Community Detection via Autoencoder-Like Nonnegative Tensor Decomposition

Community detection aims at partitioning a network into several densely connected subgraphs. Recently, nonnegative matrix factorization (NMF) has been widely adopted in many successful community detection applications. However, most existing NMF-based community detection algorithms neglect the multihop network topology and the extreme sparsity of adjacency matrices. To resolve them, we propose a novel conception of adjacency tensor, which extends adjacency matrix to multihop cases. Then, we develop a novel tensor Tucker decomposition-based community detection method—autoencoder-like nonnegative tensor decomposition (ANTD), leveraging the constructed adjacency tensor. Distinct from simply applying tensor decomposition on the constructed adjacency tensor, which only works as a decoder, ANTD also introduces an encoder component to constitute an autoencoder-like architecture, which can further enhance the quality of the detected communities. We also develop an efficient alternative updating algorithm with convergence guarantee to optimize ANTD, and theoretically analyze the algorithm complexity. Moreover, we also study a graph regularized variant of ANTD. Extensive experiments on real-world benchmark networks by comparing 27 state-of-the-art methods, validate the effectiveness, efficiency, and robustness of our proposed methods.