In this study, we deal with multi-layered networks. In practical applications, many cases where a data set can be represented with heterogeneous sources of data that may be closely related in multi-layered structure exist. In multi-layered networks, labels in one layer can benefit inference in other layers through inter-layer connections. Many of existing works, however, are only concerned with incorporating multiple networks in parallel fashion, i.e, network integration method or multi-view learning. For multi-layered networks, one has to consider an integrative approach in vertical fashion
In this thesis, we present a basic framework of graph based semi-supervised learning that can be applied to multi-layered networks. The layered structure of multiple networks, however, causes scalability issues – computational complexity and sparseness. To alleviate these problems, we propose a revised matrix inversion method consisting of Nyström method and Woodbury formula.
To verify the validity of the proposed algorithm, we applied the algorithm to artificial data and two real-world problems with biomedical data and historical data. Experiments show the performance of multi-layered network surpasses that of single-layered networks and our proposed method is not only robust for approximations with Nyström method but also computationally efficient.
