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Wolfram Language & System Documentation Center
Dendrogram
  • See Also
    • ClusteringTree
    • FindClusters
    • ClusteringComponents
    • TreePlot
  • Related Guides
    • Cluster Analysis
    • Data Visualization
    • Distance and Similarity Measures
    • Life Sciences & Medicine: Data & Computation
    • Statistical Data Analysis
    • Text Analysis
    • Natural Language Processing
    • Unsupervised Machine Learning
    • Scientific Data Analysis
    • Sequence Alignment & Comparison
    • Tree Construction & Representation
    • See Also
      • ClusteringTree
      • FindClusters
      • ClusteringComponents
      • TreePlot
    • Related Guides
      • Cluster Analysis
      • Data Visualization
      • Distance and Similarity Measures
      • Life Sciences & Medicine: Data & Computation
      • Statistical Data Analysis
      • Text Analysis
      • Natural Language Processing
      • Unsupervised Machine Learning
      • Scientific Data Analysis
      • Sequence Alignment & Comparison
      • Tree Construction & Representation

Dendrogram[{e1,e2,…}]

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

Dendrogram[{e1v1,e2v2,…}]

represents ei with vi in the constructed dendrogram.

Dendrogram[{e1,e2,…}{v1,v2,…}]

represents ei with vi in the constructed dendrogram.

Dendrogram[label1e1,label2e2,…]

represents ei using labels labeli 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
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Options  
AspectRatio  
ClusterDissimilarityFunction  
DistanceFunction  
FeatureExtractor  
Applications  
See Also
Related Guides
History
Cite this Page
BUILT-IN SYMBOL
  • See Also
    • ClusteringTree
    • FindClusters
    • ClusteringComponents
    • TreePlot
  • Related Guides
    • Cluster Analysis
    • Data Visualization
    • Distance and Similarity Measures
    • Life Sciences & Medicine: Data & Computation
    • Statistical Data Analysis
    • Text Analysis
    • Natural Language Processing
    • Unsupervised Machine Learning
    • Scientific Data Analysis
    • Sequence Alignment & Comparison
    • Tree Construction & Representation
    • See Also
      • ClusteringTree
      • FindClusters
      • ClusteringComponents
      • TreePlot
    • Related Guides
      • Cluster Analysis
      • Data Visualization
      • Distance and Similarity Measures
      • Life Sciences & Medicine: Data & Computation
      • Statistical Data Analysis
      • Text Analysis
      • Natural Language Processing
      • Unsupervised Machine Learning
      • Scientific Data Analysis
      • Sequence Alignment & Comparison
      • Tree Construction & Representation

Dendrogram

Dendrogram[{e1,e2,…}]

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

Dendrogram[{e1v1,e2v2,…}]

represents ei with vi in the constructed dendrogram.

Dendrogram[{e1,e2,…}{v1,v2,…}]

represents ei with vi in the constructed dendrogram.

Dendrogram[label1e1,label2e2,…]

represents ei using labels labeli 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

  • A Dendrogram is a tree-like diagram showing how data points cluster together hierarchically.
  • Dendrograms are typically used for customer segmentation, species classification, gene analysis and identifying natural groupings in any dataset.
  • The data elements ei 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 ei 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 Automaticthe clustering linkage algorithm to use
    DistanceFunction Automaticthe distance or dissimilarity to use
    FeatureExtractor Automatichow 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

    • AlignmentPointCenterthe default point in the graphic to align with
      AspectRatioAutomaticratio of height to width
      AxesFalsewhether to draw axes
      AxesLabelNoneaxes labels
      AxesOriginAutomaticwhere axes should cross
      AxesStyle{}style specifications for the axes
      BackgroundNonebackground color for the plot
      BaselinePositionAutomatichow to align with a surrounding text baseline
      BaseStyle{}base style specifications for the graphic
      ClusterDissimilarityFunctionAutomaticthe clustering linkage algorithm to use
      ContentSelectableAutomaticwhether to allow contents to be selected
      CoordinatesToolOptionsAutomaticdetailed behavior of the coordinates tool
      DistanceFunctionAutomaticthe distance or dissimilarity to use
      Epilog{}primitives rendered after the main plot
      FeatureExtractorAutomatichow to extract features from data
      FormatTypeTraditionalFormthe default format type for text
      FrameFalsewhether to put a frame around the plot
      FrameLabelNoneframe labels
      FrameStyle{}style specifications for the frame
      FrameTicksAutomaticframe ticks
      FrameTicksStyle{}style specifications for frame ticks
      GridLinesNonegrid lines to draw
      GridLinesStyle{}style specifications for grid lines
      ImageMargins0.the margins to leave around the graphic
      ImagePaddingAllwhat extra padding to allow for labels etc.
      ImageSizeAutomaticthe absolute size at which to render the graphic
      LabelStyle{}style specifications for labels
      MethodAutomaticdetails of graphics methods to use
      PlotLabelNonean overall label for the plot
      PlotRangeAllrange of values to include
      PlotRangeClippingFalsewhether to clip at the plot range
      PlotRangePaddingAutomatichow much to pad the range of values
      PlotRegionAutomaticthe final display region to be filled
      PreserveImageOptionsAutomaticwhether to preserve image options when displaying new versions of the same graphic
      Prolog{}primitives rendered before the main plot
      RotateLabelTruewhether to rotate y labels on the frame
      TicksAutomaticaxes ticks
      TicksStyle{}style specifications for axes ticks

Examples

open all close all

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:

See Also

ClusteringTree  FindClusters  ClusteringComponents  TreePlot

Function Repository: NewickDendrogram  PhylogeneticTreePlot

Related Guides

    ▪
  • Cluster Analysis
  • ▪
  • Data Visualization
  • ▪
  • Distance and Similarity Measures
  • ▪
  • Life Sciences & Medicine: Data & Computation
  • ▪
  • Statistical Data Analysis
  • ▪
  • Text Analysis
  • ▪
  • Natural Language Processing
  • ▪
  • Unsupervised Machine Learning
  • ▪
  • Scientific Data Analysis
  • ▪
  • Sequence Alignment & Comparison
  • ▪
  • Tree Construction & Representation

History

Introduced in 2016 (10.4) | Updated in 2017 (11.1)

Wolfram Research (2016), Dendrogram, Wolfram Language function, https://reference.wolfram.com/language/ref/Dendrogram.html (updated 2017).

Text

Wolfram Research (2016), Dendrogram, Wolfram Language function, https://reference.wolfram.com/language/ref/Dendrogram.html (updated 2017).

CMS

Wolfram Language. 2016. "Dendrogram." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2017. https://reference.wolfram.com/language/ref/Dendrogram.html.

APA

Wolfram Language. (2016). Dendrogram. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Dendrogram.html

BibTeX

@misc{reference.wolfram_2025_dendrogram, author="Wolfram Research", title="{Dendrogram}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/Dendrogram.html}", note=[Accessed: 04-February-2026]}

BibLaTeX

@online{reference.wolfram_2025_dendrogram, organization={Wolfram Research}, title={Dendrogram}, year={2017}, url={https://reference.wolfram.com/language/ref/Dendrogram.html}, note=[Accessed: 04-February-2026]}

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