The Research Of Clustering Methods And Community Structure In Complex Networks

Since the 1990s, the rapidly development of Internet information technology as a representative causes the human society stride into the network time. From the Internet to WWW, from the food cycle networks in the environment to the metabolism networks in the creatures' bodies, from the scientific research collaboration network to kinds of political networks, social networks and economic networks, from the large-scale network electronic network to the global traffic network, people live in a world full of varieties of complex networks, which makes the research of complex networks necessary. Because of the quantitative nodes and the intricate structures, it is very difficult to study complex networks. The clustering analysis and the method of finding community structures in complex networks simplify the research by classifying the whole networks into several less-nodes and simpler-structure sub networks.The clustering analysis has been developed quickly and is an extraordinary important technology in the data-mining and exploration analysis, especially is widely used in the fields of data-mining, statistics, machine study, space database technology, biology and marketing analysis etc. In recent years, finding community structure is a very popular issue in researches of complex networks. We study the community structure by clustering analysis. In this paper we did several things as follows:(1) We improved FCM (fussing clustering method) by combining the FCM with visual principle density clustering algorithm and got a new algorithm-visual principle fussing clustering method. When it is used in complex networks, to some extent it can solve the problem of being easily influenced by isolated points when we use FCM and overcome the difficulties of determining clustering number. The author applied it in WUHAN traffic network, attaining good results.(2) We gave out a new method of finding community structure on the basic of divisive algorithm and agglomerative algorithm--agglomerative algorithm based on diversity index. We also used the algorithm in classic Zachary network and found the result is in accordance with the real network. The innovation points of this paper are:(1) The traditional FCM algorithm uses the Euclidean distance for calculating the distance of two data points, but in the visual principle FCM clustering algorithm we used the number of edges of average shortest route instead.(2) The visual principle FCM clustering algorithm combined the traditional FCM algorithm with density-based clustering method by simulating visual systems, overcoming two common defects in FCM clustering methods:a) The FCM algorithm is quite easily influenced by isolated points in the data, while the visual principle FCM clustering algorithm can distinguish the isolated points and delete them.b) The FCM algorithm needs to be given the parameter beforehand, which is the clustering number. We got the parameter by increasing the radius of the neighborhood and got the optimal clustering number by the notion of survival sector.(3) The agglomerative algorithm based on diversity index we gave out is on the base of ideal of the diversity index in divisive algorithm. We used average shortest route instead of using the route of Brownian movement. Moreover, Newman subtracted the edges between communities from the edges within the communities to scale the clustering result while we used the proposition form.