Asymptotic evaluation of distance measure on high dimensional vector spaces in text mining

This paper discusses the document classification problems in text mining from the viewpoint of asymptotic statistical analysis. In the problem of text mining, the several heuristics are applied to practical analysis because of its experimental effectiveness in many case studies. The theoretical explanation about the performance of text mining techniques is required and such thinking will give us very clear idea. In this paper, the performances of distance measures used to classify the documents are analyzed from the new viewpoint of asymptotic analysis. We also discuss the asymptotic performance of IDF measure used in the information retrieval field.