Abstract:An important mesoscopic feature of social networks is that community structure is often associated with organizational and functional characteristics of the underlying networks. Uncovering this community structure is an important research direction of social network analysis, it is very important for the analysis and understanding of structure attributes and group characteristics of social networks. Recently, considerable methods have been proposed for community detection. And these methods may fall into two categories: global-based and local-based. The global-based methods partition the whole network from the global perspective, requiring complete knowledge and information of the entire network. Currently, the global methods mainly include graph partitioning, hierarchical clustering, modularity optimization, model-based methods, and so on. Nevertheless, there are some limitations in global methods. Firstly, global-based methods usually divide the whole network into communities with the aid of prior knowledge such as the network size and community number, which are usually unavailable and unpredictable in advance for huge and evolving networks. Secondly, for the large-scale and dynamic social networks, it is computationally expensive to adopt existing global approaches. The last but not the least, global methods, for network structure itself, fail to detect overlapping attribute of community fundamentally in social network. Local methods identify communities based on the local structure information and local community metric in social network analysis. The basic idea behind local approaches is that communities are essentially local structures, involving the nodes belonging to the communities themselves plus at most an extended neighborhood of them. Such structures are widespread in online social networks. Compared with global methods, local ones show strong adaptability for current social networks with increasing large scale, complexity, and dynamic nature. What is more, they are efficient to reveal local community characteristics with local knowledge of a network. Many local-based methods have been proposed to detect community structures, such as Luo Wang Promislow（LWP）, Lancichinetti Fortunato Method（LFM）, Clique Percolation Method（CPM）, Label Propagation Algorithm（LPA）, and so on. This paper aims to give a survey on community detection methods based on local optimization. We first introduce community definitions in the context of social network, as well as evaluation indexes. Then we classify these methods and compare them to local optimization methods emphatically. The main local methods are classified into four categories according to diverse optimization approaches: local expansion optimizing（LEO）, clique percolation method（CPM）, label propagation algorithms（LPAs）, and local link clustering（LLC）. LEO methods usually detect community from a source vertex by using a local optimization of a certain metric. CPMs explore overlapping communities on a large scale, which define a community as union of all k-cliques. LPAs adopt label propagation technique which identifies the densely connected groups of nodes by forming a consensus on a unique label. LLC methods regard communities as groups of links rather than nodes and naturally incorporate overlap while revealing hierarchical organization. The survey performs special analysis on the performance and differences in these methods in terms of their methodological principles. It presents a comparative discussion of several popular methods. Comparative study shows that local expansion optimizing methods are efficient to detect hierarchical and overlapping local community structure. In online social network, the formation of community mainly rely on local interaction and show strong autonomy. So local expanding methods are efficient for mining local online communities. Clique percolation methods can finding cohesive local communities and highly overlapping communities because of their strict community definition. Furthermore, label propagation algorithms show distinctive advantages in term of computational complexity, which are suitable for detecting communities in large-scale networks. In addition, local link clustering methods can naturally incorporate overlapping nodes while revealing hierarchical organization of social network. At last, the paper discusses some key problems and challenges in community detection, as well as potential future research directions.