ClusterHierarchical Class 
Namespace: Imsl.Stat
The ClusterHierarchical type exposes the following members.
Name  Description  

Compute 
Performs a hierarchical cluster analysis.
 
Equals  Determines whether the specified object is equal to the current object. (Inherited from Object.)  
Finalize  Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.)  
GetClusterMembership 
Returns the cluster membership of each observation.
 
GetHashCode  Serves as a hash function for a particular type. (Inherited from Object.)  
GetObsPerCluster 
Returns the number of observations in each cluster.
 
GetType  Gets the Type of the current instance. (Inherited from Object.)  
MemberwiseClone  Creates a shallow copy of the current Object. (Inherited from Object.)  
ToString  Returns a string that represents the current object. (Inherited from Object.) 
Name  Description  

ClusterLeftSons 
The left sons of each merged cluster.
 
ClusterLevel 
The level at which the clusters are joined.
 
ClusterRightSons 
The right sons of each merged cluster.
 
Method 
The clustering method.
 
NumberOfProcessors 
Perform the parallel calculations with the maximum possible number of
processors set to NumberOfProcessors.
 
TransformType 
The type of transformation.

Class ClusterHierarchical conducts a hierarchical cluster analysis based upon a distance matrix, or, by appropriate use of the transformation specified in the TransformType property, based upon a similarity matrix. Only the upper triangular part of the input matrix is used.
Hierarchical clustering in ClusterHierarchical proceeds as follows:
Initially, each data point is considered to be a cluster, numbered 1 to n, where n is the number of rows in the input matrix, dist.
The five methods differ primarily in how the distance matrix is updated after two clusters have been joined. The Method property specifies how the distance of the cluster just merged with each of the remaining clusters will be updated. Class ClusterHierarchical allows five methods for computing the distances. To understand these measures, suppose in the following discussion that clusters A and B have just been joined to form cluster Z, and interest is in computing the distance of Z with another cluster called C.
Method  Description 

Single  Single linkage (minimum distance). The distance from Z to C is the minimum of the distances ( A to C, B to C). 
Complete  Complete linkage (maximum distance). The distance from Z to C is the maximum of the distances ( A to C, B to C). 
AvgWithinClusters  Averagedistancewithinclusters method. The distance from Z to C is the average distance of all objects that would be within the cluster formed by merging clusters Z and C. This average may be computed according to formulas given by Anderberg (1973, page 139). 
AvgBetweenClusters  Averagedistancebetweenclusters method. The distance from Z to C is the average distance of objects within cluster Z to objects within cluster C. This average may be computed according to methods given by Anderberg (1973, page 140). 
Wards  Ward's method: Clusters are formed so as to minimize the increase in the withincluster sums of squares. The distance between two clusters is the increase in these sums of squares if the two clusters were merged. A method for computing this distance from a squared Euclidean distance matrix is given by Anderberg (1973, pages 142145). 
In general, single linkage will yield long thin clusters while complete linkage will yield clusters that are more spherical. Average linkage and Ward's linkage tend to yield clusters that are similar to those obtained with complete linkage.
Class ClusterHierarchical produces a unique representation of the binary cluster tree via the following three conventions; the fact that the tree is unique should aid in interpreting the clusters. First, when two clusters are joined and each cluster contains two or more data points, the cluster initially formed with the smallest level becomes the left son. Second, when a cluster containing more than one data point is joined with a cluster containing a single data point, the cluster with the single data point becomes the right son. Third, when two clusters containing only one object are joined, the cluster with the smallest cluster number becomes the right son.
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