| Summary: | 博士 === 國立臺灣科技大學 === 電機工程系 === 90 === The area of research in this dissertation is fuzzy c-partition clustering, which is understood to be the grouping of similar objects with the concept of fuzzy set theory to incorporate the uncertainty of the final classification results. There are three parts in this dissertation. The first part is an overview of fuzzy c-partition clustering. In the second part, two distributed approaches of genetic search strategies for fuzzy clustering are proposed to surmount the problem of huge search space in the traditional combination of evolutionary algorithms and fuzzy c-partition clustering. The distributed optimization approaches proposed can divide the huge search space into many small ones, which in effect will lower the size of the total search space. The benefit of our approaches is especially shown in clusters with shell shapes, of which the basins of attraction of local minima are very small. In the third part, a new neural architecture, the multi-synapse neural network, is developed for constrained optimization problems, whose objective functions may include high order, logarithmic, sinusoidal forms, unlike the traditional Hopfield networks which can only handle quadratic form optimization. Meanwhile, based on the application of this new architecture, a fuzzy bidirectional associative clustering network (FBACN) is proposed for fuzzy c-partition clustering according to the objective-functional method. It is well known that fuzzy c-means is a milestone algorithm in the area of fuzzy c-partition clustering. All of the following objective-functional-based fuzzy c-partition algorithms incorporate the formulas of fuzzy c-means as the prime mover in their algorithms. However, when an application of fuzzy c-partition has sophisticated constraints, the necessity of analytical solutions in a single iteration step becomes a fatal issue of the existing algorithms. The largest advantage of FBACN is that it does not need analytical solutions. For the problems on which some prior information is known, we bring a concept of the combination of part crisp and part fuzzy clustering. Basically, the FBACN is composed of two layers of recurrent networks. Layer 1 can be a Hopfield network or a multi-synapse neural network based on whether its objective function is a quadratic form or a high order form. Yet layer 2 is definitely a multi-synapse neural network. Three examples are given in part III. The first two are the famous butterfly and Anderson’s Iris data sets, which are usually utilized as benchmarks. The last one is a data set with two concentric circles used to demonstrate the constrained fuzzy c-partition.
|
|---|
