Beyond existing multi-view clustering, this paper studies a more realistic clustering scenario, referred to as incomplete multi-view clustering, where a number of data instances are missing in certain views. To tackle this problem, we explore spectral perturbation theory. In this work, we show a strong link between perturbation risk bounds and incomplete multi-view clustering. That is, as the similarity matrix fed into spectral clustering is a quantity bounded in magnitude O(1), we transfer the missing problem from data to similarity and tailor a matrix completion method for incomplete similarity matrix. Moreover, we show that the minimization of perturbation risk bounds among different views maximizes the final fusion result across all views. This provides a solid fusion criteria for multi-view data. We motivate and propose a Perturbation-oriented Incomplete multi-view Clustering (PIC) method. Experimental results demonstrate the effectiveness of the proposed method.

Nonnegative matrix factorization (NMF) and symmetric NMF (SymNMF) have been shown to be effective for clustering linearly separable data and nonlinearly separable data, respectively. Nevertheless, many practical applications demand constrained algorithms in which a small number of constraints in the form of must-link and cannot-link are available. In this paper, we propose an NMF-based constrained clustering framework in which the similarity between two points on a must-link is enforced to approximate 1 and the similarity between two points on a cannot-link is enforced to approximate 0. We then formulate the framework using NMF and SymNMF to deal with clustering of linearly separable data and nonlinearly separable data, respectively. Furthermore, we present multiplicative update rules to solve them and show the correctness and convergence. Experimental results on various text data sets, University of California, Irvine (UCI) data sets, and gene expression data sets demonstrate the superiority of our algorithms over existing constrained clustering algorithms.

The fast spread of hate speech on social media impacts the Internet environment and our society by increasing prejudice and hurting people. Detecting hate speech has aroused broad attention in the field of natural language processing. Although hate speech detection has been addressed in recent work, this task still faces two inherent unsolved challenges. The first challenge lies in the complex semantic information conveyed in hate speech, particularly the interference of insulting words in hate speech detection. The second challenge is the imbalanced distribution of hate speech and non-hate speech, which may significantly deteriorate the performance of models. To tackle these challenges, we propose a novel dual contrastive learning (DCL) framework for hate speech detection. Our framework jointly optimizes the self-supervised and the supervised contrastive learning loss for capturing span-level information beyond the token-level emotional semantics used in existing models, particularly detecting speech containing abusive and insulting words. Moreover, we integrate the focal loss into the dual contrastive learning framework to alleviate the problem of data imbalance. We conduct experiments on two publicly available English datasets, and experimental results show that the proposed model outperforms the state-of-the-art models and precisely detects hate speeches.