Parallel algorithms for hierarchical clustering
Hierarchical clustering is a common method used to determine clusters of similar data points in multidimensional spaces. O( n 2) algorithms are known for this problem [3,4,11,19]. This paper reviews important results for sequential algorithms and describes previous work on parallel algorithms for hi...
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| Vydané v: | Parallel computing Ročník 21; číslo 8; s. 1313 - 1325 |
|---|---|
| Hlavný autor: | |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Amsterdam
Elsevier B.V
01.08.1995
Elsevier |
| Predmet: | |
| ISSN: | 0167-8191, 1872-7336 |
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| Abstract | Hierarchical clustering is a common method used to determine clusters of similar data points in multidimensional spaces.
O(
n
2) algorithms are known for this problem [3,4,11,19]. This paper reviews important results for sequential algorithms and describes previous work on parallel algorithms for hierarchical clustering. Parallel algorithms to perform hierarchical clustering using several distance metrics are then described. Optimal PRAM algorithms using
n/log
n processors are given for the average link, complete link, centroid, median, and minimum variance metrics. Optimal butterfly and tree algorithms using
n/log
n processors are given for the centroid, median, and minimum variance metrics. Optimal asymptotic speedups are achieved for the best practical algorithm to perform clustering using the single link metric on a
n/log
n processor PRAM, butterfly, or tree. |
|---|---|
| AbstractList | Hierarchical clustering is a common method used to determine clusters of similar data points in multidimensional spaces.
O(
n
2) algorithms are known for this problem [3,4,11,19]. This paper reviews important results for sequential algorithms and describes previous work on parallel algorithms for hierarchical clustering. Parallel algorithms to perform hierarchical clustering using several distance metrics are then described. Optimal PRAM algorithms using
n/log
n processors are given for the average link, complete link, centroid, median, and minimum variance metrics. Optimal butterfly and tree algorithms using
n/log
n processors are given for the centroid, median, and minimum variance metrics. Optimal asymptotic speedups are achieved for the best practical algorithm to perform clustering using the single link metric on a
n/log
n processor PRAM, butterfly, or tree. |
| Author | Olson, Clark F. |
| Author_xml | – sequence: 1 givenname: Clark F. surname: Olson fullname: Olson, Clark F. email: clarko@cs.cornell.edu organization: Computer Science Department, Cornell University, Ithaca, NY 14853, USA |
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| Cites_doi | 10.1080/01621459.1963.10500845 10.1016/0167-8191(89)90037-9 10.1093/comjnl/9.4.373 10.1002/j.1538-7305.1957.tb01515.x 10.1093/comjnl/16.1.30 10.1016/0167-8191(89)90036-7 10.1093/comjnl/20.4.364 10.1145/50087.50096 10.1093/comjnl/26.4.354 10.1016/0743-7315(90)90105-X 10.1108/eb026836 10.1109/71.89059 10.1007/BF01890115 10.1007/BF01386390 |
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| Keywords | Butterfly network Parallel algorithm Hierarchical clustering Pattern analysis PRAM algorithm Aggregation Sequential Optimal algorithm Multidimensional space Metric Optimization |
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| References | Driscoll, Gabow, Shrairman, Tarjan (BIB6) 1959; 31 Lance, Williams (BIB9) 1967; 9 Sibson (BIB19) 1973; 16 Day, Edelsbrunner (BIB3) 1984; 1 Dijkstra (BIB5) 1959; 1 Olson (BIB13) 1985 Prim (BIB14) 1957; 36 Rivera, Ismail, Zapata (BIB17) 1990; 8 Murtagh (BIB12) 1985 Rasmussen, Willett (BIB16) April 1991; 45 Benes̆ (BIB1) 1965 Kruskal (BIB8) 1956; 7 Murtagh (BIB11) 1983; 26 Bruynooghe (BIB2) 1989 Li, Fang (BIB10) 1989; 11 Zapata (BIB21) 1989; 11 Ranka, Sahni (BIB15) April 1991; 2 Rohlf (BIB18) 1973; 16 Defays (BIB4) 1977; 20 Ward (BIB7) 1963; 58 Yao (BIB20) 1982; 4 Driscoll (10.1016/0167-8191(95)00017-I_BIB6) 1959; 31 Benes̆ (10.1016/0167-8191(95)00017-I_BIB1) 1965 Bruynooghe (10.1016/0167-8191(95)00017-I_BIB2) 1989 Murtagh (10.1016/0167-8191(95)00017-I_BIB11) 1983; 26 Zapata (10.1016/0167-8191(95)00017-I_BIB21) 1989; 11 Kruskal (10.1016/0167-8191(95)00017-I_BIB8) 1956; 7 Lance (10.1016/0167-8191(95)00017-I_BIB9) 1967; 9 Li (10.1016/0167-8191(95)00017-I_BIB10) 1989; 11 Rivera (10.1016/0167-8191(95)00017-I_BIB17) 1990; 8 Olson (10.1016/0167-8191(95)00017-I_BIB13) 1985 Rasmussen (10.1016/0167-8191(95)00017-I_BIB16) 1991; 45 Yao (10.1016/0167-8191(95)00017-I_BIB20) 1982; 4 Dijkstra (10.1016/0167-8191(95)00017-I_BIB5) 1959; 1 Day (10.1016/0167-8191(95)00017-I_BIB3) 1984; 1 Defays (10.1016/0167-8191(95)00017-I_BIB4) 1977; 20 Ranka (10.1016/0167-8191(95)00017-I_BIB15) 1991; 2 Prim (10.1016/0167-8191(95)00017-I_BIB14) 1957; 36 Rohlf (10.1016/0167-8191(95)00017-I_BIB18) 1973; 16 Ward (10.1016/0167-8191(95)00017-I_BIB7) 1963; 58 Murtagh (10.1016/0167-8191(95)00017-I_BIB12) 1985 Sibson (10.1016/0167-8191(95)00017-I_BIB19) 1973; 16 |
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O(
n
2) algorithms are known for this... |
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| SubjectTerms | Algorithmics. Computability. Computer arithmetics Applied sciences Butterfly network Computer science; control theory; systems Exact sciences and technology Hierarchical clustering Parallel algorithm Pattern analysis PRAM algorithm Theoretical computing |
| Title | Parallel algorithms for hierarchical clustering |
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