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The success of fuzzy clustering relies heavily on the features of the input data. However, traditional fuzzy clustering methods focus on primitive features that represent the physical properties of data, such as the shape and color of objects. Usually, these properties could only capture the local distribution of data, while ignoring the global structure of data. Fortunately, by performing spectral analysis on the similarity graph of data, spectral clustering methods explore more on the global structure. However, capturing a decent global structure by constructing an ideal similarity graph is not easy. In this paper, we propose a novel fuzzy clustering method, the bilevel fuzzy clustering via adaptive similarity graphs fusion (BFCS), to solve the problems mentioned above at the same time. On the one hand, the global data structure is investigated by building an adaptive similarity graph using autoweighted fusion. On the other hand, the consistent memberships for both fuzzy clustering and spectral clustering are formulated into one objective function to simultaneously retain the local physical properties and the global data structure. Notably, the proposed method shows good scalability, and the bilevel structure of the algorithm makes its application to large datasets easy. Extensive experiments demonstrate the promising clustering performance of the proposed BFCS on synthetic and real datasets. [ABSTRACT FROM AUTHOR]

A new distance in finite graphs is defined through a game-theoretic approach. This distance arises when solving the problem about the fair cost, for a node in a graph, of attaining access to another node. The distance indicates the level of difficulty in the communication between any pair of nodes, on the understanding that the fewer paths there are between two nodes and the more nodes there are that form those paths, the greater the distance is. [ABSTRACT FROM AUTHOR]