Linear Fuzzy Clustering for Mixed Databases Based on Optimal Scaling

Fuzzy c-Varieties (FCV) is a tool for linear fuzzy clustering and is also applicable to local principal component analysis, in which each low-dimensional subspace is estimated considering data partition. In real applications, it is often the case that a database to be analyzed includes not only numerical variables but also nominal variables. Optimal scaling is a useful approach to multivariate analysis for mixed databases and has been applied to linear model estimation. This paper proposes a new algorithm for linear fuzzy clustering that can handle nominal variables using the optimal scaling approach. The iterative algorithm includes an additional step of calculating numerical scores of categorical variables.