## On Clustering Using Random Walks (2001)

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Venue: | Foundations of Software Technology and Theoretical Computer Science 2245 |

Citations: | 26 - 0 self |

### BibTeX

@INPROCEEDINGS{Harel01onclustering,

author = {David Harel and Yehuda Koren},

title = {On Clustering Using Random Walks},

booktitle = {Foundations of Software Technology and Theoretical Computer Science 2245},

year = {2001},

pages = {18--41},

publisher = {Springer-Verlag}

}

### Years of Citing Articles

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### Abstract

We propose a novel approach to clustering, based on deterministic analysis of random walks on the weighted graph associated with the clustering problem. The method is centered around what we shall call \emph{separating operators}, which are applied repeatedly to sharpen the distinction between the weights of inter-cluster edges (the so-called separators), and those of intra-cluster edges. These operators can be used as a stand-alone for some problems, but become particularly powerful when embedded in a classical multi-scale framework and/or enhanced by other known techniques, such as agglomerative clustering. The resulting algorithms are simple, fast and general, and appear to have many useful applications.

### Citations

2161 |
Algorithms for Clustering Data
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- 1988
(Show Context)
Citation Context ...g methods have been used in computer vision [11,2], VLSI design [4], data mining [3], web page clustering , and gene expression analysis. Prior literature on the clustering problem is huge, see e.g., =-=[7]-=-. However, to a large extent the problem remains elusive, and there is still a dire need for a clustering method that is natural and robust, yet very efficient in dealing with large data sets. In this... |

795 | A fast and high quality multilevel scheme for partitioning irregular graphs
- Karypis, Kumar
- 1998
(Show Context)
Citation Context ...-scale representation of the graph consist of various coarse abstractions that allow us to view the graph on different scales, that differ in the level of abstraction they represent. For example, see =-=[10,11].s-=-On Clustering Using Random Walks 35 Fig. 11. Data sets taken from [9] (see [6] for clearer color versions of this figure and of Figs. 12–15). 6.1 The General Scheme In our context, we find that the ... |

338 | K.: ROCK: A Robust Clustering Algorithm for Categorical Attributes
- Guha, Rastogi, et al.
- 2000
(Show Context)
Citation Context ...lls for discovering natural groups in data sets, and identifying abstract structures that might reside there. Clustering methods have been used in computer vision [11,2], VLSI design [4], data mining =-=[3]-=-, web page clustering , and gene expression analysis. Prior literature on the clustering problem is huge, see e.g., [7]. However, to a large extent the problem remains elusive, and there is still a di... |

212 | CHAMELEON: A Hierarchical Clustering Algorithm Using Dynamic Modeling
- Karypis, Han, et al.
- 1999
(Show Context)
Citation Context ...oint-Sets We now illustrate the ability of our method to cluster “correctly” 2D sets of points, in a number of typical cases, some of which have been shown to be problematic for agglomerative meth=-=ods [9]-=-. (More extensive examples are given in Subsection 5.1.) For a short version of this paper that deals with clustering spatial data, see [5]. We have used 10-mutual neighborhood graphs for modeling the... |

121 | R.: Fast multiscale image segmentation
- Sharon, Brandt, et al.
- 2000
(Show Context)
Citation Context ...ble to a wide variety of areas. It calls for discovering natural groups in data sets, and identifying abstract structures that might reside there. Clustering methods have been used in computer vision =-=[11,2]-=-, VLSI design [4], data mining [3], web page clustering , and gene expression analysis. Prior literature on the clustering problem is huge, see e.g., [7]. However, to a large extent the problem remain... |

43 | A new approach to effective circuit clustering
- Hagen, Kahng
- 1992
(Show Context)
Citation Context ...y of areas. It calls for discovering natural groups in data sets, and identifying abstract structures that might reside there. Clustering methods have been used in computer vision [11,2], VLSI design =-=[4]-=-, data mining [3], web page clustering , and gene expression analysis. Prior literature on the clustering problem is huge, see e.g., [7]. However, to a large extent the problem remains elusive, and th... |

29 | Clustering Spatial Data Using Random Walks
- Harel, Koren
(Show Context)
Citation Context ... have been shown to be problematic for agglomerative methods [9]. (More extensive examples are given in Subsection 5.1.) For a short version of this paper that deals with clustering spatial data, see =-=[5]. We-=- have used 10-mutual neighborhood graphs for modeling the points. The k-mutual neighborhood graph contains all edges 〈a, b〉 for which a is one of the k nearest neighbors of b, and b is one of the ... |

27 |
Stochastic image segmentation by typical cuts
- Gdalyahu, Weinshall, et al.
- 1999
(Show Context)
Citation Context ...ble to a wide variety of areas. It calls for discovering natural groups in data sets, and identifying abstract structures that might reside there. Clustering methods have been used in computer vision =-=[11,2]-=-, VLSI design [4], data mining [3], web page clustering , and gene expression analysis. Prior literature on the clustering problem is huge, see e.g., [7]. However, to a large extent the problem remain... |

6 |
Automatic Clustering via Boundary Extraction for Mining Massive Point
- Estivill-Castro, Lee, et al.
(Show Context)
Citation Context ...usters, whose sizes are below half of the average cluster size, as noise, and simply omits them showing only the larger clusters. Figure 12shows the result of the algorithm applied to a data set from =-=[1]. -=-We show two levels in the hierarchy, representing two possible decompositions. We are particularly happy with the algorithm’s ability to break the cross shaped cluster into 4 highly connected cluste... |

2 |
On the Nature of Structure and its
- Stein, Niggemann
- 1999
(Show Context)
Citation Context ...de the clusters, and have higher weights than those of the separators. We demonstrate this method by several examples. Consider Figure 4, which contains an almost uniformly weighted graph, taken from =-=[12]-=-. We experimented with both separating operators, each one with a four-fold iteration. The NS operator was used with k = 3 and simk (x, y) dfn = f k (x, y) and the CE operator with k = 2, other choice... |

2 |
Data Clustering by Markovian Relaxation and the
- Tishby, Slonim
- 2000
(Show Context)
Citation Context ...s in time and space complexity of Θ(n 3 ) and Θ(n 2 ), respectively, even on bounded degree graphs. A recent algorithm that uses deterministic analysis of random walks for cluster analysis is that o=-=f [13]. T-=-he approach there is quite different from ours. Also, its time and space complexity appear to be Ω(n 3 ) and Θ(n 2 ), respectively, even for bounded degree graphs. A recently published graph-based ... |