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hierarchicalclustering

hierarchical clustering

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HIERARCHICAL CLUSTERING - In data mining and statistics, hierarchical clustering (also called hierarchical cluster analysis or HCA) is a method of cluster analysis which seeks...

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Hierarchical clustering description
In data mining and statistics, hierarchical clustering (also called hierarchical cluster analysis or HCA) is a method of cluster analysis which seeks to build a hierarchy of clusters. Strategies for hierarchical clustering generally fall into two types: * Agglomerative: This is a "bottom up" approach: each observation starts in its own cluster, and pairs of clusters are merged as one moves up the hierarchy. * Divisive: This is a "top down" approach: all observations start in one cluster, and splits are performed recursively as one moves down the hierarchy.In general, the merges and splits are determined in a greedy manner. The results of hierarchical clustering are usually presented in a dendrogram. * The standard algorithm for hierarchical agglomerative clustering (HAC) has a time complexity of * * * * * * O * * * ( * * n * * 3 * * * ) * * * {\displaystyle {\mathcal {O}}(n^{3})} * and requires * * * * * * O * * * ( * * n * * 2 * * * ) * * * {\displaystyle {\mathcal {O}}(n^{2})} * memory, which makes it too slow for even medium data sets. However, for some special cases, optimal efficient agglomerative methods (of complexity * * * * * * O * * * ( * * n * * 2 * * * ) * * * {\displaystyle {\mathcal {O}}(n^{2})} * ) are known: SLINK for single-linkage and CLINK for complete-linkage clustering. With a heap the runtime of the general case can be reduced to * * * * * * O * * * ( * * n * * 2 * * * log * ⁡ * n * ) * * * {\displaystyle {\mathcal {O}}(n^{2}\log n)} * at the cost of further increasing the memory requirements. In many programming languages, the memory overheads of this approach are too large to make it practically usable. * Except for the special case of single-linkage, none of the algorithms (except exhaustive search in * * * * * * O * * * ( * * 2 * * n * * * ) * * * {\displaystyle {\mathcal {O}}(2^{n})} * ) can be guaranteed to find the optimum solution. * Divisive clustering with an exhaustive search is * * * * * * O * * * ( * * 2 * * n * * * ) * * * {\displaystyle {\mathcal {O}}(2^{n})} * , but it is common to use faster heuristics to choose splits, such as k-means.

Hierarchical clustering description

In data mining and statistics, hierarchical clustering (also called hierarchical cluster analysis or HCA) is a method of cluster analysis which seeks to build a hierarchy of clusters. Strategies for hierarchical clustering generally fall into two types:
* Agglomerative: This is a "bottom up" approach: each observation starts in its own cluster, and pairs of clusters are merged as one moves up the hierarchy.
* Divisive: This is a "top down" approach: all observations start in one cluster, and splits are performed recursively as one moves down the hierarchy.In general, the merges and splits are determined in a greedy manner. The results of hierarchical clustering are usually presented in a dendrogram.
* The standard algorithm for hierarchical agglomerative clustering (HAC) has a time complexity of
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* at the cost of further increasing the memory requirements. In many programming languages, the memory overheads of this approach are too large to make it practically usable.
* Except for the special case of single-linkage, none of the algorithms (except exhaustive search in
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* , but it is common to use faster heuristics to choose splits, such as k-means.

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