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The standard algorithm for hierarchical agglomerative clustering (HAC) has a time complexity of () and requires () memory, which makes it too slow for even medium data sets. . However, for some special cases, optimal efficient agglomerative methods (of complexity ()) are known: SLINK [2] for single-linkage and CLINK [3] for complete-linkage clusteri
The average silhouette of the data is another useful criterion for assessing the natural number of clusters. The silhouette of a data instance is a measure of how closely it is matched to data within its cluster and how loosely it is matched to data of the neighboring cluster, i.e., the cluster whose average distance from the datum is lowest. [8]
Cluster analysis is for example used to identify groups of schools or students with similar properties. Typologies From poll data, projects such as those undertaken by the Pew Research Center use cluster analysis to discern typologies of opinions, habits, and demographics that may be useful in politics and marketing.
Ward's minimum variance method is a special case of the objective function approach originally presented by Joe H. Ward, Jr. [1] Ward suggested a general agglomerative hierarchical clustering procedure, where the criterion for choosing the pair of clusters to merge at each step is based on the optimal value of an objective function. This ...
Example of the typical "elbow" pattern used for choosing the number of clusters even emerging on uniform data. Even on uniform random data (with no meaningful clusters) the curve follows approximately the ratio 1/k where k is the number of clusters parameter, causing users to see an "elbow" to mistakenly choose some "optimal" number of clusters ...
Many problems in data analysis concern clustering, grouping data items into clusters of closely related items. Hierarchical clustering is a version of cluster analysis in which the clusters form a hierarchy or tree-like structure rather than a strict partition of the data items. In some cases, this type of clustering may be performed as a way ...
The method is also known as nearest neighbour clustering. The result of the clustering can be visualized as a dendrogram, which shows the sequence in which clusters were merged and the distance at which each merge took place. [3] Mathematically, the linkage function – the distance D(X,Y) between clusters X and Y – is described by the expression
In a hierarchical model, observations are grouped into clusters, and the distribution of an observation is determined not only by common structure among all clusters but also by the specific structure of the cluster where this observation belongs. So a random effect component, different for different clusters, is introduced into the model.