{"author":[{"first_name":"William","last_name":"Day","full_name":"Day, William"},{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"}],"month":"01","language":[{"iso":"eng"}],"extern":"1","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","title":"Efficient algorithms for agglomerative hierarchical clustering methods","intvolume":"         1","date_published":"1984-01-01T00:00:00Z","abstract":[{"lang":"eng","text":"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.\r\nWhenevern 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."}],"citation":{"mla":"Day, William, and Herbert Edelsbrunner. “Efficient Algorithms for Agglomerative Hierarchical Clustering Methods.” <i>Journal of Classification</i>, vol. 1, Springer, 1984, pp. 7–24, doi:<a href=\"https://doi.org/10.1007/BF01890115\">10.1007/BF01890115</a>.","short":"W. Day, H. Edelsbrunner, Journal of Classification 1 (1984) 7–24.","ista":"Day W, Edelsbrunner H. 1984. Efficient algorithms for agglomerative hierarchical clustering methods. Journal of Classification. 1, 7–24.","ieee":"W. Day and H. Edelsbrunner, “Efficient algorithms for agglomerative hierarchical clustering methods,” <i>Journal of Classification</i>, vol. 1. Springer, pp. 7–24, 1984.","chicago":"Day, William, and Herbert Edelsbrunner. “Efficient Algorithms for Agglomerative Hierarchical Clustering Methods.” <i>Journal of Classification</i>. Springer, 1984. <a href=\"https://doi.org/10.1007/BF01890115\">https://doi.org/10.1007/BF01890115</a>.","apa":"Day, W., &#38; Edelsbrunner, H. (1984). Efficient algorithms for agglomerative hierarchical clustering methods. <i>Journal of Classification</i>. Springer. <a href=\"https://doi.org/10.1007/BF01890115\">https://doi.org/10.1007/BF01890115</a>","ama":"Day W, Edelsbrunner H. Efficient algorithms for agglomerative hierarchical clustering methods. <i>Journal of Classification</i>. 1984;1:7-24. doi:<a href=\"https://doi.org/10.1007/BF01890115\">10.1007/BF01890115</a>"},"publist_id":"1998","date_created":"2018-12-11T12:07:04Z","doi":"10.1007/BF01890115","article_processing_charge":"No","publication":"Journal of Classification","publisher":"Springer","status":"public","_id":"4121","volume":1,"main_file_link":[{"url":"https://link.springer.com/article/10.1007%2FBF01890115"}],"article_type":"original","page":"7 - 24","year":"1984","publication_identifier":{"issn":["0176-4268"],"eissn":["1432-1343"]},"day":"01","publication_status":"published","type":"journal_article","date_updated":"2022-01-27T14:16:27Z","quality_controlled":"1","oa_version":"None"}