## A Clustering Algorithm based on Graph Connectivity (1999)

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Venue: | Information Processing Letters |

Citations: | 101 - 3 self |

### BibTeX

@ARTICLE{Hartuv99aclustering,

author = {Erez Hartuv and Ron Shamir},

title = {A Clustering Algorithm based on Graph Connectivity},

journal = {Information Processing Letters},

year = {1999},

volume = {76},

pages = {175--181}

}

### Years of Citing Articles

### OpenURL

### Abstract

We have developed a novel algorithm for cluster analysis that is based on graph theoretic techniques.

### Citations

1500 |
A k-means clustering algorithm
- Hartigan, Wong
(Show Context)
Citation Context ...t. The cluster separation and homogeneity goals described above can be interpreted in various ways for optimization. Numerous approaches exist depending on the specific objective function chosen (cf. =-=[10, 1, 20, 6, 21, 18, 5]-=-). We briefly review the approaches that are most related to our work. (Definitions and terminology will be given in Section 2.) Matula [12, 13, 14, 15] was the first to observe the usefulness of high... |

710 |
Cluster Analysis for Applications
- Anderberg
- 1973
(Show Context)
Citation Context ...t. The cluster separation and homogeneity goals described above can be interpreted in various ways for optimization. Numerous approaches exist depending on the specific objective function chosen (cf. =-=[10, 1, 20, 6, 21, 18, 5]-=-). We briefly review the approaches that are most related to our work. (Definitions and terminology will be given in Section 2.) Matula [12, 13, 14, 15] was the first to observe the usefulness of high... |

337 |
Graph algorithms
- Even
- 1979
(Show Context)
Citation Context ...proaches with ours. 2 The HCS Algorithm In this section we describe the Highly Connected Subgraphs (HCS) algorithm for cluster analysis. We first review some standard graph-theoretic definitions (cf. =-=[3, 2]-=-). The edge-connectivity (or simply the connectivity) k(G) of a graph G is the minimum number k of edges whose removal results in a disconnected graph. If k(G) = l then G is called an l-connected 2 gr... |

268 | An optimal graph theoretic approach to data clustering: Theory and its application to image segmentation
- Wu, Leahy
- 1993
(Show Context)
Citation Context ...t with higher connectivity. This may cause the splitting of some real clusters that contain several highly cohesive parts. Minimum cuts in capacitated similarity graphs were also used by Wu and Leahy =-=[22]-=-. The number of clusters K is assumed to be known for their algorithm. The K \Gamma 1 smallest cuts in G are computed (e.g., using the Gomory-Hu algorithm [4]) and their removal produces a K-partition... |

234 |
Multi-terminal Network Flows
- Gomory, Hu
- 1961
(Show Context)
Citation Context ...ty graphs were also used by Wu and Leahy [22]. The number of clusters K is assumed to be known for their algorithm. The K \Gamma 1 smallest cuts in G are computed (e.g., using the Gomory-Hu algorithm =-=[4]-=-) and their removal produces a K-partition of the data. The resulting K-partition of G has two desirable properties: (1) it minimizes the largest inter-subgraph mincut among all possible K-partitions ... |

174 |
Distance in graphs
- Buckley, Harary
- 1990
(Show Context)
Citation Context ...proaches with ours. 2 The HCS Algorithm In this section we describe the Highly Connected Subgraphs (HCS) algorithm for cluster analysis. We first review some standard graph-theoretic definitions (cf. =-=[3, 2]-=-). The edge-connectivity (or simply the connectivity) k(G) of a graph G is the minimum number k of edges whose removal results in a disconnected graph. If k(G) = l then G is called an l-connected 2 gr... |

129 |
Mathematical Classification and Clustering
- Mirkin
- 1996
(Show Context)
Citation Context ...t. The cluster separation and homogeneity goals described above can be interpreted in various ways for optimization. Numerous approaches exist depending on the specific objective function chosen (cf. =-=[10, 1, 20, 6, 21, 18, 5]-=-). We briefly review the approaches that are most related to our work. (Definitions and terminology will be given in Section 2.) Matula [12, 13, 14, 15] was the first to observe the usefulness of high... |

79 |
Mathematical Taxonomy
- Jardine, Sibson
- 1971
(Show Context)
Citation Context |

74 |
Cluster analysis and mathematical programming
- Hansen, Jaumard
- 1997
(Show Context)
Citation Context ...luster analysis is a fundamental problem in experimental science, where one wishes to classify observations into groups or categories. It is an old problem with a history going back to Aristotle (cf. =-=[5]-=-). It has applications in biology, medicine, economics, psychology, astrophysics and numerous other fields. The application that motivated this study was gene expression in molecular biology. Contribu... |

71 | Minimum cuts in near-linear time
- Karger
- 2000
(Show Context)
Citation Context ...g a minimum cut in an unweighted graph require O(nm) steps, and are due to Matula [16] and Nagamochi and Ibaraki [19]. The fastest randomized algorithm is due to Karger and requires O(m log 3 n) time =-=[11]-=-. 3 Properties of HCS Clustering. In this section we prove some properties of the clusters produced by the HCS algorithm. These demonstrate the homogeneity and the separation of the solution. 3 G 2 G ... |

