Simultaneous optimization for robust correlation estimation in partially observed social network

Correlation estimation plays a critical role in numerous applications of social network analysis. Traditionally, the numerical records of the interaction between users are used as quantitative metrics of correlation. The deficiencies are threefold. Firstly, a single source of interaction is far from sufficient to reveal the underlying correlation. Secondly, the data available are often partially observed result from the imperfection in data acquisition and storage techniques, thereby jeopardizing the reliability of estimation. Thirdly, the inference from the explicit features to the implicit correlation is far from straightforward. Simply taking interaction as correlation is neither theoretically nor practically plausible. The former issue can be addressed via matrix completion, whereas the latter is essentially a self-expressive matrix representation problem. Instead of solving the two problems separately, in this paper, we propose a simultaneous optimization algorithm for robust correlation estimation based on partially observed data. In this way, the global, rather than local, optima can be achieved in an effective manner. The experiments on both synthetic and real-world social network data demonstrate the advantage of the proposed method.