Semiflat L-cluster methods

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Abstract

In previous work, an order theoretic model for cluster analysis has been developed, and flat cluster methods characterized in terms of their compatibility with respect to the set of residuated mappings on the non-negative reals. This suggests the possibility of classifying cluster methods according to their compatibility properties with respect to residuated mappings. Such a program is herewith initiated. Semiflat cluster methods are defined and characterized by their compatibility with respect to those residuated mappings θ for which θ+ (0) = 0. It is also shown how these methods fit into an earlier graph theoretic model for cluster analysis that was developed by Jardine and Sibson.

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