Cluster

Purpose

Hierarchical Cluster Analysis with dendrograms.

Synopsis

[results,fig] = cluster(data,labels,options)

[results,fig] = cluster(data,options)

Description

cluster(data) performs unsupervised hierarchical cluster analysis (HCA) on the input data data, using one of several different clustering algorithms, defined in the options structure.

Cluster Analysis methods can be classified into two main categories: agglomerative and partitional. Agglomerative methods begin with each object being it's own cluster, and proceed to combine (agglomerate) the closest clusters into larger ones. Partitional methods start with a single cluster containing all objects, and proceed to divide the objects into additional clusters. The figure below illustrates the different clustering methods available in the cluster function.

 field (including K-Nearest-Neighbor (KNN), furthest neighbor, and Ward's method) or K-means clustering algorithm and plots a dendrogram. The input is (data) class double or DataSet.

Optional input labels can be used to put labels on the dendrogram plots. For data M by N then labels must be a character array with M rows. When labels is not specified and data is class "double", the dendrogram is plotted using sample numbers. When labels is not specified and data is a DataSet object, the dendrogram is plotted using sample labels included in the DataSet object. If the DataSet labels field is empty it will use sample numbers.

The output is a dendrogram showing the sample distances.

Note: Calling cluster with no inputs starts the graphical user interface (GUI) for this analysis method.

Outputs

• results = a structure containing results of the clustering (defined below)
• fig = the handle to any plot created.

The results output containing the following fields:

• dist : the distance threshold at which each cluster forms.
• class : the classes of each sample (columns of class) for each distance (rows of class).
• order : the order of the samples which locates similar samples nearest to each other (this is the order used for the plots).
• linkage : a table of linkages where each row indicates a linkage of one group to another. Each row in the matrix represents one group. The first two columns indicate the sample or group numbers which were linked to form the group. The final column indicates the distance between linked items. Group numbers start at m+1 (where m is the number of samples in the input dat matrix) thus, row j of this matrix is group number m+j. This matrix can be used with the statistics toolbox dendogram function.

The (results.class) matrix can be used with the (results.dist) matrix to determine clusters of samples for any distance using:

  results   = cluster(data);                      %do cluster
  ind       = max(find(results.dist<threshold));  %user-desired threshold
  thisclass = results.class(ind,:);               %grab arbitrary classes

Options

options = a structure array with the following fields:

plots : ['none' | {'final'} ] Governs plotting. When set to 'none', the distance/cluster matrix is returned, 'final' returns a dendrogram plot showing sample distances.

algorithm: [ ] clustering algorithm. May be one of the following:

knn : K-Nearest Neighbor {DEFAULT}

fn : Furthest Neighbor

avgpair : Average Paired Distance

med : Median

cnt : Centroid

ward : Ward's Method

kmeans : K-means

preprocessing : {[ ]} Preprocessing structure or keyword (see PREPROCESS),

pca : [ {'off'} | 'on' ] if 'on' then CLUSTER performs PCA first and clustering on the scores,

ncomp : [ ] number of PCA factors to use {default = [ ], the user is prompted to select the number of factors from the SSQ table},

mahalanobis : [ {'off'} | 'on' ] if 'on' then a Mahalanobis distance on the scores is used,

slack : [0] integer number indicating how many samples can be "overridden" when two class branches merge. If the smaller of the two classes has no more than this number of samples, the branch will be absorbed into the larger class. This feature is only valid when classes are supplied in the input data. A value of 0 (zero) disables this feature.

See Also

analysis, corrmap, dbscan, gcluster, simca