  We consider the clustering problem of attributed graphs. Our challenge is how
we can design an effective and efficient clustering method that precisely
captures the hidden relationship between the topology and the attributes in
real-world graphs. We propose Non-linear Attributed Graph Clustering by
Symmetric Non-negative Matrix Factorization with Positive Unlabeled Learning.
The features of our method are three holds. 1) it learns a non-linear
projection function between the different cluster assignments of the topology
and the attributes of graphs so as to capture the complicated relationship
between the topology and the attributes in real-world graphs, 2) it leverages
the positive unlabeled learning to take the effect of partially observed
positive edges into the cluster assignment, and 3) it achieves efficient
computational complexity, $O((n^2+mn)kt)$, where $n$ is the vertex size, $m$ is
the attribute size, $k$ is the number of clusters, and $t$ is the number of
iterations for learning the cluster assignment. We conducted experiments
extensively for various clustering methods with various real datasets to
validate that our method outperforms the former clustering methods regarding
the clustering quality.
