CHARACTERIZATIONS OF NEAREST AND FARTHEST NEIGHBOR ALGORITHMS BY CLUSTERING ADMISSIBILITY CONDITIONS

Monotone admissibility for clustering algorithms was introduced in Fis her and Van Ness [Biometrika 58, 91-104 (1971)]. The present paper dis cusses monotone admissibility for a broad class of clustering algorith ms called the Lance and Williams algorithms. Necessary and sufficient conditions for Lance and Williams algorithms to be monotone admissible are discussed here. It is shown that the only such algorithms which a re monotone admissible are nearest neighbor and farthest neighbor. (C) 1998 Published by Elsevier Ltd on behalf of the Pattern Recognition S ociety. All rights reserved.