Co-representation, which co-represents samples and features, has been widely used in various machine learning tasks, such as document clustering, gene expression analysis, and recommendation systems. It not only reveals the cluster structure of both samples and features, but also reveals the sample–feature correlation. Given a tabular data matrix, co-representation usually exhibits as the co-occurrence structures of rows and columns. However, identifying such structured patterns in complex real-world data can be very challenging. To address this problem, we propose an unsupervised discriminative co-representation learning model based on multidimensional scaling (DCLMDS). The main novelty is that DCLMDS introduces a co-representation learning term to ensure the discriminability between co-occurrence structures. As a result, the co-representation learned by DCLMDS contains richer information of the underlying correlation between samples and features within data. This could subsequently enhance the capacity of machines and systems for processing complex real-world information more proficiently. Furthermore, inspired by the fuzzy set theory, we integrate fuzzy membership degree that can accurately capture the uncertainty within data, thus enabling DCLMDS to learn a more effective co-representation in a soft manner. To evaluate the performance of DCLMDS, we conduct extensive experiments on 18 datasets, and the results demonstrate that DCLMDS can generate both accurate and discriminative co-representation, which well meets our desired outcomes.

Co-clustering is the simultaneous clustering of the samples and attributes of a data matrix that provides deeper insight into data than traditional clustering. However, there is a lack of representation learning algorithms that serve this mechanism of co-clustering, and the current representation learning algorithms are limited to the sample perspective and lack the use of information in the attribute perspective. To solve this problem, in this article, ctSNE , a co-representation learning model based on t-distributed stochastic neighbor embedding, is proposed for unsupervised co-clustering, where ctSNE makes the dataset representation outputted more discriminative of row and column clusters (i.e. co-discrimination). On the basis of t-distributed stochastic neighbor embedding retaining the sample data distribution and local data structure, the philosophy of collaboration is introduced (i.e., row and column hidden relationship information) so that the ctSNE model is equipped with co-representation learning capability, which can effectively improve the performance of co-clustering. To prove the effectiveness of the ctSNE model, several classic co-clustering algorithms are used to check the co-representation performance of ctSNE, and a novel internal index based on an internal clustering index, known as total inertia, is proposed to demonstrate the effect of co-clustering. The numerous experimental results show that ctSNE has tremendous co-representation capability and can significantly improve the performance of co-clustering algorithms.

Representation learning based on autoencoders has received great concern for its potential ability to capture valuable latent information. Conventional autoencoders pursue minimal reconstruction error, but in most machine learning tasks such as classification and clustering, the discrimination of feature representation is also important. To address this limitation, an enhanced self-supervised discriminative fuzzy autoencoder (FAE) is innovatively proposed, which focuses on exploring information within data to guide the unsupervised training process and enhancing feature discrimination in a self-supervised manner. In FAE, fuzzy membership is applied to provide a means of self-supervised, which allows FAE can not only utilize AE’s outstanding representation learning capabilities but can also transform the original data into another space with improved discrimination. First, the objective function corresponding to FAE is proposed by reconstruction loss and clustering oriented loss simultaneously. Subsequently, Mini-Batch Gradient Descent is applied to infer the objective function and the detailed process is illustrated step by step. Finally, empirical studies on clustering tasks have demonstrated the superiority of FAE over the state of the art.