A new biplot procedure with joint classification of objects and variables by fuzzy c-means clustering

Abstract

Biplot is a technique for obtaining a low-dimensional configuration of the data matrix in which both the objects and the variables of the data matrix are jointly represented as points and vectors, respectively. However, biplots with a large number of objects and variables remain difficult to interpret. Therefore, in this research, we propose a new biplot procedure that allows us to interpret a large data matrix. In particular, the objects and variables are classified into a small number of clusters by using fuzzy c-means clustering and the resulting clusters are simultaneously biplotted in lower-dimensional space. This procedure allows us to understand the configurations easily and to grasp the fuzzy memberships of the objects and variables to the clusters. A simulation study and real data example are also provided to demonstrate the effectiveness of the proposed procedure.

Multivariate Dynamics of Ecuadorian Universities in Their Scientific Production in WoS: Post- Pandemic Period.

“…To obtain a better representation of Universities and publication sources (Open Access and Subscription) this dataset was represented in a dynamic HJ-Biplot over the period 2019-2021 15 , the objective is to obtain the quality of the data representations with the following information:…”

Fuzzy data analysis and classification

“…Some of the most influential pioneer works on the subject are, among others, those by Ruspini (1969Ruspini ( , 1970, Tamura et al (1971), Dunn (1973Dunn ( , 1974, Bezdek (1973Bezdek ( , 1974Bezdek ( , 1980, and Bezdek et al (1984), which have inspired both applications and many further methodologies. At present, this is one of the most successful topics involving Fuzzy Sets and Statistical theories, and the number of research papers on it is unquestionably growing [among the most recent ones see, for instance, the approaches in Liu et al (2013), Gong et al (2014), Yamashita and Mayekawa (2015), Ruan et al (2016), and Nguyen-Trang and Vo- Van (2017)], and it appears often either combined with or supporting other data analysis problems. In more detail, useful references to the extensive literature on the fuzzy clustering (from both theoretical and applicative points of view) can be found in the chapter on the fuzzy clustering by D'Urso (2016), the seminal monograph by Bezdek (1981), the books by Jain and Dubes (1988), De Oliveira and Pedrycz (2007), Miyamoto et al (2008) As remarked by D'Urso (2017a), there are different uncertainty-based clustering methods that can be considered extensions, variants and alternatives of the fuzzy clustering for non-fuzzy/standard data, like -possibilistic clustering [see, for instance, Krishnapuram and Keller (1993)], -shadowed clustering [see, for instance, Pedrycz (1998) Fuzzy approaches to analyze crisp/standard data, have not been carried out as exhaustively as fuzzy clustering ones for the same data.…”