Abstract
Fuzzy c-Varieties(FCV) is a tool for linear fuzzy clustering and is also applicable to local principal component analysis (local PCA), in which each low-dimensional subspace is estimated considering data partition. Although the clustering criterion in FCV is distances between data points and prototypical linear varieties, the criterion can also be defined based on least square approximation. Optimal scaling is a useful approach to multivariate analysis for mixed databases and has been applied to linear model estimation. This paper proposes two formulations of local PCA for mixed databases based on optimal scaling, in which a conventional FCV and linear fuzzy clustering using least square approximation are enhanced. The proposed algorithms include a step of calculating numerical scores of categorical variables in addition to the ordinary alternative optimization.
