Efficient algorithms for agglomerative hierarchical clustering methods

W. Day, H. Edelsbrunner, Journal of Classification 1 (1984) 7–24.

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Abstract
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. Whenevern objects are characterized byk-tuples of real numbers, they may be clustered by any of a family of centroid SAHN clustering methods. These methods are based on a geometric model in which clusters are represented by points ink-dimensional real space and points being agglomerated are replaced by a single (centroid) point. For this model, we have solved a class of special packing problems involving point-symmetric convex objects and have exploited it to design an efficient centroid clustering algorithm. Specifically, we describe a centroid SAHN clustering algorithm that requires 0(n 2) time, in the worst case, for fixedk and for a family of dissimilarity measures including the Manhattan, Euclidean, Chebychev and all other Minkowski metrics.
Publishing Year
Date Published
1984-01-01
Journal Title
Journal of Classification
Volume
1
Issue
1
Page
7 - 24
IST-REx-ID

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Day W, Edelsbrunner H. Efficient algorithms for agglomerative hierarchical clustering methods. Journal of Classification. 1984;1(1):7-24. doi:10.1007/BF01890115
Day, W., & Edelsbrunner, H. (1984). Efficient algorithms for agglomerative hierarchical clustering methods. Journal of Classification, 1(1), 7–24. https://doi.org/10.1007/BF01890115
Day, William, and Herbert Edelsbrunner. “Efficient Algorithms for Agglomerative Hierarchical Clustering Methods.” Journal of Classification 1, no. 1 (1984): 7–24. https://doi.org/10.1007/BF01890115.
W. Day and H. Edelsbrunner, “Efficient algorithms for agglomerative hierarchical clustering methods,” Journal of Classification, vol. 1, no. 1, pp. 7–24, 1984.
Day W, Edelsbrunner H. 1984. Efficient algorithms for agglomerative hierarchical clustering methods. Journal of Classification. 1(1), 7–24.
Day, William, and Herbert Edelsbrunner. “Efficient Algorithms for Agglomerative Hierarchical Clustering Methods.” Journal of Classification, vol. 1, no. 1, Springer, 1984, pp. 7–24, doi:10.1007/BF01890115.

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