Gaussian Kernel Fuzzy C-Means Algorithm for Service Resource Allocation

With respect to the cluster problem of the evaluation information of mass customers in service management, a cluster algorithm of new Gaussian kernel FCM (fuzzy C-means) is proposed based on the idea of FCM. First, the paper defines a Euclidean distance formula between two data points and makes them cluster adaptively based on the distance classification approach and nearest neighbors in deleting relative data. Second, the defects of the FCM algorithm are analyzed, and a solution algorithm is designed based on the dual goals of obtaining a short distance between whole classes and long distances between different classes. Finally, an example is given to illustrate the results compared with the existing FCM algorithm.

On the honeycomb conjecture for Robin Laplacian eigenvalues

We prove that the optimal cluster problem for the sum/the max of the first Robin eigenvalue of the Laplacian, in the limit of a large number of convex cells, is asymptotically solved by (the Cheeger sets of) the honeycomb of regular hexagons. The same result is established for the Robin torsional rigidity. In the specific case of the max of the first Robin eigenvalue, we are able to remove the convexity assumption on the cells.

Fast Ant Colony Optimization for Clustering

<p>Data clustering is popular data analysis approaches, which used to organizing data into sensible clusters based on similarity measure, where data within a cluster are similar to each other but dissimilar to that of another cluster. In the recently, the cluster problem has been proven as NP-hard problem, thus, it can be solved with meta-heuristic algorithms, such as the particle swarm optimization (PSO), genetic algorithm (GA), and ant colony optimization (ACO), respectively. This paper proposes an algorithm called Fast Ant Colony Optimization for Clustering (FACOC) to reduce the computation time of Ant Colony Optimization (ACO) in clustering problem. FACOC is developed by the motivation that a redundant computation is occurred in ACO for clustering. This redundant computation can be cut in order to reduce the computation time of ACO for clustering. The proposed FACOC algorithm was verified on 5 well-known benchmarks. Experimental result shows that by cutting this redundant computation, the computation time can be reduced about 28% while only suffering a small quality degradation.</p>