Joint Recovery and Representation Learning for Robust Correlation Estimation based on Partially Observed Data

In social network, correlation estimation is a critical problem with promising application prospect. Numerical records of the interaction can serve as informative reflections of the correlation between users. However, due to the noise during data acquisition and storage as well as the privacy concern, the interaction data are usually partially observed. Moreover, even if the complete interaction is obtained, the underlying correlation should be further revealed. In this paper, we propose a novel joint recovery and representation learning method for robust correlation estimation based on partially observed data. We formulate the approximation of unobserved interaction data as a matrix recovery problem, whereas pose the inference of underlying correlation as a self-expressive matrix representation problem. By incorporating these two problem into a unified process, the complete data and the underlying correlation are optimized simultaneously in an effective manner. Advantage of the proposed method is demonstrated by experiments of community detection tasks on real-world social network data.