Comments on 'Parallel Algorithms for Hierarchical Clustering and Cluster Validity'

In the above-titled paper (ibid., vol.12, no.11, p.1088-92, Nov. 1990), parallel implementations of hierarchical clustering algorithms that achieve O(n/sup 2/) computational time complexity and thereby improve on the baseline of sequential implementations are described. The latter are stated to be O(n/sup 3/), with the exception of the single-link method. The commenter points out that state-of-the-art hierarchical clustering algorithms have O(n/sup 2/) time complexity and should be referred to in preference to the O(n/sup 3/) algorithms, which were described in many texts in the 1970s. Some further references in the parallelizing of hierarchic clustering algorithms are provided. >

[1]  Robin Sibson,et al.  SLINK: An Optimally Efficient Algorithm for the Single-Link Cluster Method , 1973, Comput. J..

[2]  Bruce W. Weide,et al.  Optimal Expected-Time Algorithms for Closest Point Problems , 1980, TOMS.

[3]  J. Juan Programme de classification hiérarchique par l'algorithme de la recherche en chaîne des voisins réciproques , 1982 .

[4]  H. Edelsbrunner,et al.  Efficient algorithms for agglomerative hierarchical clustering methods , 1984 .

[5]  C. R. Sergeant Linear and Combinatorial Programming , 1977 .

[6]  Leslie G. Valiant,et al.  Computational limitations on learning from examples , 1988, JACM.

[7]  Xiaobo Li,et al.  Parallel Algorithms for Hierarchical Clustering and Cluster Validity , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[8]  D. Defays,et al.  An Efficient Algorithm for a Complete Link Method , 1977, Comput. J..

[9]  Fionn Murtagh,et al.  Multidimensional clustering algorithms , 1985 .

[10]  Michel Bruynooghe,et al.  Méthodes nouvelles en classification automatique de données taxinomiques nombreuses , 1977 .

[11]  C. de Rham,et al.  La classification hiérarchique ascendante selon la méthode des voisins réciproques , 1980 .

[12]  Edie M. Rasmussen,et al.  Efficiency of Hierarchic Agglomerative Clustering using the ICL Distributed array Processor , 1989, J. Documentation.

[13]  Yiyu Yao,et al.  Query formulation in linear retrieval models , 1990, J. Am. Soc. Inf. Sci..

[14]  Saburo Muroga,et al.  Threshold logic and its applications , 1971 .

[15]  Fionn Murtagh,et al.  A Survey of Recent Advances in Hierarchical Clustering Algorithms , 1983, Comput. J..

[16]  Leslie G. Valiant,et al.  A theory of the learnable , 1984, STOC '84.

[17]  J. J. Rocchio,et al.  Relevance feedback in information retrieval , 1971 .

[18]  Fionn Murtagh Expected-Time Complexity Results for Hierarchic Clustering Algorithms Which Use Cluster Centres , 1983, Inf. Process. Lett..

[19]  F. James Rohlf,et al.  A Probabilistic Minimum Spanning Tree Algorithm , 1978, Inf. Process. Lett..

[20]  J. Stoer,et al.  Convexity and Optimization in Finite Dimensions I , 1970 .