Dendrogram

Dendrogram[{e₁,e₂,…}]

constructs a dendrogram from the hierarchical clustering of the elements e₁, e₂, ….

Dendrogram[{e₁v₁,e₂v₂,…}]

represents e_i with v_i in the constructed dendrogram.

Dendrogram[{e₁,e₂,…}{v₁,v₂,…}]

represents e_i with v_i in the constructed dendrogram.

Dendrogram[label₁e₁,label₂e₂,…]

represents e_i using labels label_i in the constructed dendrogram.

Dendrogram[data,orientation]

constructs an oriented dendrogram according to orientation.

Dendrogram[tree]

constructs the dendrogram corresponding to weighted tree tree.

Details and Options

The data elements e_i can be numbers; numeric lists, matrices, or tensors; lists of Boolean elements; strings or images; geo positions or geographical entities; and colors, as well as combinations of these. If the e_i are lists, matrices, or tensors, each must have the same dimensions.
By default, Dendrogram is oriented from top to bottom. Possible orientations are: Top, Left, Right, and Bottom.
Trees on which to compute Dendrogram can only be weighted on vertices.
Dendrogram has the same options as Graphics, with the following additions and changes: [List of all options]

ClusterDissimilarityFunction	Automatic	the clustering linkage algorithm to use
DistanceFunction	Automatic	the distance or dissimilarity to use
FeatureExtractor	Automatic	how to extract features from data

Dendrogram evaluated on a weighted tree only displays the graph as a dendrogram, therefore only the options of Graphics will change the final result.
By default, Dendrogram will preprocess the data automatically unless either a DistanceFunction or a FeatureExtractor is specified.
ClusterDissimilarityFunction defines the intercluster dissimilarity, given the dissimilarities between member elements.
Possible settings for ClusterDissimilarityFunction include:

	"Average"	average intercluster dissimilarity
	"Centroid"	distance from cluster centroids
	"Complete"	largest intercluster dissimilarity
	"Median"	distance from cluster medians
	"Single"	smallest intercluster dissimilarity
	"Ward"	Ward's minimum variance dissimilarity
	"WeightedAverage"	weighted average intercluster dissimilarity
		a pure function

The function f defines a distance from any two clusters.
The function f needs to be a real-valued function of the DistanceMatrix.

List of all options

AlignmentPoint	Center	the default point in the graphic to align with
AspectRatio	Automatic	ratio of height to width
Axes	False	whether to draw axes
AxesLabel	None	axes labels
AxesOrigin	Automatic	where axes should cross
AxesStyle	{}	style specifications for the axes
Background	None	background color for the plot
BaselinePosition	Automatic	how to align with a surrounding text baseline
BaseStyle	{}	base style specifications for the graphic
ClusterDissimilarityFunction	Automatic	the clustering linkage algorithm to use
ContentSelectable	Automatic	whether to allow contents to be selected
CoordinatesToolOptions	Automatic	detailed behavior of the coordinates tool
DistanceFunction	Automatic	the distance or dissimilarity to use
Epilog	{}	primitives rendered after the main plot
FeatureExtractor	Automatic	how to extract features from data
FormatType	TraditionalForm	the default format type for text
Frame	False	whether to put a frame around the plot
FrameLabel	None	frame labels
FrameStyle	{}	style specifications for the frame
FrameTicks	Automatic	frame ticks
FrameTicksStyle	{}	style specifications for frame ticks
GridLines	None	grid lines to draw
GridLinesStyle	{}	style specifications for grid lines
ImageMargins	0.	the margins to leave around the graphic
ImagePadding	All	what extra padding to allow for labels etc.
ImageSize	Automatic	the absolute size at which to render the graphic
LabelStyle	{}	style specifications for labels
Method	Automatic	details of graphics methods to use
PlotLabel	None	an overall label for the plot
PlotRange	All	range of values to include
PlotRangeClipping	False	whether to clip at the plot range
PlotRangePadding	Automatic	how much to pad the range of values
PlotRegion	Automatic	the final display region to be filled
PreserveImageOptions	Automatic	whether to preserve image options when displaying new versions of the same graphic
Prolog	{}	primitives rendered before the main plot
RotateLabel	True	whether to rotate y labels on the frame
Ticks	Automatic	axes ticks
TicksStyle	{}	style specifications for axes ticks

Examples

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Basic Examples (4)

Obtain a dendrogram from a list of numbers:

Obtain a dendrogram from a weighted tree:

Obtain a dendrogram from a list of cities and place the labels on the left:

Obtain a cluster hierarchy from a list of Boolean entries:

Scope (7)

Obtain a dendrogram from a list of colors and display it to the left:

Compare the result with Dendrogram applied to the result of ClusteringTree:

Obtain a dendrogram from a heterogeneous dataset:

Compare it with the dendrogram of the colors:

Generate a sequence of random reals:

Obtain the dendrogram with the labeling given by the rounded reals:

Compute the dendrogram from an Association:

Compare it with the dendrogram of its Values:

Compare it with the dendrogram of its Keys:

Generate a dendrogram from a list of numbers:

Show the axis to compare distances between subclusters:

Generate a dendrogram from a list of vectors:

Display the result using vertical labeling:

Display the result using the ArrayPlot of the vectors as labeling:

Obtain a dendrogram from a list of images:

Options (6)

AspectRatio (3)

By default, the ratio of the height to width for the plot is determined automatically:

Make the height the same as the width with AspectRatio1:

Specify the height to width ratio:

ClusterDissimilarityFunction (1)

Generate a list of random colors:

Obtain a cluster hierarchy from the list using the "Centroid" linkage:

Obtain a cluster hierarchy from the list using the "Single" linkage:

Obtain a cluster hierarchy from the list using a different "ClusterDissimilarityFunction":

DistanceFunction (1)

Generate a list of random vectors:

Obtain a dendrogram using the automatically chosen DistanceFunction and plot the axis:

Obtain a dendrogram using the EuclideanDistance and compare the values on the axis:

Obtain a dendrogram using a different DistanceFunction:

FeatureExtractor (1)

Obtain a dendrogram from a list of pictures:

Use a different FeatureExtractor to extract features:

Use the Identity FeatureExtractor to leave the data unchanged:

Applications (1)

Generate a list of random colors and compute its dendrogram with the distances on the y axis:

Compute the ClusteringTree for the same data by merging clusters that are closer than 0.65:

Compute the Dendrogram of the above graph:

Construct a Manipulate to visualize how clusters merge when the distance threshold increases: