Graph clustering is a fundamental technique in machine learning that has widespread applications in various fields. Deep Nonnegative Matrix Factorization (DNMF) was recently emerged to cope with the extraction of several layers of features, and it has been demonstrated to achieve remarkable results on unsupervised tasks. While DNMF has been applied for analyzing graphs, the effectiveness of the current DNMF approaches for graph clustering is generally unsatisfactory: these methods are intrinsically data representation models, and their objective functions do not capture cluster structures, also ignores direction which is crucial in the directed graph clustering problems. To overcome these downsides, this paper proposes a graph-specific DNMF model based on the Asymmetric NMF which can handle undirected and directed graphs. Inspired by hierarchical graph clustering and graph summarization approaches, the Deep Asymmetric Nonnegative Matrix Factorization (DAsNMF) is introduced for the directed graph clustering problem. In a pseudo-hierarchical clustering setting, DAsNMF decomposes the input graph to extract low-level to high-level node representations and graph representations (summarized graphs). In addition, the asymmetric cosine and PageRank-based similarities are imposed on the proposed model to preserve the local and global graph structures. The learning process is formulated as a unified optimization problem to jointly train representation learning model and clustering model. The extensive experimental studies validate the effectiveness of the proposed method on directed graphs.
