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EFFICIENT ALGORITHMS FOR AGGLOMERATIVE HIERARCHICAL-clustering methodS

JOURNAL OF CLASSIFICATION 1984年第1期1卷 7-24页

作者： DAY, WHE EDELSBRUNNER, H GRAZ TECH UNIV INST INFORMAT VERARBEITUNGA-8010 GRAZAUSTRIA

Whenevern objects are characterized by a matrix of pairwise dissimilarities, they may be clustered by any of a number of sequential, agglomerative, hierarchical, nonoverlapping (sahn) clustering methods. These sahn clustering methods are defined by a paradigmatic algorithm that usually requires 0(n ³) time, in the worst case, to cluster the objects. An improved algorithm (Anderberg 1973), while still requiring 0(n ³) worst-case time, can reasonably be expected to exhibit 0(n ²) expected behavior. By contrast, we describe a sahn clustering algorithm that requires 0(n ² logn) time in the worst case. When sahn clustering methods exhibit reasonable space distortion properties, further improvements are possible. We adapt a sahn clustering algorithm, based on the efficient construction of nearest neighbor chains, to obtain a reasonably general sahn clustering algorithm that requires in the worst case 0(n ²) time and space.

关键词： Algorithm complexity Algorithm design Centroid clustering method Geometric model sahn clustering method

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INVESTIGATION OF PROPORTIONAL LINK LINKAGE clustering methodS

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JOURNAL OF CLASSIFICATION 1985年第2-3期2卷 239-254页

作者： DAY, WHE EDELSBRUNNER, H GRAZ TECH UNIV INST INFORMATIONSVERARBEITUNG A-8010 GRAZ AUSTRIA

Proportional link linkage (PLL) clustering methods are a parametric family of monotone invariant agglomerative hierarchical clustering methods. This family includes the single, minimedian, and complete linkage clustering methods as special cases;its members are used in psychological and ecological applications. Since the literature on clustering space distortion is oriented to quantitative input data, we adapt its basic concepts to input data with only ordinal significance and analyze the space distortion properties of PLL methods. To enable PLL methods to be used when the number n of objects being clustered is large, we describe an efficient PLL algorithm that operates in O(N2 log n) time and O(n2) space.

关键词： Algorithm complexity Algorithm design Integer link linkage clustering method Monotone invariance sahn clustering method Space distortion

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