Generalization of FCv and robust shell clustering based on least absolute deviations

Abstract

Generalized Principal Component Analysis (Generalized PCA) is a useful extension of the PCA algorithm for estimating a suitable non-linear coordinate system when sample data points have non-linear distribution. The non -linear models derived by Generalized PCA is closely related to shell clustering that partitions data sets into several shell-shape fuzzy clusters by extracting local circles or ellipses as the prototypes of clusters. This paper proposes a robust shell clustering technique by generalizing a linear fuzzy clustering algorithm based on least absolute deviations. The proposed method is a hybrid technique of local minor component analysis and FCM-type fuzzy clustering in the enlarged data space and can be regarded as an application of Fuzzy c-Varieties (FCV) algorithm for capturing local non-linear singularities. The tuning of the trade-off parameter makes it possible to derive stable clustering results that are robust to the initial partitioning. Numerical example composed of a comparison with the possibilistic shell clustering method shows the characteristic properties of our method.