Multidimensional Scaling Orienting Discriminative Co-Representation Learning

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.