Graph convolutional network for compositional data

Abstract

Graph convolutional network (GCN) has garnered significant attention and become a powerful tool for learning graph representations. However, when dealing with compositional data prevalent in various fields, the traditional GCN faces theoretical challenges due to the intrinsic constraints of such data. This paper generalizes the spectral graph theory in simplex space, aiming to address the graph structures among observations for compositional data analysis and to extend GCN by assigning mathematical objects of compositions to each vertex of a graph. We propose the graph Fourier transformation in simplex space, based on which a compositional graph convolutional network (CGCN) layer is introduced. This novel layer enables a GCN to appropriately capture the sample space of compositional data, allowing it to handle compositional features as model inputs. We then propose a new GCN architecture called COMP-GCN, incorporating the CGCN layer at the initial stage. We evaluate the effectiveness of COMP-GCN through simulation studies and two real-world applications: stock networks derived from co-investors in the Chinese stock market and student social networks based on co-locations in campus activities. The results demonstrate its superior performance over competitive methods with modest additional computational cost compared to traditional GCN. Our findings suggest the potential of the proposed model to inspire a new class of powerful algorithms for graph inference on compositional data in virtue of the generalization of graph convolution on simplex space.