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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.

MSC:
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
Software:
Algorithm 39; UCI-ml
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