Dendrogram

Dendrogram[{e1,e2,…}]

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

Dendrogram[{e1v1,e2v2,…}]

represents ei with vi in the constructed dendrogram.

Dendrogram[{e1,e2,…}{v1,v2,…}]

represents ei with vi in the constructed dendrogram.

Dendrogram[label1e1,label2e2,…]

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

  • 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:
  • ClusterDissimilarityFunctionAutomaticthe 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.

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 AspectRatio1:

Specify the height to width ratio:

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:

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_2022_dendrogram, author="Wolfram Research", title="{Dendrogram}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/Dendrogram.html}", note=[Accessed: 10-June-2023 ]}

BibLaTeX

@online{reference.wolfram_2022_dendrogram, organization={Wolfram Research}, title={Dendrogram}, year={2017}, url={https://reference.wolfram.com/language/ref/Dendrogram.html}, note=[Accessed: 10-June-2023 ]}