Modal-Regression-Based Structured Low-Rank Matrix Recovery for Multiview Learning

Incomplete Multiview Clustering Based on Consensus Information

In contrast to traditional single-view clustering methods, multiview clustering (MVC) approaches aim to extract, analyze, and integrate structural information from diverse perspectives, providing a more comprehensive understanding of internal data structures. However, with an increasing number of views, maintaining the integrity of view information becomes challenging, giving rise to incomplete MVC (IMVC) methods. While existing IMVC methods have shown notable performance on many incomplete multiview (IMV) databases, they still grapple with two key shortcomings: 1) they treat the information of each view as a whole, disregarding the differences among samples within each view; and 2) they rely on eigenvalue and eigenvector operations on the view matrix, limiting their scalability for large-scale samples and views. To overcome these limitations, we propose a novel multiview clustering with consistent information (IMVC-CI) of sample points. Our method explores the multiview information set of sample points to extract consensus structural information and subsequently restores unknown information in each view. Importantly, our approach operates independently on individual sample points, eliminating the need for eigenvalue and eigenvector operations on the view information matrix and facilitating parallel computation. This significantly enhances algorithmic efficiency and mitigates challenges associated with dimensionality. Experimental results on various public datasets demonstrate that our algorithm outperforms state-of-the-art IMVC methods in terms of clustering performance and computational efficiency. The code for our article has been uploaded to https://github.com/PhdJiayiTang/IMVC-CI.git.

Multiple Self-Adaptive Correlation-Based Multiview Multilabel Learning

In order to process multiview multilabel, multilabel, and multiview data, current learning algorithms are designed on the basis of data characteristics, correlations, etc. While these algorithms cannot express correlations among different features, instances, labels in within-view, cross-view, and consensus-view representations self-adaptively and relative accurately. To this end, this study takes the classical multiple correlations-based model as the basis and explores some laws of self-adaptive change for those correlations in multiple representations. The proposed algorithm is called multiple self-adaptive correlation-based multiview multilabel learning (MuSC-MVML). Extensive experiments on 38 datasets demonstrate the superiority of MuSC-MVML and some conclusions are addressed. 1) MuSC-MVML outperforms most compared algorithms in statistical in terms of AUC and its performance is also stable; 2) the computational cost of MuSC-MVML is moderate and on most datasets, MuSC-MVML has a relatively fast convergence; and 3) introducing some laws of self-adaptive change for those correlations can improve the ability of MuSC-MVML to process multiview multilabel datasets effectively and express correlations in multiple representations better. Furthermore, this study explains the reason that why we use alternating optimization strategy to optimize the model of MuSC-MVML and provides some suggestions that how to modify the model of MuSC-MVML to process incomplete multiview multilabel datasets with noise.

A Review of Convex Clustering From Multiple Perspectives: Models, Optimizations, Statistical Properties, Applications, and Connections

Traditional partition-based clustering is very sensitive to the initialized centroids, which are easily stuck in the local minimum due to their nonconvex objectives. To this end, convex clustering is proposed by relaxing K -means clustering or hierarchical clustering. As an emerging and excellent clustering technology, convex clustering can solve the instability problems of partition-based clustering methods. Generally, convex clustering objective consists of the fidelity and the shrinkage terms. The fidelity term encourages the cluster centroids to estimate the observations and the shrinkage term shrinks the cluster centroids matrix so that their observations share the same cluster centroid in the same category. Regularized by the lpn -norm ( pn ∈ {1,2,+∞} ), the convex objective guarantees the global optimal solution of the cluster centroids. This survey conducts a comprehensive review of convex clustering. It starts with the convex clustering as well as its nonconvex variants and then concentrates on the optimization algorithms and the hyperparameters setting. In particular, the statistical properties, the applications, and the connections of convex clustering with other methods are reviewed and discussed thoroughly for a better understanding the convex clustering. Finally, we briefly summarize the development of convex clustering and present some potential directions for future research.

Modal-Regression-Based Broad Learning System for Robust Regression and Classification

A novel neural network, namely, broad learning system (BLS), has shown impressive performance on various regression and classification tasks. Nevertheless, most BLS models may suffer serious performance degradation for contaminated data, since they are derived under the least-squares criterion which is sensitive to noise and outliers. To enhance the model robustness, in this article we proposed a modal-regression-based BLS (MRBLS) to tackle the regression and classification tasks of data corrupted by noise and outliers. Specifically, modal regression is adopted to train the output weights instead of the minimum mean square error (MMSE) criterion. Moreover, the l2,1 -norm-induced constraint is used to encourage row sparsity of the connection weight matrix and achieve feature selection. To effectively and efficiently train the network, the half-quadratic theory is used to optimize MRBLS. The validity and robustness of the proposed method are verified on various regression and classification datasets. The experimental results demonstrate that the proposed MRBLS achieves better performance than the existing state-of-the-art BLS methods in terms of both accuracy and robustness.

Modal Regression-Based Graph Representation for Noise Robust Face Hallucination

Manifold learning-based face hallucination technologies have been widely developed during the past decades. However, the conventional learning methods always become ineffective in noise environment due to the least-square regression, which usually generates distorted representations for noisy inputs they employed for error modeling. To solve this problem, in this article, we propose a modal regression-based graph representation (MRGR) model for noisy face hallucination. In MRGR, the modal regression-based function is incorporated into graph learning framework to improve the resolution of noisy face images. Specifically, the modal regression-induced metric is used instead of the least-square metric to regularize the encoding errors, which admits the MRGR to robust against noise with uncertain distribution. Moreover, a graph representation is learned from feature space to exploit the inherent typological structure of patch manifold for data representation, resulting in more accurate reconstruction coefficients. Besides, for noisy color face hallucination, the MRGR is extended into quaternion (MRGR-Q) space, where the abundant correlations among different color channels can be well preserved. Experimental results on both the grayscale and color face images demonstrate the superiority of MRGR and MRGR-Q compared with several state-of-the-art methods.