Linear fuzzy clustering techniques with missing values and their application to local principal component analysis

In this paper, we propose two methods for partitioning an incomplete data set with missing values into several linear fuzzy clusters by extracting local principal components. One is an extension of fuzzy c-varieties clustering that can be regarded as the algorithm for the local principal component analysis of fuzzy covariance matrices. The other is a simultaneous application of fuzzy clustering and principal component analysis of fuzzy correlation matrices. Both methods estimate prototypes ignoring only missing values and they need no preprocessing of data such as the elimination of samples with missing values or the imputation of missing elements. Numerical examples show that the methods provide useful tools for interpretation of the local structures of a database.