Linear Fuzzy Clustering of Mixed Databases Based on Cluster-wise Optimal Scaling of Categorical Variables

This paper proposes a new approach to linear fuzzy clustering of mixed databases, in which categorical variables are quantified in each cluster based on optimal scaling. The objective function of the Fuzzy c-Varieties (FCV) clustering is defined using least squares criterion, and local principal component analysis (local PCA) is then performed in each cluster considering quantified scores of categorical variables. The new approach quantifies categorical variables in each cluster so that they suit the local linear model of the cluster. So, this is the second approach to optimal scaling in linear fuzzy clustering and contrasts to the global approach where categorical variables are quantified so that they suit for constructing a single numerical data space. The clustering algorithm is an enhanced FCV algorithm that includes an additional step for quantifying categorical variables in each cluster, and is useful for revealing cluster-wise mutual dependencies among numerical and nominal variables rather than for revealing geometrical relationships among data samples.