- See Also
-
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
-
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 [{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.
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
- 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]
-
- 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 .
-
ImageMargins 0. the margins to leave around the graphicPreserveImageOptions Automatic whether to preserve image options when displaying new versions of the same graphic
List of all options
Examples
open all close allBasic 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
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: 17-November-2025]}
BibLaTeX
@online{reference.wolfram_2025_dendrogram, organization={Wolfram Research}, title={Dendrogram}, year={2017}, url={https://reference.wolfram.com/language/ref/Dendrogram.html}, note=[Accessed: 17-November-2025]}