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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
Ward's minimum variance method can be defined and implemented recursively by a Lance–Williams algorithm. The Lance–Williams algorithms are an infinite family of agglomerative hierarchical clustering algorithms which are represented by a recursive formula for updating cluster distances at each step (each time a pair of clusters is merged).
Hierarchical clustering is one method for finding community structures in a network. The technique arranges the network into a hierarchy of groups according to a specified weight function. The data can then be represented in a tree structure known as a dendrogram.
The notion of a cluster, as found by different algorithms, varies significantly in its properties. Understanding these "cluster models" is key to understanding the differences between the various algorithms. Typical cluster models include: Connectivity model s: for example, hierarchical clustering builds models based on distance connectivity.
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]
The Automatic Local Density Clustering Algorithm (ALDC) is an example of the new research focused on developing automatic density-based clustering. ALDC works out local density and distance deviation of every point, thus expanding the difference between the potential cluster center and other points.
In the theory of cluster analysis, the nearest-neighbor chain algorithm is an algorithm that can speed up several methods for agglomerative hierarchical clustering.These are methods that take a collection of points as input, and create a hierarchy of clusters of points by repeatedly merging pairs of smaller clusters to form larger clusters.
WPGMA (Weighted Pair Group Method with Arithmetic Mean) is a simple agglomerative (bottom-up) hierarchical clustering method, generally attributed to Sokal and Michener. [ 1 ] The WPGMA method is similar to its unweighted variant, the UPGMA method.