Linear discriminant analysis (LDA) is a very popular supervised feature extraction method and has been extended to different variants. However, classical LDA has the following problems: 1) The obtained discriminant projection does not have good interpretability for features. 2) LDA is sensitive to noise. 3) LDA is sensitive to the selection of number of projection directions. In this paper, a novel feature extraction method called robust sparse linear discriminant analysis (RSLDA) is proposed to solve the above problems. Specifically, RSLDA adaptively selects the most discriminative features for discriminant analysis by introducing the l2;1 norm. An orthogonal matrix and a sparse matrix are also simultaneously introduced to guarantee that the extracted features can hold the main energy of the original data and enhance the robustness to noise, and thus RSLDA has the potential to perform better than other discriminant methods. Extensive experiments on six databases demonstrate that the proposed method achieves the competitive performance compared with other state-of-the-art feature extraction methods. Moreover, the proposed method is robust to the noisy data.

An important underlying assumption that guides the success of the existing multiview learning algorithms is the full observation of the multiview data. However, such rigorous precondition clearly violates the common-sense knowledge in practical applications, where in most cases, only incomplete fractions of the multiview data are given. The presence of the incomplete settings generally disables the conventional multiview clustering methods. In this article, we propose a simple but effective incomplete multiview clustering (IMC) framework, which simultaneously considers the local geometric information and the unbalanced discriminating powers of these incomplete multiview observations. Specifically, a novel graph-regularized matrix factorization model, on the one hand, is developed to preserve the local geometric similarities of the learned common representations from different views. On the other hand, the semantic consistency constraint is introduced to stimulate these view-specific representations toward a unified discriminative representation. Moreover, the importance of different views is adaptively determined to reduce the negative influence of the unbalanced incomplete views. Furthermore, an efficient learning algorithm is proposed to solve the resulting optimization problem. Extensive experimental results performed on several incomplete multiview datasets demonstrate that the proposed method can achieve superior clustering performance in comparison with some state-of-the-art multiview learning methods.

Conventional multiview clustering seeks to partition data into respective groups based on the assumption that all views are fully observed. However, in practical applications, such as disease diagnosis, multimedia analysis, and recommendation system, it is common to observe that not all views of samples are available in many cases, which leads to the failure of the conventional multiview clustering methods. Clustering on such incomplete multiview data is referred to as incomplete multiview clustering (IMC). In view of the promising application prospects, the research of IMC has noticeable advances in recent years. However, there is no survey to summarize the current progresses and point out the future research directions. To this end, we review the recent studies of IMC. Importantly, we provide some frameworks to unify the corresponding IMC methods and make an in-depth comparative analysis for some representative methods from theoretical and experimental perspectives. Finally, some open problems in the IMC field are offered for researchers. The related codes are released at https://github.com/DarrenZZhang/Survey_IMC .

In real-world applications, it is often that the collected multi-view data are incomplete, i.e., some views of samples are absent. Existing clustering methods for incomplete multi-view data all focus on obtaining a common representation or graph from the available views but neglect the hidden information of missing views and information imbalance of different views. To solve these problems, a novel method, called adaptive graph completion based incomplete multi-view clustering (AGC_IMC), is proposed in this paper. Specifically, AGC_IMC develops a joint framework for graph completion and consensus representation learning, which mainly contains three components, i.e., within-view preservation, between-view inferring, and consensus representation learning. To reduce the negative influence of information imbalance, AGC_IMC introduces some adaptive weights to balance the importance of different views during the consensus representation learning. Importantly, AGC_IMC has the potential to recover the similarity graphs of all views with the optimal cluster structure, which encourages it to obtain a more discriminative consensus representation. Experimental results on five well-known datasets show that AGC_IMC significantly outperforms the state-of-the-art methods.