A new biplot procedure with joint classification of objects and variables by fuzzy \(c\)-means clustering. (English) Zbl 1414.62022

Summary: 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.


62A86 Fuzzy analysis in statistics
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
62H25 Factor analysis and principal components; correspondence analysis
15A18 Eigenvalues, singular values, and eigenvectors


UCI-ml; Algorithm 39
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