Anomaly detection has attracted much attention in recent years since it plays a crucial role in many domains. Various anomaly detection approaches have been proposed, among which one-class support vector machine (OCSVM) is a popular one. In practice, data used for anomaly detection can be distributively collected via wireless sensor networks. Besides, as the data usually arrive at the nodes sequentially, online detection method that can process streaming data is preferred. In this paper, we formulate a distributed online OCSVM for anomaly detection over networks and get a decentralized cost function. To get the decentralized implementation without transmitting the original data, we use a random approximate function to replace the kernel function. Furthermore, to find an appropriate approximate dimension, we add a sparse constraint into the decentralized cost function to get another one. Then we minimize these two cost functions by stochastic gradient descent and derive two distributed algorithms. Some theoretical analysis and experiments are performed to show the effectiveness of the proposed algorithms. Experimental results on both synthetic and real datasets reveal that both of the proposed algorithms achieve low misdetection rates and high true positive rates. Compared with other state-of-the-art anomaly detection methods, the proposed distributed algorithms not only show good anomaly detection performance, but also require relatively short running time and low CPU memory consumption.

As a robust nonlinear similarity measure, the maximum correntropy criterion (MCC) has been successfully applied to active noise control (ANC) for impulsive noise. The default kernel function of the filtered-x maximum correntropy criterion (FxMCC) algorithm is the Gaussian kernel, which is desirable in many cases for its smooth and strict positive-definite, However, it is not always the best choice. In this study, a filtered-x generalized maximum correntropy criterion (FxGMCC) algorithm is proposed, which adopts the generalized Gaussian density (GGD) function as its kernel. The FxGMCC algorithm has greater robust ability against non-Gaussian environments, but, it still adopts a single error norm which exhibits poor convergence rate and noise reduction performance. To surmount this problem, an improved FxGMCC (IFxGMCC) algorithm with continuous mixed Lp-norm is proposed. Moreover, to make a trade-off between fast convergence rate and low steady-state misalignment, a convexly combined IFxGMCC (C-IFxGMCC) algorithm is further developed. The stability mechanism and computational complexity of the proposed algorithms are analyzed. Simulation results in the context of different impulsive noises as well as the real noise signals verify that the proposed algorithms are superior to most of the existing robust adaptive algorithms.

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.

This work develops robust diffusion recursive least squares algorithms to mitigate the performance degradation often experienced in networks of agents in the presence of impulsive noise. The first algorithm minimizes an exponentially weighted least-squares cost function subject to a time-dependent constraint on the squared norm of the intermediate update at each node. A recursive strategy for computing the constraint is proposed using side information from the neighboring nodes to further improve the robustness. We also analyze the mean-square convergence behavior of the proposed algorithm. The second proposed algorithm is a modification of the first one based on the dichotomous coordinate descent iterations. It has a performance similar to that of the former, however its complexity is significantly lower especially when input regressors of agents have a shift structure and it is well suited to practical implementation. Simulations show the superiority of the proposed algorithms over previously reported techniques in various impulsive noise scenarios.

In this paper, a variable step-size widely linear complex-valued affine projection algorithm (VSS-WLCAPA) is proposed for processing noncircular signals. The variable stepsize (VSS) is derived by minimizing the power of the augmented noise-free a posteriori error vector, which speeds up the convergence and reduces the steady-state misalignment. By exploiting the evolution of the covariance matrix of the weight error vector, we provide insight into the theoretical behavior of the VSSWLCAPA algorithm. In the analysis, we take into account the dependency between the weight error vector and the noise vector, which is useful for accuracy of the theoretical prediction. To evaluate the mean step-size, the probability density function of the magnitude of the error is derived by employing polar coordinate transformation. Moreover, a special case when the projection order reduces to one is analysed in detail. The presented theoretical analysis is different from existing methodologies for analyzing affine projection algorithms due to the use of the Kronecker product. Simulation results for system identification scenarios demonstrate the merits of the proposed algorithm and verify the accuracy of the theoretical analysis. Wind prediction experiments support the superiority of the proposed VSS-WLCAPA as well.

As an effective method for power system forecasting-aided state estimation (FASE), the unscented Kalman filter (UKF) based on correntropy has been widely used in recent years, ensuring the safe and reliable operation of power systems. In this article, to address the impulsive noise, Laplacian noise, bad measurement data, and sudden load change, a robust UKF algorithm based on generalized maximum mixture correntropy (GMMC-UKF) criterion is proposed for FASE, in which the kernel is composed of two generalized Gaussian functions. Specifically, we use a statistical linearization technique to unify the state error and measurement error in the cost function and obtain the optimal value of state estimation by fixed-point iteration. The effectiveness of the proposed algorithm for FASE is verified on IEEE 14-, 30-, and 57-bus test systems under a variety of abnormal situations. Compared with traditional correntropy algorithms, the GMMC-UKF shows more accurate estimation and stronger robustness.