Fuzzy Overlapping Modularity Clustering for Symmetric-tensor Based Graph

While existing graph clustering methods can only be oriented to classical graphic data, this study as the first attempt focuses on the proposed symmetric-tensor based graph and its clustering algorithm. To this end, the concept of fuzzy overlapping modularity is defined and then is extended into its generalized version for symmetric-tensor based graph. Subsequently, based on the principle of maximizing the symmetric-tensor based fuzzy overlapping modularity, a novel learning objective is derived for fuzzy clustering, and the corresponding clustering algorithm FOMC is also proposed. In addition, with only one additional hyperparameter, the semi-supervised clustering algorithm SFOMC is also derived for symmetric-tensor based graph with some labeled samples. Extensive experimental results on synthetic and real benchmarking datasets verify the clustering power of both FOMC and SFOMC on symmetric-tensor based graphs. In particular, FOMC achieves 13.94% improvement over the average performance of the comparative methods on the adopted real networks, and SFOMC's clustering performance increment becomes 1.799 times higher than the average value of the comparative methods when samples have been labeled from 5% to 25% in the adopted graphs.