{"type":"ScholarlyArticle","title":"Discerning Linkage-Based Algorithms among Hierarchical Clustering Methods","authors":[{"name":"Margareta Ackerman","slug":"margareta-ackerman","given":"Margareta","family":"Ackerman","affiliation":""},{"name":"Shai Ben-David","slug":"shai-ben-david","given":"Shai","family":"Ben-David","affiliation":""}],"abstract":"Selecting a clustering algorithm is a perplexing task. Yet since different algorithms may yield dramatically different outputs on the same data, the choice of algorithm is crucial. When selecting a clustering algorithm, users tend to focus on cost-related considerations (software purchasing costs, running times, etc). Differences concerning the output of the algorithms are not usually considered. Recently, a formal approach for selecting a clustering algorithm has been proposed (Ackerman, Ben-David, and Loker, NIPS 2010). The approach involves distilling abstract properties of the input-output behavior of different clustering paradigms and classifying algorithms based on these properties. In this paper, we extend this approach into the hierarchical setting. The class of linkage-based algorithms is perhaps the most popular class of hierarchical algorithms. We identify two properties of hierarchical algorithms, and prove that linkage-based algorithms are the only ones that satisfy both of these properties. Our characterization clearly delineates the difference between linkage-based algorithms and other hierarchical algorithms. We formulate an intuitive notion of locality of a hierarchical algorithm that distinguishes between linkage-based and global hierarchical algorithms like bisecting k-means, and prove that popular divisive hierarchical algorithms produce clusterings that cannot be produced by any linkage-based algorithm.","doi":"10.5591/978-1-57735-516-8/IJCAI11-195","url":"https://ijcai.org/proceedings/2011/195","pdf":"https://ijcai.org/proceedings/2011/0195.pdf","markdown":"https://ijcai.org/proceedings/2011/195.md","bibtex":"https://ijcai.org/proceedings/2011/bibtex/195","volume":{"slug":"2011","title":"Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2011","url":"https://ijcai.org/proceedings/2011/","year":2011,"location":"Barcelona, Catalonia, Spain","dates":"16–22 July 2011","editors":"Toby Walsh","isbn":"978-1-57735-512-0; 978-1-57735-513-7; 978-1-57735-514-4; 978-1-57735-515-1; 978-1-57735-516-8","publisher":"AAAI Press/International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":null,"track":"","number":195,"pages":{"first":1140,"last":1144},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}