Fuzzy cluster-scaled principal component analysis for mixed data and its application of educational effect based on device selection

Abstract

This paper proposes a fuzzy cluster-scaled principal component analysis (fuzzy cluster-scaled PCA) for mixed data, which consists of both numerical and categorical data with respect to quantitative and qualitative variables. The fuzzy cluster-scaled PCA has been proposed for high-dimension, low-sample size (HDLSS) data in which the number of variables (or dimensions) is much larger than the number of objects (or samples). In this case, the target data is only for the numerical data. The proposed fuzzy cluster-scaled PCA in this paper can be applied to the mixed type of HDLSS data by utilizing the feature of the fuzzy cluster-scaled correlation, which is decomposed into two parts: the first part is the correlation of classification structures between variables and the second part is the correlation between variables. Then, the first part can be adapted to the categorical data, and the second part can be used for the numerical data through the same objects. Several numerical examples used data from a survey concerned with the relationship between students’ choice of devices and scores of examination/class marks to measure the educational effect show a better performance of this proposed method, and insightful, important information on educational effectiveness is clarified.