This paper proposes Low-rank matrix factorization induced Adaptive divergent Graph learning for Fuzzy Clustering (LAGFC). This is a clustering model that unifies low-rank matrix factorization, adaptive graph learning, and fuzzy clustering to holistically exploit both global and local structural information. Unlike conventional graph-based methods that decouple graph construction and label inference into separate steps, LAGFC directly generates cluster labels by incorporating a divergence regularization term during adaptive graph learning, enabling end-to-end optimization. To enhance robustness against noisy data, the proposed method adopts the Maximum Correntropy Criterion as a distance metric, effectively suppressing outlier influence. An efficient iterative optimization algorithm, grounded in Fenchel conjugate theory and block coordinate update techniques, is developed to solve the model, and theoretical guarantees of convergence are provided. Comprehensive experiments on seven real-world image datasets demonstrate that LAGFC outperforms twelve state-of-the-art clustering methods across diverse scenarios in most cases, validating its accuracy and robustness.

This article proposes a novel low-rank matrix factorization model for semisupervised image clustering. In order to alleviate the negative effect of outliers, the maximum correntropy criterion (MCC) is incorporated as a metric to build the model. To utilize the label information to improve the clustering results, a constraint graph learning framework is proposed to adaptively learn the local structure of the data by considering the label information. Furthermore, an iterative algorithm based on Fenchel conjugate (FC) and block coordinate update (BCU) is proposed to solve the model. The convergence properties of the proposed algorithm are analyzed, which shows that the algorithm exhibits both objective sequential convergence and iterate sequential convergence. Experiments are conducted on six real-world image datasets, and the proposed algorithm is compared with eight state-of-the-art methods. The results show that the proposed method can achieve better performance in most situations in terms of clustering accuracy and mutual information.

Convolutional neural networks (CNNs) have been commonly applied in the area of the Electroencephalography (EEG)-based Motor Imagery (MI) classification, significantly pushing the boundary of the state-of-the-art. In order to simultaneously decode the discriminative features and eliminate the negative effects of non-Gaussian noise and outliers in the motor imagery data, in this abstract, we propose a novel robust supervision signal, called Correntropy based Center Loss (CCL), for CNN training, which utilizes the correntropy induced distance as the objective measure. It is encouraging to see that the CNN model trained by the combination of softmax loss and CCL loss outperforms the state-of-the-art models on two public datasets.

This paper proposed a new semi-supervised algorithm combined with Mutual-cross Imperial Competition Algorithm (MCICA) optimizing Support Vector Machine (SVM) for motion imagination EEG classification, which not only reduces the tedious and time-consuming training process and enhances the adaptability of Brain Computer Interface (BCI), but also utilizes the MCICA to optimize the parameters of SVM in the semi-supervised process. This algorithm combines mutual information and cross validation to construct objective function in the semi-supervised training process, and uses the constructed objective function to establish the semi-supervised model of MCICA for optimizing the parameters of SVM, and finally applies the selected optimal parameters to the data set Iva of 2005 BCI competition to verify its effectiveness. The results showed that the proposed algorithm is effective in optimizing parameters and has good robustness and generalization in solving small sample classification problems.

Concept factorization (CF) has shown its great advantage for both clustering and data representation and is particularly useful for image representation. Compared with nonnegative matrix factorization (NMF), CF can be applied to data containing negative values. However, the performance of CF method and its extensions will degenerate a lot due to the negative effects of outliers, and CF is an unsupervised method that cannot incorporate label information. In this article, we propose a novel CF method, with a novel model built based on the maximum correntropy criterion (MCC). In order to capture the local geometry information of data, our method integrates the robust adaptive embedding and CF into a unified framework. The label information is utilized in the adaptive learning process. Furthermore, an iterative strategy based on the accelerated block coordinate update is proposed. The convergence property of the proposed method is analyzed to ensure that the algorithm converges to a reliable solution. The experimental results on four real-world image data sets show that the new method can almost always filter out the negative effects of the outliers and outperform several state-of-the-art image representation methods.

In order to efficiently utilize the information in the data and eliminate the negative effects of outliers in the principal component analysis (PCA) method, in this paper, we propose a novel robust sparse PCA method based on maximum correntropy criterion (MCC) with high-order manifold constraints called the RHSPCA. Compared with the traditional PCA methods, the proposed RHSPCA has the following benefits: 1) the MCC regression term is more robust to outliers than the MSE-based regression term; 2) thanks to the high-order manifold constraints, the low-dimensional representations can preserve the local relations of the data and greatly improve the clustering and classification performance for image processing tasks; and 3) in order to further counteract the adverse effects of outliers, the MCC-based samples' mean is proposed to better centralize the data. We also propose a new solver based on the half-quadratic technique and accelerated block coordinate update strategy to solve the RHSPCA model. Extensive experimental results show that the proposed method can outperform the state-of-the-art robust PCA methods on a variety of image processing tasks, including reconstruction, clustering, and classification, on outliers contaminated datasets.

High-dimensional data contain not only redundancy but also noises produced by the sensors. These noises are usually non-Gaussian distributed. The metrics based on Euclidean distance are not suitable for these situations in general. In order to select the useful features and combat the adverse effects of the noises simultaneously, a robust sparse subspace learning method in unsupervised scenario is proposed in this paper based on the maximum correntropy criterion that shows strong robustness against outliers. Furthermore, an iterative strategy based on half quadratic and an accelerated block coordinate update is proposed. The convergence analysis of the proposed method is also carried out to ensure the convergence to a reliable solution. Extensive experiments are conducted on real-world data sets to show that the new method can filter out the outliers and outperform several state-of-the-art unsupervised feature selection methods.