Single-Linkage Clustering Algorithm
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A Single-Linkage Clustering Algorithm is a bottom-up hierarchical clustering algorithm that ...
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- Counter-Example(s):
- See: Dendrogram, Non-Spherical Dataset.
References
2015
- (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/Single-linkage_clustering Retrieved:2015-1-16.
- Single-linkage clustering is one of several methods of agglomerative hierarchical clustering. In the beginning of the process, each element is in a cluster of its own. The clusters are then sequentially combined into larger clusters, until all elements end up being in the same cluster. At each step, the two clusters separated by the shortest distance are combined. The definition of 'shortest distance' is what differentiates between the different agglomerative clustering methods. In single-linkage clustering, the link between two clusters is made by a single element pair, namely those two elements (one in each cluster) that are closest to each other. The shortest of these links that remains at any step causes the fusion of the two clusters whose elements are involved. The method is also known as nearest neighbour clustering. The result of the clustering can be visualized as a dendrogram, which shows the sequence of cluster fusion and the distance at which each fusion took place. [1]
Mathematically, the linkage function – the distance D(X,Y) between clusters X and Y – is described by the expression :[math]\displaystyle{ D(X,Y)=\min_{x\in X, y\in Y} d(x,y), }[/math]
where X and Y are any two sets of elements considered as clusters, and d(x,y) denotes the distance between the two elements x and y.
A drawback of this method is the so-called chaining phenomenon, which refers to the gradual growth of a cluster as one element at a time gets added to it. This may lead to impractically heterogeneous clusters and difficulties in defining classes that could usefully subdivide the data.
- Single-linkage clustering is one of several methods of agglomerative hierarchical clustering. In the beginning of the process, each element is in a cluster of its own. The clusters are then sequentially combined into larger clusters, until all elements end up being in the same cluster. At each step, the two clusters separated by the shortest distance are combined. The definition of 'shortest distance' is what differentiates between the different agglomerative clustering methods. In single-linkage clustering, the link between two clusters is made by a single element pair, namely those two elements (one in each cluster) that are closest to each other. The shortest of these links that remains at any step causes the fusion of the two clusters whose elements are involved. The method is also known as nearest neighbour clustering. The result of the clustering can be visualized as a dendrogram, which shows the sequence of cluster fusion and the distance at which each fusion took place. [1]
- ↑ Legendre, P. & Legendre, L. 1998. Numerical Ecology. Second English Edition. 853 pages.
1989
- (Seifoddini, 1989) ⇒ Hamid K. Seifoddini. (1989). “Single Linkage Versus Average Linkage Clustering in Machine Cells Formation Applications." Computers & Industrial Engineering, 16(3).
1969
- (Gower & Ross, 1969) ⇒ John C. Gower, and G. J. S. Ross. (1969) "Minimum Spanning Trees and Single Linkage Cluster Analysis.” In: Applied Statistics.