Multivariate generalized Gaussian distribution (MGGD) has been an attractive solution to many signal processing problems due to its simple yet flexible parametric form, which requires the estimation of only a few para...
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Multivariate generalized Gaussian distribution (MGGD) has been an attractive solution to many signal processing problems due to its simple yet flexible parametric form, which requires the estimation of only a few parameters, i.e., the scatter matrix and the shape parameter. Existing fixed-point (FP) algorithms provide an easy to implement method for estimating the scatter matrix, but are known to fail, giving highly inaccurate results, when the value of the shape parameter increases. Since many applications require flexible estimation of the shape parameter, we propose a new FP algorithm, Riemannian averaged FP (RA-FP), which can effectively estimate the scatter matrix for any value of the shape parameter. We provide the mathematical justification of the convergence of the RA-FP algorithm based on the Riemannian geometry of the space of symmetric positive definite matrices. We also show using numerical simulations that the RA-FP algorithm is invariant to the initialization of the scatter matrix and provides significantly improved performance over existing FP and method-of-moments (MoM) algorithms for the estimation of the scatter matrix.
The maximum correntropy criterion (MCC) has received increasing attention in signal processing and machine learning due to its robustness against outliers (or impulsive noises). Some gradient based adaptive filtering ...
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The maximum correntropy criterion (MCC) has received increasing attention in signal processing and machine learning due to its robustness against outliers (or impulsive noises). Some gradient based adaptive filtering algorithms under MCC have been developed and available for practical use. The fixed-point algorithms under MCC are, however, seldom studied. In particular, too little attention has been paid to the convergence issue of the fixed-point MCC algorithms. In this letter, we will study this problem and give a sufficient condition to guarantee the convergence of a fixed-point MCC algorithm.
The second-order Volterra (SOV) filter demonstrates excellent performance for modeling nonlinear systems. The main disadvantage of the adaptive SOV filter is that the number of coefficients increases exponentially wit...
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The second-order Volterra (SOV) filter demonstrates excellent performance for modeling nonlinear systems. The main disadvantage of the adaptive SOV filter is that the number of coefficients increases exponentially with memory length, which hinders its practical applications. To circumvent this problem, the sparse-interpolated Volterra filter has been developed. However, the existing algorithms only investigated the performance of gradient-based interpolators and their performance may degrade for combating impulsive noise. A novel fixed-point fully adaptive interpolated Volterra filter under recursive maximum correntropy (FPFAIV-RMC) algorithm is proposed. In particular, the coefficients of the sparse SOV filter are adapted by the RMC algorithm and the coefficients of the interpolator are updated by the fixed-point algorithm under RMC. Additionally, the convergence of the FPFAIV-RMC algorithm is analyzed. The efficacy of the FPFAIV-RMC algorithm is validated by simulations for nonlinear system identification, nonlinear acoustic echo cancellation (NLAEC), and prediction in impulsive noise.
As the performance of hardware is limited, the focus has been to develop objective, optimized and computationally efficient algorithms for a given task. To this extent, fixed-point and approximate algorithms have been...
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As the performance of hardware is limited, the focus has been to develop objective, optimized and computationally efficient algorithms for a given task. To this extent, fixed-point and approximate algorithms have been developed and successfully applied in many areas of research. In this paper we propose a feature selection method based on fixed-point algorithm and show its application in the field of human cancer classification using DNA microarray gene expression data. In the fixed-point algorithm, we utilize between-class scatter matrix to compute the leading eigenvector. This eigenvector has been used to select genes. In the computation of the eigenvector, the eigenvalue decomposition of the scatter matrix is not required which significantly reduces its computational complexity and memory requirement.
Minimum error entropy with fiducial points (MEEF) has gained significant attention due to its excellent performance in mitigating the adverse effects of non-Gaussian noise in the fields of machine learning and signal ...
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Minimum error entropy with fiducial points (MEEF) has gained significant attention due to its excellent performance in mitigating the adverse effects of non-Gaussian noise in the fields of machine learning and signal processing. However, the original MEEF algorithm suffers from high computational complexity due to the double summation of error samples. The quantized MEEF (QMEEF), proposed by Zheng et al. alleviates this computational burden through strategic quantization techniques, providing a more efficient solution. In this paper, we extend the application of these techniques to the complex domain, introducing complex QMEEF (CQMEEF). We theoretically introduce and prove the fundamental properties and convergence of CQMEEF. Furthermore, we apply this novel method to the training of a range of Linear-in-parameters (LIP) models, demonstrating its broad applicability. Experimental results show that CQMEEF achieves high precision in regression tasks involving various noise-corrupted datasets, exhibiting effectiveness under unfavorable conditions, and surpassing existing methods across critical performance metrics. Consequently, CQMEEF not only offers an efficient computational alternative but also opens up new avenues for dealing with complex data in regression tasks.
Nonlinear matrix equation X - Sigma(m)(i=1) A(i)*X(-1)A(i) = Q has wide applications in control theory, dynamic planning, interpolation theory and random filtering. In this paper, a fixed-point accelerated iteration m...
