On weighted principal component analysis for interval-valued data and its dynamic feature

This paper presents a weighted principal component analysis (WPCA) for interval-valued data by using the result of fuzzy clustering. In this method, we consider two data structures. One is a classification structure and the other is a data structure captured by principal components. The classification structure is used for estimating the weights and the data structure captured by principal components is used for self analysis. By considering the two structures, we can reduce the risk of a wrong assumption for the true data structure, when compared with the conventional methods which assume only one data structure. Moreover, we investigate the dynamic feature of the principal components under the assumption of linear transformation from minimum values of the interval-valued data to a weighted combination of minimum and maximum values of the interval-valued data. Several numerical examples show the better performance of the proposed method.