Semi-supervised learning for hierarchically structured networks

A set of data can be obtained from different hierarchical levels in diverse domains, such as multi-levels of genome data in omics, domestic/global indicators in finance, ancestors/descendants in phylogenetics, genealogy, and sociology. Such layered structures are often represented as a hierarchical network. If a set of different data is arranged in such a way, then one can naturally devise a network-based learning algorithm so that information in one layer can be propagated to other layers through interlayer connections. Incorporating individual networks in layers can be considered as an integration in a serial/vertical manner in contrast with parallel integration for multiple independent networks. The hierarchical integration induces several problems on computational complexity, sparseness, and scalability because of a huge-sized matrix. In this paper, we propose two versions of an algorithm, based on semi-supervised learning, for a hierarchically structured network. The naive version utilizes existing method for matrix sparseness to solve label propagation problems. In its approximate version, the loss in accuracy versus the gain in complexity is exploited by providing analyses on error bounds and complexity. The experimental results show that the proposed algorithms perform well with hierarchically structured data, and, outperform an ordinary semi-supervised learning algorithm. (C) 2019 Elsevier Ltd. All rights reserved.