Algorithms for Finding Multivariate Discriminant Rules for Classification and Regression Trees

Progress in technologies for data input, such as POS (Point Of Sales) systems, and technologies for data storage, such as high density magnetic or optical recording devices, have made it easier for enterprises to collect massive amounts of data and to store them on hard disk at a very low cost. From the early 90’s, many enterprises have been interested in extracting previously unnoticed information that inspires new marketing strategies from these huge databases. Technologies for extracting such information, or knowledge, from huge databases are called “data mining.” Data mining covers technologies for association analysis, classification and regression, cluster analysis, and evolution analysis. Most of these have been widely studied in the field of databases, statistics, and machine learning. Data mining, in general, is focusing on efficiency so that we can handle emerging huge databases whose size is too large to be processed by the conventional techniques. Among these technologies, the author focused on the association analysis and the classification and regression in this dissertation. The author considered association rules on numerical attributes while conventional data mining can only effective for categorical attributes. The accomplishment significantly expanded applications of the association analysis. Then, the author explored classification and regression problems. By utilizing techniques developed for the numerical association rules, the author proposed accurate and comprehensive classification and regression trees. Among these accomplishments, primary contributions of the author are the works on the classification and regression problems. In general, huge databases often contain many attributes and there are many correlations among attributes. However, conventional data mining techniques cannot handle correlations well. In the statistics literature, multivariate analysis methods have been used to handle correlations in numerical databases. Many statistical methods, such as “principal component analysis,” “factor analysis,” and so forth, are categorized as multivariate analysis. Most of the methods in the multivariate analysis assume a linear correlation. Such conventional techniques are effective for data that have linear correlations. However, data contain various types of correlations that cannot be handled by the conventional methods. In order to handle various types of correlations, the author proposed multivariate optimized discriminant rules that can be defined on more than one attribute and presented efficient algorithms for finding the rules. The algorithms efficiently find multivariate discriminant rules