This method uses a low-rank approximation of the covariance matrix and offers a compromise between Numerical Complexity and convergence. In the first part of the article, the authors describe the method briefly. In the second part, they apply it to filtered spindles to find an adequate agreement with a model of spindles that they put forward. Finally, it is concluded that there are different sorts of spindles according to frequency variation.

D. Henry - One of the best experts on this subject based on the ideXlab platform.

  • Enhanced high resolution spectral analysis of sleep spindles
    Proceedings of 16th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 1
    Co-Authors: O. Caspary, M. Tomczak, N. Di Renzo, Marc Mouze-amady, D. Henry
    Abstract:

    A method to extract the spectral components from spindles of sleep electroencephalograms (EEG) is proposed. High resolution (HR) spectral methods are used which yield better results than Fourier transform (FT) or parametric estimators. A zoom function is produced to reduce their Numerical Complexity and increase their resolution. The method allows to clearly separate the different spectral components (spindles, K complexes, background activity), and should be considered for spectral analysis of various short EEG transients.

Hassani Messaoud - One of the best experts on this subject based on the ideXlab platform.

  • Design and comparative study of online kernel methods identification of nonlinear system in RKHS space
    Artificial Intelligence Review, 2012
    Co-Authors: Okba Taouali, Elyes Elaissi, Hassani Messaoud
    Abstract:

    This paper proposes the design and a comparative study of two proposed online kernel methods identification in the reproducing kernel Hilbert space and other two kernel method existing in the literature. The two proposed methods, titled SVD-KPCA, online RKPCA. The two other techniques named Sliding Window Kernel Recursive Least Square and the Kernel Recursive Least Square. The considered performances are the Normalized Means Square Error, the consumed time and the Numerical Complexity. All methods are evaluated by handling a chemical process known as the Continuous Stirred Tank Reactor and Wiener-Hammerstein benchmark.