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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. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a quantized kernel least mean square algorithm with a fixed memory budget, named QKLMS-FB. In order to deal with the growing support inherent in online kernel methods, the proposed algorithm utilizes a pruning criterion, called significance measure, based on a weighted contribution of the existing data centers. The basic idea of the proposed methodology is to discard the center with the smallest influence on the whole system, when a new sample is included in the dictionary. The significance measure can be updated recursively at each step which is suitable for online operation. Furthermore, the proposed methodology does not need any a priori knowledge about the data and its computational complexity is linear with the center number. Experiments show that the proposed algorithm successfully prunes the least “significant” centers and preserves the important ones, resulting in a compact KLMS model with little loss in accuracy. [Copyright &y& Elsevier]

Concept factorization (CF) has attracted widespread attention for its promising performance in document clustering. Among various CF variants, graph-regularized CF is the most impressive type, which can improve clustering effectiveness by exploring structural information. Nevertheless, their clustering efficiency is restricted by the following considerations: (1) the introduction of the full-sample graph is accompanied by an increase in computational complexity; (2) most of them require intensive multiplications in optimization, which impair the optimization efficiency. To address these issues, in this work, we propose an anchor-graph regularized orthogonal concept factorization (AROCF) method to enhance the clustering efficiency and effectiveness in document clustering tasks. Firstly, AROCF approximates the full-sample graph with a small-scale anchor graph to reduce the complexity of graph construction from quadratic to linear. Then, one of the factor matrices is constrained as the cluster indicator matrix in our method, which can avoid extra efficiency loss in K-means after optimization. Finally, an orthogonal constraint is employed to restrict the freedom of factorization to increase the clustering effectiveness. To optimize the AROCF model, we develop a fast optimization strategy by combining the trace and orthogonality of matrices. Extensive experiments on various document datasets demonstrate the effectiveness and efficiency of AROCF. [ABSTRACT FROM AUTHOR]

• A novel correntropy based semi-supervised NMF method is proposed for image clustering. • The proposed method is analysed in terms of convergence, robustness, and computational complexity. • The relationships between the proposed method and several typical NMF based methods are discussed. • Experimental results show the effectiveness and robustness of the proposed method in image clustering tasks. Nonnegative matrix factorization (NMF) is a powerful dimension reduction method, and has received increasing attention in various practical applications. However, most traditional NMF based algorithms are sensitive to noisy data, or fail to fully utilize the limited supervised information. In this paper, a novel robust semi-supervised NMF method, namely correntropy based semi-supervised NMF (CSNMF), is proposed to solve these issues. Specifically, CSNMF adopts a correntropy based loss function instead of the squared Euclidean distance (SED) in constrained NMF to suppress the influence of non-Gaussian noise or outliers contaminated in real world data, and simultaneously uses two types of supervised information, i.e., the pointwise and pairwise constraints, to obtain the discriminative data representation. The proposed method is analyzed in terms of convergence, robustness and computational complexity. The relationships between CSNMF and several previous NMF based methods are also discussed. Extensive experimental results show the effectiveness and robustness of CSNMF in image clustering tasks, compared with several state-of-the-art methods. [ABSTRACT FROM AUTHOR]

• A variant of the quantized minimum error entropy (QMEE) algorithm is proposed. • The mean square convergence performance analysis for QMEE algorithm is given. • The theoretical values of the steady-state EMSE for QMEE algorithm are validated by simulations. • QMEE algorithm is applied in electroencephalo (EEG) de-noising task. Adaptive filtering algorithms have been widely used in many areas, among which the minimum error entropy (MEE) algorithm is a superior choice, due to its excellent performance in the non-Gaussian noise situations. However, the computational complexity of the MEE algorithm is expensive, which leads to the computational bottlenecks, especially for large-scale datasets. In order to address the problem, we propose an adaptive filtering algorithm based on the quantized minimum error entropy (QMEE) criterion with an online quantization method, named QMEE algorithm. Moreover, we analyze the transient behavior characteristic and derive an approximate analytical expression for the steady-state excess mean square error (EMSE) based on the Taylor expansion. The extensive simulation results in linear modeling and electroencephalogram (EEG) denoising task demonstrate that the proposed method can outperform other robust adaptive filtering algorithms. [ABSTRACT FROM AUTHOR]

Nonnegative matrix factorization (NMF) has attracted increasing attention in data mining and machine learning. However, existing NMF methods have some limitations. For example, some NMF methods seriously suffer from noisy data contaminated by outliers, or fail to preserve the geometric information of the data and guarantee the sparse parts-based representation. To overcome these issues, in this paper, a robust and sparse NMF method, called correntropy based dual graph regularized nonnegative matrix factorization with local coordinate constraint (LCDNMF) is proposed. Specifically, LCDNMF incorporates the geometrical information of both the data manifold and the feature manifold, and the local coordinate constraint into the correntropy based objective function. The half-quadratic optimization technique is utilized to solve the nonconvex optimization problem of LCDNMF, and the multiplicative update rules are obtained. Furthermore, some properties of LCDNMF including the convergence, relation with gradient descent method, robustness, and computational complexity are analyzed. Experiments of clustering demonstrate the effectiveness and robustness of the proposed LCDNMF method in comparison to several state-of-the-art methods on six real world image datasets. • The LCDNMF algorithm is proposed. • The convergence and relation with gradient descent method of LCDNMF is analyzed. • The robustness and computational complexity of LCDNMF is also analyzed. • Experiment results show the effectiveness and robustness of LCDNMF. [ABSTRACT FROM AUTHOR]

The adaptive variable step-size technique is an effective way to improve the convergence rate of an adaptive filtering algorithm. However, for most existing variable step-size sign algorithm against impulsive noise, either the performance is not good enough, or the calculation is complex. In this paper, a correntropy inspired variable step-size method for sign algorithm is proposed. The new variable step-size method is computationally simple and robust to impulsive noises. Theoretical analysis and simulation results demonstrate that the proposed algorithm can achieve desirable performance with low computational complexity in presence of impulsive noises. [ABSTRACT FROM AUTHOR]

To improve the performance and reduce the computational complexity, a novel sign adaptation scheme for convex combination of adaptive filters is proposed. By using a sign adaptation scheme, the proposed scheme slightly reduces the computational complexity of the basic combination of mixing parameter, and improves the robustness of mixing parameter. Moreover, to obtain fast convergence property during the period of convergence transition in different environments, the instantaneous transfer scheme is applied to the proposed algorithm. The instantaneous transfer scheme has lower computational complexity than that of the basic combination of least mean square (basic-CLMS) algorithms. Simulation results in the context of system identification under time-invariant and time-variant systems demonstrate that the proposed algorithm based on the instantaneous transfer scheme has lower computational complexity and faster convergence rate than that of the basic-CLMS algorithm during period of convergence transitions. [ABSTRACT FROM AUTHOR]