Web Mining and Social Networking: Techniques and ... - tud.ttu.ee

68 3 Algorithms and Techniquesthat the incurring cost will be minimized. This assumption is quite reasonable in real worldthat the evolution of real observations is gradually and properly in a longitudinal manner.In [164], Lin et al. proposed a framework for analyzing communities and their evolutionin dynamic networks. In their approach, they first introduced a cost function to measure thequality of community structure at a certain time t and assumed the forming of stable communitystructure is really dependent on the minimization of the cost function. In particular, thecost function consists of two aspects - a snapshot cost and a temporal cost:cost = α ·CS+(1 − α) ·CT (3.15)The snapshot cost is then determined by the distribution difference between the real similaritymatrix of nodes within the network and the calculated similarity matrix of the formed communitystructures. That is, the snapshot cost is the KL-divergence between the above mentionedsimilarity matrix. On the other hand, the temporal cost indicates the distribution differencebetween the similarity matrices at two consecutive time stamps using the same formula. Combiningthese two types of cost gives the whole cost measure, which is used to guide the communitystructure detection. Hence the analysis of community structures and their evolutionsis converted to an optimization problem of finding appropriate communities that minimizesthe whole cost. To solve the optimization problem, an iterative algorithm is devised to alternativelyupdate the requested community structures until an optimization solution is reached.More details is referred to [164].SummaryIn this chapter, we review and summarize some commonly used algorithms and techniques inthe applications of web data mining, web recommendation and social network analysis. Themathematical formulations and algorithmic descriptions are elaborately organized into ninesections. It is expected that this chapter provides a technically detailed reference resource forreaders to proceed the further chapters.