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As a novel similarity measure that is defined as the expectation of a kernel function between two random variables, correntropy has been successfully applied in robust machine learning and signal processing to combat large outliers. The kernel function in correntropy is usually a zero-mean Gaussian kernel. In a recent work, the concept of mixture correntropy (MC) was proposed to improve the learning performance, where the kernel function is a mixture Gaussian kernel, namely, a linear combination of several zero-mean Gaussian kernels with different widths. In both correntropy and MC, the center of the kernel function is, however, always located at zero. In the present work, to further improve the learning performance, we propose the concept of multikernel correntropy (MKC), in which each component of the mixture Gaussian kernel can be centered at a different location. The properties of the MKC are investigated and an efficient approach is proposed to determine the free parameters in MKC. Experimental results show that the learning algorithms under the maximum MKC criterion (MMKCC) can outperform those under the original maximum correntropy criterion (MCC) and the maximum MC criterion (MMCC). [ABSTRACT FROM AUTHOR]

Multi-view clustering has received widespread attention owing to its effectiveness by integrating multi-view data appropriately, but traditional algorithms have limited applicability to large-scale real-world data due to their high computational complexity and low robustness. Focusing on the aforementioned issues, we propose an efficient and robust multi-view clustering algorithm with anchor graph regularization (ERMC-AGR). In this work, a novel anchor graph regularization (ARG) is designed to improve the quality of the learned embedded anchor graph (EAG), and the obtained EAG is decomposed by nonnegative matrix factorization (NMF) under correntropy criterion to acquire clustering results directly. Different from the traditional graph regularization that needs to construct a large-scale Laplacian matrix pertaining to the all-sample graph, our lightweight AGR, constructed from the perspective of anchors, can reduce the computational complexity significantly while improving the EAG quality. Moreover, a factor matrix of NMF is constrained to be the cluster indicator matrix to omit additional k-means after optimization. Subsequently, correntropy is utilized to improve the effectiveness and robustness of ERMC-AGR owing to its promising performance to complex noises and outliers. Extensive experiments on real-world datasets and noisy datasets show that ERMC-ARG can improve the clustering efficiency and robustness while ensuring comparable or even better effectiveness. [ABSTRACT FROM AUTHOR]

In recent years, correntropy has been successfully applied to robust adaptive filtering to eliminate adverse effects of impulsive noises or outliers. Correntropy is generally defined as the expectation of a Gaussian kernel between two random variables. This definition is reasonable when the error between the two random variables is symmetrically distributed around zero. For the case of asymmetric error distribution, the symmetric Gaussian kernel is however inappropriate and cannot adapt to the error distribution well. To address this problem, in this brief we propose a new variant of correntropy, named asymmetric correntropy, which uses an asymmetric Gaussian model as the kernel function. In addition, a robust adaptive filtering algorithm based on asymmetric correntropy is developed and its steady-state convergence performance is analyzed. Simulations are provided to confirm the theoretical results and good performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Graph-based clustering commonly provides promising clustering effectiveness as it can preserve samples' local geometric information. Inspired by it, multi-view graph clustering was developed to integrate complementary information among graphs of diverse views and it has received intensive attention recently. Nevertheless, on the one hand, most existing methods require extra k-means after obtaining embedding representations to generate a discrete cluster indicator, which reduces effectiveness due to the two-stage mismatch. On the other hand, numerous complex noises in real-world multi-view data challenge the robustness of existing clustering methods. In this paper, we established a discrete correntropy-based multi-view anchor-graph clustering (DCMAC) model that not only emphasizes the aforementioned issues but also makes use of anchor graphs to improve the efficiency of the graph construction stage. To optimize this non-convex model, we propose a fast half-quadratic-based coordinate descent strategy to acquire the discrete cluster indicator directly without extra k-means. Furthermore, we extend the DCMAC model to a single-view form and provide optimization strategies for it. Extensive experiments illustrate that the proposed method is effective and robust compared to those advanced baselines. • A new discrete correntropy-based multi-view anchor-graph clustering (DCMAC) model is proposed. • A novel half-quadratic-based coordinate descent algorithm is proposed to solve the DCMAC model. • To handle single-view clustering instances, DCMAC is extended to a single-view form named DCAC. • Numerous experiments demonstrate the outstanding effectiveness and robustness of DCMAC. [ABSTRACT FROM AUTHOR]