Extraction of Local Principal Component Independent of External Criteria by Fuzzy Clustering

Abstract

This paper proposes a technique of local principal component analysis which extracts principal components independent of some external criteria. Fuzzy c-Regression Models is used to estimate the parameters of regression models with a fuzzy c-partitioning of the data. We decompose the fuzzy scatter matrix of each cluster into two matrices. One is closely related to the external criteria and the other is independent of them. Principal components independent of the external criteria are obtained from the decomposed fuzzy scatter matrix of each cluster.