2001 Volume 13 Issue 6 Pages 680-688
Fuzzy c-Varieties (FCV) clustering proposed by Bezdek et al. is a linear clustering method whose prototypes are linear carieties and can be regarded as a technique for extracting local principal components. In spite of its usefulness, the FCV algorithm cannot deal with an incomplete data set including missing values without elimination or imputation of data. In this paper, we propose a method for partitioning an incomplete data set including missing values into several fuzzy clusters using local principal components. First, FCV clustering is defined as the technique for the extraction of local principal components based on the minimization of the least square criterion, which performs the lower rank approximation of the data matrix. While the objective function of FCV clustering is based on the minimization of the distances between data points and prototypical linear varieties, the same objective function can be derived from the least square criterion under a certain condition. Second, a new technique for dealing with incomplete data sets is proposed by extending the method to extract local principal components. Numerical example shows the characteristic properties of our method.
