A Framework for Accurate Community Detection on Signed Networks Using Adversarial Learning

Abstract

In this paper, we propose a framework for embedding-based community detection on signed networks, namely <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>A</i></u> dversarial learning of <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>B</i></u> alanced triangle for <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>C</i></u> ommunity detection, in short <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math>${\sf ABC}$</tex-math></inline-formula> . It first represents all the nodes of a signed network as vectors in low-dimensional embedding space and conducts a clustering algorithm ( <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e.g.,</b> <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> -means) on vectors, thereby detecting a community structure in the network. When performing the embedding process, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math>${\sf ABC}$</tex-math></inline-formula> learns only the edges belonging to balanced triangles whose edge signs follow the balance theory, significantly excluding noise edges in learning. To address the sparsity of balanced triangles in a signed network, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math>${\sf ABC}$</tex-math></inline-formula> learns not only the edges in balanced <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">real</i> -triangles but those in balanced <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">virtual</i> -triangles that do not actually exist but are produced by our generator. Finally, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math>${\sf ABC}$</tex-math></inline-formula> employs adversarial learning to generate more-realistic balanced virtual-triangles with less noise edges. Through extensive experiments using seven real-world networks, we validate the effectiveness of (1) learning edges belonging to balanced real/virtual-triangles and (2) employing adversarial learning for signed network embedding. We show that <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math>${\sf ABC}$</tex-math></inline-formula> consistently and significantly outperforms the state-of-the-art community detection methods in all datasets.