ε-connectedness In Weak Distance Measure Spaces And A Note About Competitive And Cooperative Learning Algorithm

The connectedness on metric space is a basic and intitionsitiscconception (maybe many people are interested in topology for it). This paper is theresult of the combination of the connected theory and clustering analysis. Thereare two problems are discussed: (1)The connectedness on weak distance measurespace (weak distance measure is the generalization of measure,probability measureand distinct measure); (2)Competitive and Cooperative Learning approach will beintrduced and a record about this algorithm will be advanced. The former is theextension of the connected theory on measure space,the latter has the similar basicidea with the connectedness. The main content of this paper is as follows:In chapter 1, preparation knowledge. Firstly, defines some notions,gives somesymbols and dependency conclutions we will be used in chapter 2, such as, weakdistance measure, continuous mapping, some properties of continuous mapping,ε-compressing mapping and product weak distance etc. Scondly, simply introducedsome clustering knowledge will be used in chapter 3. Summarize the developmentand research significance about seval alogrithms.In chapter 2, we have studiedε-connectedness in weak distance measure space.First,ε-connectedness (connectedness) are defined in weak distance measure space,some properties and equivalent conditions about connected set are given. Then,we discussed seveal properties ofε-connectedness. For example,union of a familyof connected sets which satisfies some conditions is connected.ε-connectedness isproducted and maintained under theε-Compressing mapping. Last,ε-connectedregion,locallyε-connectedness are defined and seval qualities are studied aboutthem.In chapter 3, Competitive and Cooperative Learning approach is described indetail. We found the deficiency of CCL through the numerical experimentation andadvanced an propositional solution to improve it. Last,we inspected that thosereconmendation is elective and the result of clustering are more precise via manyexperiments.