45 | An algorithm for clustering cDNAs for gene expression analysis
- Hartuv, Schmitt, et al.
- 1999
(Show Context)
Citation Context ... University of Washington, Seattle. 0 Portions of this paper appeared in a preliminary version in the Proceedings of the Third International Conference on Computational Molecular Biology (RECOMB '99) =-=[8]-=-. 1 in which vertices correspond to elements and edges connect elements with similarity values above some threshold. In that graph, clusters are highly connected subgraphs, defined as subgraphs whose ... |

27 |
k-components, clusters and slicings in graphs
- Matula
- 1972
(Show Context)
Citation Context ...pecific objective function chosen (cf. [10, 1, 20, 6, 21, 18, 5]). We briefly review the approaches that are most related to our work. (Definitions and terminology will be given in Section 2.) Matula =-=[12, 13, 14, 15]-=- was the first to observe the usefulness of high connectivity in similarity graphs to cluster analysis. Matula's approach is based on the cohesiveness function, defined for every vertex and edge of a ... |

26 |
Computing Edge Connectivity In Multigraphs And Capacitated Graphs
- Nagamochi, Ibaraki
- 1992
(Show Context)
Citation Context ...at in many applications N !! n. The current fastest deterministic algorithms for finding a minimum cut in an unweighted graph require O(nm) steps, and are due to Matula [16] and Nagamochi and Ibaraki =-=[19]-=-. The fastest randomized algorithm is due to Karger and requires O(m log 3 n) time [11]. 3 Properties of HCS Clustering. In this section we prove some properties of the clusters produced by the HCS al... |

22 | An algorithm for clustering cDNA fingerprints, Genomics 66
- Hartuv, Schmitt, et al.
- 2000
(Show Context)
Citation Context ...e presence of relatively high noise levels, and to outperform a previous algorithm for that problem [17]. It has also obtained promising results in a blind test with experimental gene expression data =-=[8, 9]-=-. Further details can be found in [7]. Previous graph theoretic approaches: Due to its wide applicability, cluster analysis has been addressed by numerous authors in various disciplines in the past. T... |

20 |
Graph theoretic techniques for cluster analysis algorithms,” in Class$cation and
- Matula
- 1977
(Show Context)
Citation Context ...pecific objective function chosen (cf. [10, 1, 20, 6, 21, 18, 5]). We briefly review the approaches that are most related to our work. (Definitions and terminology will be given in Section 2.) Matula =-=[12, 13, 14, 15]-=- was the first to observe the usefulness of high connectivity in similarity graphs to cluster analysis. Matula's approach is based on the cohesiveness function, defined for every vertex and edge of a ... |

16 |
Determining edge connectivity in O(nm
- Matula
- 1987
(Show Context)
Citation Context ...n vertices and m edges. Note that in many applications N !! n. The current fastest deterministic algorithms for finding a minimum cut in an unweighted graph require O(nm) steps, and are due to Matula =-=[16]-=- and Nagamochi and Ibaraki [19]. The fastest randomized algorithm is due to Karger and requires O(m log 3 n) time [11]. 3 Properties of HCS Clustering. In this section we prove some properties of the ... |

13 |
Clustering and classification: Background and current directions
- Sokal
- 1977
(Show Context)
Citation Context |

8 |
Cluster analysis via graph theoretic techniques
- Matula
- 1970
(Show Context)
Citation Context ...pecific objective function chosen (cf. [10, 1, 20, 6, 21, 18, 5]). We briefly review the approaches that are most related to our work. (Definitions and terminology will be given in Section 2.) Matula =-=[12, 13, 14, 15]-=- was the first to observe the usefulness of high connectivity in similarity graphs to cluster analysis. Matula's approach is based on the cohesiveness function, defined for every vertex and edge of a ... |

6 |
Clone clustering by hybridization
- Milosavljevic, Strezoska, et al.
- 1995
(Show Context)
Citation Context ...d tested intensively on gene expression simulated data and was shown to give good results even in the presence of relatively high noise levels, and to outperform a previous algorithm for that problem =-=[17]-=-. It has also obtained promising results in a blind test with experimental gene expression data [8, 9]. Further details can be found in [7]. Previous graph theoretic approaches: Due to its wide applic... |

3 |
Cluster Analysis by Highly Connected Subgraphs with Applications to cDNA Clustering
- Hartuv
- 1998
(Show Context)
Citation Context ...ls, and to outperform a previous algorithm for that problem [17]. It has also obtained promising results in a blind test with experimental gene expression data [8, 9]. Further details can be found in =-=[7]-=-. Previous graph theoretic approaches: Due to its wide applicability, cluster analysis has been addressed by numerous authors in various disciplines in the past. The cluster separation and homogeneity... |

3 |
The cohesive strength of graphs
- Matula
- 1969
(Show Context)
Citation Context |