Siyuan Peng

Robust Hammerstein Adaptive Filtering under Maximum Correntropy Criterion

The maximum correntropy criterion (MCC) has recently been successfully applied to adaptive filtering. Adaptive algorithms under MCC show strong robustness against large outliers. In this work, we apply the MCC criterion to develop a robust Hammerstein adaptive filter. Compared with the traditional Hammerstein adaptive filters, which are usually derived based on the well-known mean square error (MSE) criterion, the proposed algorithm can achieve better convergence performance especially in the presence of impulsive non-Gaussian (e.g., α-stable) noises. Additionally, some theoretical results concerning the convergence behavior are also obtained. Simulation examples are presented to confirm the superior performance of the new algorithm.

Constrained maximum correntropy adaptive filtering

Abstract Constrained adaptive filtering algorithms have been extensively studied in many applications. Most existing constrained adaptive filtering algorithms are developed under the mean square error (MSE) criterion, which is an ideal optimality criterion under Gaussian noises. This assumption however fails to model the behavior of non-Gaussian noises found in practice. Motivated by the robustness and simplicity of maximum correntropy criterion (MCC) for non-Gaussian impulsive noises, this paper proposes a new adaptive filtering algorithm called constrained maximum correntropy criterion (CMCC). Specifically, CMCC incorporates a linear constraint into a MCC filter to solve a constrained optimization problem explicitly. The proposed adaptive filtering algorithm is easy to implement, has low computational complexity, and can significantly outperform those MSE based constrained adaptive algorithms in heavy-tailed impulsive noises. Additionally, the mean square convergence behaviors are studied under energy conservation relation, and a sufficient condition to ensure the mean square convergence and the steady-state mean square deviation (MSD) of the CMCC algorithm are obtained. Simulation results confirm the theoretical predictions under both Gaussian and non-Gaussian noises, and demonstrate the excellent performance of the novel algorithm by comparing it with other conventional methods.

Minimum Error Entropy Algorithms with Sparsity Penalty Constraints

Recently, sparse adaptive learning algorithms have been developed to exploit system sparsity as well as to mitigate various noise disturbances in many applications. In particular, in sparse channel estimation, the parameter vector with sparsity characteristic can be well estimated from noisy measurements through a sparse adaptive filter. In previous studies, most works use the mean square error (MSE) based cost to develop sparse filters, which is rational under the assumption of Gaussian distributions. However, Gaussian assumption does not always hold in real-world environments. To address this issue, we incorporate in this work an l1-norm or a reweighted l1-norm into the minimum error entropy (MEE) criterion to develop new sparse adaptive filters, which may perform much better than the MSE based methods, especially in heavy-tailed non-Gaussian situations, since the error entropy can capture higher-order statistics of the errors. In addition, a new approximator of l0-norm, based on the correntropy induced metric (CIM), is also used as a sparsity penalty term (SPT). We analyze the mean square convergence of the proposed new sparse adaptive filters. An energy conservation relation is derived and a sufficient condition is obtained, which ensures the mean square convergence. Simulation results confirm the superior performance of the new algorithms.

Nonlinear spline adaptive filtering under maximum correntropy criterion

The nonlinear spline adaptive filtering under least mean square (SAF-LMS) uses the mean square error (MSE) based cost function to identify the Wiener-type nonlinear systems, which is rational under the assumption of Gaussian distributions. However, the mere second-order statistics are often not suitable for nonlinear and/or non-Gaussian systems. To address this issue, a new nonlinear adaptive filter, called nonlinear spline adaptive filtering under maximum correntropy criterion (SAF-MCC), is proposed in this work. Compared with the SAF-LMS, the SAF-MCC uses the maximum correntropy criterion (MCC) to replace the MSE criterion to improve the convergence performance especially in heavy-tailed non-Gaussian environments. Simulation results confirm the superior performance of the new algorithm.

An improved proportionate least mean p-power algorithm for adaptive filtering

The least mean p-power error criterion has been successfully used in adaptive filtering due to its strong robustness against large outliers. In this paper, we develop a new adaptive filtering algorithm, named the proportionate least mean p-power (PLMP) algorithm, which uses the mean p-power error as the adaptation cost function. Compared with the standard proportionate normalized least mean square algorithm, the PLMP can achieve much better performance in terms of the mean square deviation, especially in the presence of impulsive non-Gaussian noises. The mean and mean square convergence of the proposed algorithm are analyzed, and some related theoretical results are also obtained. Simulation results are presented to verify the effectiveness of our proposed algorithm.

Correntropy based graph regularized concept factorization for clustering

Abstract Concept factorization (CF) technique is one of the most powerful approaches for feature learning, and has been successfully adopted in a wide range of practical applications such as data mining, computer vision, and information retrieval. Most existing concept factorization methods mainly minimize the square of the Euclidean distance, which is seriously sensitive to non-Gaussian noises or outliers in the data. To alleviate the adverse influence of this limitation, in this paper, a robust graph regularized concept factorization method, called correntropy based graph regularized concept factorization (GCCF), is proposed for clustering tasks. Specifically, based on the maximum correntropy criterion (MCC), GCCF is derived by incorporating the graph structure information into our proposed objective function. A half-quadratic optimization technique is adopted to solve the non-convex objective function of the GCCF method effectively. In addition, algorithm analysis of GCCF is studied. Extensive experiments on real world datasets demonstrate that the proposed GCCF method outperforms seven competing methods for clustering applications.

Kernel least mean square based on conjugate gradient

Kernel least mean square (KLMS) algorithm has been successfully applied in fields of adaptive filtering and online learning due to their ability to solve sequentially nonlinear problems by implicitly mapping the input signal to a high-dimensional reproducing kernel Hilbert space (RKHS). In this paper, we propose a novel adaptive algorithm called KLMS based on conjugate gradient (KLMS-CG), which uses the orthogonal search directions, instead of using the traditional steepest descent approach, to improve the convergence speed. Further, the quantized KLMS based on conjugate gradient (QKLMS-CG) is proposed to curb the growth of network. Simulation results indicate that the new algorithm can converge faster than the original KLMS while maintaining excellent accuracy.

Adaptive convex combination filter under minimum error entropy criterion

Minimum error entropy (MEE) is a robust adaption criterion and has been successfully applied to adaptive filtering, which can outperform the well-known minimum mean square error (MSE) criterion especially in the present of non-Gaussian noise. However, the adaptive algorithms under MEE are still subject to a compromise between convergence speed and steady-state mean square deviation (MSD). To address this issue, we propose in this paper an adaptive convex combination filter under MEE (CMEE), which is derived by using a convex combination of two MEE-based adaptive algorithms of different step-sizes. Monte Carlo simulation results confirm that the new algorithm can achieve fast convergence speed while keeping a desirable performance.