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Nonlinear matrix equation X - Sigma(m)(i=1) A(i)*X(-1)A(i) = Q has wide applications in control theory, dynamic planning, interpolation theory and random filtering. In this paper, a fixed-point accelerated iteration method is proposed, and based on the basic characteristics of the Thompson distance, the convergence and error estimation of the proposed algorithm are proved. Numerical comparison experiments show that the proposed algorithm is feasible and effective.
This letter presents an inner and outer estimation for the basin of attraction of the power flow in power distribution networks. The proposed methodology can be used to define the convergence region of the power flow ...
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This letter presents an inner and outer estimation for the basin of attraction of the power flow in power distribution networks. The proposed methodology can be used to define the convergence region of the power flow algorithm and to estimate the minimum and maximum voltage of the grid without explicitly solving the power flow equations. Numerical experiments in the three-phase unbalanced IEEE 906 nodes test system show the use of the proposed methodology. Results include convergence analysis as well as a quasi-dynamic simulation considering 1440 different scenarios of load and renewable power generation.
this article, we present a general optimization framework that leverages structured sparsity to achieve superior recovery results. The traditional method for solving the structured sparse objectives based on L-2,L-0-n...
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this article, we present a general optimization framework that leverages structured sparsity to achieve superior recovery results. The traditional method for solving the structured sparse objectives based on L-2,L-0-norm is to use the L-2,L-1-norm as a convex surrogate. However, such an approximation often yields a large performance gap. To tackle this issue, we first provide a framework that allows for a wide range of surrogate functions (including non-convex surrogates), which exhibits better performance in harnessing structured sparsity. Moreover, we develop a fixedpointalgorithm that solves a key underlying non-convex structured sparse recovery optimization problem to global optimality with a guaranteed super-linear convergence rate. Building on this, we consider three specific applications, i.e., outlier pursuit, supervised feature selection, and structured dictionary learning, which can benefit from the proposed structured sparsity optimization framework. In each application, how the optimization problem can be formulated and thus be relaxed under a generic surrogate function is explained in detail. We conduct extensive experiments on both synthetic and real-world data and demonstrate the effectiveness and efficiency of the proposed framework.
The instantaneous frequency (IF) is an important feature for the analysis of nonstationary signals. For IF estimation, the time-frequency representation (TFR)-based algorithm is used in a common class of methods. TFR-...
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The instantaneous frequency (IF) is an important feature for the analysis of nonstationary signals. For IF estimation, the time-frequency representation (TFR)-based algorithm is used in a common class of methods. TFR-based methods always need the representation concentrated around the "true" IFs and the number of components within the signal. In this paper, we propose a novel method to adaptively estimate the IFs of nonstationary signals, even for weak components of the signals. The proposed technique is not based on the TFR: it is based on the frequency estimation operator (FEO), and the short-time Fourier transform (STFT) is used as its basis. As we know, the FRO is an exact estimation of the IF for weak frequency-modulated (FM) signals, but is not appropriate for strong FM modes. Through theoretical derivation, we determine that the fixedpoints of the FEOwith respect to the frequency are equivalent to the ridge of the STFT spectrum. Furthermore, the IF of the linear chirp signals is just the fixedpoints of the FEO. Therefore, we apply the fixed-point algorithm to the FEO to realize the precise and reliable estimation of the IF, even for highly FM signals. Finally, the results using synthetic and real signals show the utility of the proposed method for IF estimation and that it is more robust than the compared method. It should be noted that the proposed method employing the FEO only computes the first-order differential of the STFT for the chirp-like signals, while it can provide a result derived using the second-order estimation operator. Moreover, this new method is effective for the IF estimation of weak components within a signal.
In recent years, the sparse system identification (SSI) has received increasing attention, and various sparsity-aware adaptive algorithms based on the minimum mean square error (MMSE) criterion have been developed, wh...
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In recent years, the sparse system identification (SSI) has received increasing attention, and various sparsity-aware adaptive algorithms based on the minimum mean square error (MMSE) criterion have been developed, which are optimal under the assumption of Gaussian distributions. However, the Gaussian assumption does not always hold in real-world environments. The maximum correntropy criterion (MCC) is used to replace the MMSE criterion to suppress the heavy-tailed non-Gaussian noises. For some more complex non-Gaussian noises such as those from multimodal distributions, the minimum error entropy (MEE) criterion can outperform MCC although it is computationally somewhat more expensive. To improve the performance of SSI in non-Gaussian noises, in this brief we develop a class of sparsity-aware MEE algorithms with the fixedpoint iteration (MEE-FP) by incorporating the zero-attracting (l(1)-norm), reweighted zero-attracting (reweighted l(1)-norm) and correntropy induced metric (CIM) penalty terms into the cost function. The corresponding algorithms are termed as ZA-MEE-FP, RZA-MEE-FP, and CIM-MEE-FP, which can achieve better performance than the original MEE-FP algorithm and the MCC based sparsity-aware algorithms. Simulation results confirm the excellent performance of the new algorithms.
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