Clustering on multi-layer graphs via subspace analysis on Grassmann manifolds

Relationships between entities in datasets are often of multiple types, which can naturally be modeled by a multi-layer graph; a common vertex set represents the entities and the edges on different layers capture different types of relationships between the entities. In this paper, we address the problem of analyzing multi-layer graphs and propose methods for clustering the vertices by efficiently merging the information provided by the multiple modalities. We propose to combine the characteristics of individual graph layers using tools from subspace analysis on a Grassmann manifold. The resulting combination can then be viewed as a low dimensional representation of the original data which preserves the most important information from diverse types of relationships between entities. We use this information in new clustering methods and test our algorithm on several synthetic and real world datasets to demonstrate its efficiency

Multi-GCN: Graph Convolutional Networks for Multi-View Networks, with Applications to Global Poverty

With the rapid expansion of mobile phone networks in developing countries, large-scale graph machine learning has gained sudden relevance in the study of global poverty. Recent applications range from humanitarian response and poverty estimation to urban planning and epidemic containment. Yet the vast majority of computational tools and algorithms used in these applications do not account for the multi-view nature of social networks: people are related in myriad ways, but most graph learning models treat relations as binary. In this paper, we develop a graph-based convolutional network for learning on multi-view networks. We show that this method outperforms state-of-the-art semi-supervised learning algorithms on three different prediction tasks using mobile phone datasets from three different developing countries. We also show that, while designed specifically for use in poverty research, the algorithm also outperforms existing benchmarks on a broader set of learning tasks on multi-view networks, including node labelling in citation networks

Structure fusion based on graph convolutional networks for semi-supervised classification

Suffering from the multi-view data diversity and complexity for semi-supervised classification, most of existing graph convolutional networks focus on the networks architecture construction or the salient graph structure preservation, and ignore the the complete graph structure for semi-supervised classification contribution. To mine the more complete distribution structure from multi-view data with the consideration of the specificity and the commonality, we propose structure fusion based on graph convolutional networks (SF-GCN) for improving the performance of semi-supervised classification. SF-GCN can not only retain the special characteristic of each view data by spectral embedding, but also capture the common style of multi-view data by distance metric between multi-graph structures. Suppose the linear relationship between multi-graph structures, we can construct the optimization function of structure fusion model by balancing the specificity loss and the commonality loss. By solving this function, we can simultaneously obtain the fusion spectral embedding from the multi-view data and the fusion structure as adjacent matrix to input graph convolutional networks for semi-supervised classification. Experiments demonstrate that the performance of SF-GCN outperforms that of the state of the arts on three challenging datasets, which are Cora,Citeseer and Pubmed in citation networks

Adaptation of K-means-type algorithms to the Grassmann manifold, An

2019 Spring.Includes bibliographical references.The Grassmann manifold provides a robust framework for analysis of high-dimensional data through the use of subspaces. Treating data as subspaces allows for separability between data classes that is not otherwise achieved in Euclidean space, particularly with the use of the smallest principal angle pseudometric. Clustering algorithms focus on identifying similarities within data and highlighting the underlying structure. To exploit the properties of the Grassmannian for unsupervised data analysis, two variations of the popular K-means algorithm are adapted to perform clustering directly on the manifold. We provide the theoretical foundations needed for computations on the Grassmann manifold and detailed derivations of the key equations. Both algorithms are then thoroughly tested on toy data and two benchmark data sets from machine learning: the MNIST handwritten digit database and the AVIRIS Indian Pines hyperspectral data. Performance of algorithms is tested on manifolds of varying dimension. Unsupervised classification results on the benchmark data are compared to those currently found in the literature