Abstract
Fuzzy c-Varieties (FCV) clustering is a linear fuzzy clustering algorithm that partitions a data set into several linear clusters using linear varieties as prototypes of clusters. Although the goal of the FCV clustering is unsupervised classification of non-labeled data sets, it can be regarded as a simultaneous approach to principal component analysis (PCA) and fuzzy clustering since the basis vectors of prototypical linear varieties are often identified with local principal component vectors. This paper reviews four PCA models and discusses the connections between linear fuzzy clustering algorithm and local PCA models based on different concepts. While the standard FCV algorithm is the modified version of the PCA model based on fitting low-dimensional sub-space, the same clustering result can be derived by considering estimation of latent variables that keep the original information as well as possible. In this sense, linear fuzzy clustering is a new approach to local multivariate analysis, in which fuzzy partitioning plays a role for classification of samples. It is expected that the new concept for local multivariate analysis stimulates future studies with similar ideas.
