关键词: 复杂网络, 社团结构, 模块密度, 核方法, 半指导聚类

Abstract: In recent years，the problem of community structure detection has attracted more and more attention and many approaches have been proposed.In this context，Li et al recently propose modularity density objective function for community detec-
ting called the D function.Empirically，higher values of the D function have been shown to correlate well with good community structures.However，optimization of the function is a NP-hard problem.In this paper，how to optimize the D function can be formulated as a semi-supervised approach problem.The equivalence of the semi-supervised and the kernel k-means based on modularity density are also proved and a new semi-supervised kernel clustering approach is proposed.The approach is illustrated and compared with direct kernel approach based on modularity density by using a classic computer generated networks.Experimental results show the significance of the proposed approach，particularly，in the cases when community structure is obscure.

Key words: complex networks, community structure, modularity density, kernel approach, semi-supervised clustering