Cellular Automaton For Super-paramagnetic Clustering Of Data And Its Applications

The main task of clustering is to partition a given data set into homogeneous groups(clusters) in such a way that patterns within a cluster are more similar to each other than patternsbelonging to different clusters. The clustering problem has been addressed in many fields anddisciplines, which reflects its broad appeal and usefulness as one of the steps in exploratory dataanalysis.In1996, Domany et al. presented Super-paramagnetic Clustering based on the physicalproperties of an inhomogeneous ferromagnetic model: A data set is regarded as a Potts magneticsystem and a short-range interaction is introduced between the neighboring spins. The system ismade to evolve automatically under the function of the spin-spin interaction and the thermalmotion, and finally, at a proper temperature, the system will reach the super-paramagnetic phase,in which the spins (data points) will form into a number of ‘magnetic domains’(data clusters).This overcomes the disadvantage that an assumption about the data structure must be made inadvance as traditional clustering algorithm does.In order to simulate the parallelism of super-paramagnetic clustering better, we havebasically realized super-paramagnetic clustering using cellular automaton based on spatialdynamics. Focusing on the problems of the cellular automaton of super-paramagnetic clustering,what have been done are as follows:1. For solving the problem in locating the super-paramagnetic phase, constructed anapproximate linear function about the temperature T to scan T non-homogeneously throughresearching the structure of a lot of data sets, and improved the efficiency of locating thesuper-paramagnetic phase.2. Introduced four forms of interaction to the cellular automata of super-paramagneticclustering, and compared the clustering under different interactions. In order to master the wayof setting parameters, we researched some data sets with3different structures, using the cellularautomaton of super-paramagnetic clustering, and get some principles to set q and K.3. The cellular automaton of super-paramagnetic clustering is applied to imagesegmentation, and designed an image segmentation cellular automaton based onsuper-paramagnetic clustering to realize the segmentation of gray images and color images.