Fast Integration for Multiple Graphs with Neumann Approximation

Taehwan Yun, Myung Jun Kim, Hyunjung Shin

Abstract: Graph-based models have gained much interest in the domain of machine learning as they offer the advantage of handling data that reside on complex structures. From various models that encounter graph-structured data, graph-based semi-supervised learning (SSL) have shown successful results in multiple applications. The key idea behind SSL is the spreading process of labels through the edges and the problem boils down to keeping the graph Laplacian intact. Meanwhile, with the rapid growth in availability of data, there exist multiple descriptions of graphs for the same set of data points. Each graph contains complementary information to one another, and it would be beneficial to integrate all the available information. In this paper, we propose an SSL-based fast graph integration method that employs approximation in the maximum likelihood estimation process of finding the combination. The proposed approximation utilizes the connection between the covariance and its Neumann series, which allows us to avoid explicit matrix inversion. Empirically, the proposed method achieved competitive performance with significant improvements in computational time when compared to other method.