Clustering of relational data containing noise and outliers

The concept of noise clustering algorithm is applied to several fuzzy relational data clustering algorithms to make them more robust against noise and outliers. The methods considered include techniques proposed by Roubens (1978), Hathaway et al. (1994) and FANNY by Kaufman and Rouseeuw (1990). A new fuzzy relational data clustering (FRC) algorithm is proposed through generalization of FANNY. The FRC algorithm is shown to have the same objective functional as the relational fuzzy c-means algorithm. However, through use of direct objective function minimization based on the Lagrangian multiplier technique, the necessary conditions for minimization are derived without imposition of the restriction that the relational data is derived from Euclidean measure of distance from object data. Robustness of the new algorithm is demonstrated through several examples