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Robust matrix completion aims to recover a low-rank matrix from a subset of noisy entries perturbed by complex noises. Traditional matrix completion algorithms are always based on $l_2$ -norm minimization and are sensitive to non-Gaussian noise with outliers. In this paper, we propose a novel robust and fast matrix completion method based on the maximum correntropy criterion (MCC). The correntropy-based error measure is utilized instead of the $l_2$ -based error norm to improve robustness against noise. By using the half-quadratic optimization technique, the correntropy-based optimization can be transformed into a weighted matrix factorization problem. Two efficient algorithms are then derived: an alternating minimization-based algorithm and an alternating gradient descent-based algorithm. These algorithms do not require the singular value decomposition (SVD) to be calculated for each iteration. Furthermore, an adaptive kernel width selection strategy is proposed to accelerate the convergence speed as well as improve the performance. A comparison with existing robust matrix completion algorithms is provided by simulations and shows that the new methods can achieve better performance than the existing state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

Robust sparse signal recovery against impulsive noise is a core issue in many applications. Numerous methods have been proposed to recover the sparse signal from measurements corrupted by various impulsive noises, but most of them either lack theoretical guarantee for robust sparse recovery or are not efficient enough for large-scale problems. To this end, a general optimization problem for robust sparse signal recovery, which includes many existing works as concrete instances, is analyzed by a freshly defined Double Null Space Property (DNSP), and its solution is proved to be able to robustly reconstruct the sparse signal under mild conditions. Moreover, for computational tractability, weakly convex sparsity-inducing penalties are applied to the general problem, and properties of the solution to the resultant non-convex problem are further studied. Based on these properties, an algorithm named Robust Projected Generalized Gradient (RPGG) is devised to solve the weakly convex problem. Theoretical results prove that the sparse signal can be precisely reconstructed by RPGG from compressive measurements with sparse noise or robustly recovered from those with impulsive noise. Meanwhile, simulations demonstrate that RPGG with tuned parameters outperforms other robust sparse recovery algorithms. [ABSTRACT FROM AUTHOR]

Nonlinear similarity measures defined in kernel space, such as correntropy, can extract higher order statistics of data and offer potentially significant performance improvement over their linear counterparts especially in non Gaussian signal processing and machine learning. In this paper, we propose a new similarity measure in kernel space, called the kernel risk-sensitive loss (KRSL), and provide some important properties. We apply the KRSL to adaptive filtering and investigate the robustness, and then develop the MKRSL algorithm and analyze the mean square convergence performance. Compared with correntropy, the KRSL can offer a more efficient performance surface, thereby enabling a gradient-based method to achieve faster convergence speed and higher accuracy while still maintaining the robustness to outliers. Theoretical analysis results and superior performance of the new algorithm are confirmed by simulation. [ABSTRACT FROM PUBLISHER]

As a robust nonlinear similarity measure in kernel space, correntropy has received increasing attention in domains of machine learning and signal processing. In particular, the maximum correntropy criterion (MCC) has recently been successfully applied in robust regression and filtering. The default kernel function in correntropy is the Gaussian kernel, which is, of course, not always the best choice. In this paper, we propose a generalized correntropy that adopts the generalized Gaussian density (GGD) function as the kernel, and present some important properties. We further propose the generalized maximum correntropy criterion (GMCC) and apply it to adaptive filtering. An adaptive algorithm, called the GMCC algorithm, is derived, and the stability problem and steady-state performance are studied. We show that the proposed algorithm is very stable and can achieve zero probability of divergence (POD). Simulation results confirm the theoretical expectations and demonstrate the desirable performance of the new algorithm. [ABSTRACT FROM AUTHOR]

Recently, the information potential (IP) of order \alpha, defined as the argument of the log in the \alpha-order Renyi entropy, has been successfully used as an information theoretic criterion for supervised adaptive system training. In this paper, we use the survival function (or equivalently the distribution function) of an absolute value transformed random variable to define a new information potential, named the survival information potential (SIP). Compared with the IP, the SIP has some advantages, such as validity in a wide range of distributions, robustness, and the simplicity in computation. The properties of SIP and a simple formula for computing the empirical SIP are given in the paper. Finally, the SIP criterion is applied in adaptive system training, and simulation examples on FIR adaptive filtering, kernel adaptive filtering, and time delay neural networks (TDNNs) training are presented to demonstrate the performance. [ABSTRACT FROM PUBLISHER]