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Single-linkage clustering. In statistics, single-linkage clustering is one of several methods of hierarchical clustering. It is based on grouping clusters in bottom-up fashion (agglomerative clustering), at each step combining two clusters that contain the closest pair of elements not yet belonging to the same cluster as each other.
ALGLIB implements several hierarchical clustering algorithms (single-link, complete-link, Ward) in C++ and C# with O(n²) memory and O(n³) run time. ELKI includes multiple hierarchical clustering algorithms, various linkage strategies and also includes the efficient SLINK, [2] CLINK [3] and Anderberg algorithms, flexible cluster extraction ...
Popular choices are known as single-linkage clustering (the minimum of object distances), complete linkage clustering (the maximum of object distances), and UPGMA or WPGMA ("Unweighted or Weighted Pair Group Method with Arithmetic Mean", also known as average linkage clustering). Furthermore, hierarchical clustering can be agglomerative ...
Complete-linkage clustering is one of several methods of agglomerative hierarchical clustering. At 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.
Single linkage (minimum method, nearest neighbor) Average linkage ; Complete linkage (maximum method, furthest neighbor) Different studies have already shown empirically that the Single linkage clustering algorithm produces poor results when employed to gene expression microarray data and thus should be avoided. K-means clustering
Cluster analysis: clustering points in the plane, single-linkage clustering (a method of hierarchical clustering), graph-theoretic clustering, and clustering gene expression data. Constructing trees for broadcasting in computer networks. Image registration and segmentation – see minimum spanning tree-based segmentation.
Alternative linkage schemes include single linkage clustering, complete linkage clustering, and WPGMA average linkage clustering. Implementing a different linkage is simply a matter of using a different formula to calculate inter-cluster distances during the distance matrix update steps of the above algorithm.
Because the topology of a finite point cloud is trivial, clustering methods (such as single linkage) are used to produce the analogue of connected sets in the preimage () when MAPPER is applied to actual data. Mathematically speaking, MAPPER is a variation of the Reeb graph.
The nearest-neighbor chain algorithm constructs a clustering in time proportional to the square of the number of points to be clustered. This is also proportional to the size of its input, when the input is provided in the form of an explicit distance matrix. The algorithm uses an amount of memory proportional to the number of points, when it ...
Several standard clustering algorithms such as single linkage, complete linkage, and group average method have a recursive formula of the above type. A table of parameters for standard methods is given by several authors. [2] [3] [4] Ward's minimum variance method can be implemented by the Lance–Williams formula.