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FindClusters
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FindClusters

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FindClusters[{e1,e2,…}]

partitions the ei into clusters of similar elements.

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FindClusters[{e1v1,e2v2,…}]

returns the vi corresponding to the ei in each cluster.

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FindClusters[data,n]

partitions data into n clusters.

Details and Options

  • FindClusters partitions a list into sublists (clusters) of similar elements. The number and composition of the clusters is influenced by the input data, the method and the evaluation criterion used. The elements can belong to a variety of data types, including numerical, textual and image, as well as dates and times.
  • Clustering is typically used to find classes of elements such as customer types, animal taxonomies, document topics, etc. in an unsupervised way. For supervised classification, see Classify.
  • Labels for the input examples ei can be given in the following formats:
  • {e1,e2,…}use the ei themselves
    {e1v1,e2v2,…}a list of rules between the element ei and the label vi
    {e1,e2,…}{v1,v2,…}a rule between all the elements and all the labels
    label1e1,label2e2,…the labels as Association keys
  • The number of clusters can be specified in the following ways:
  • Automaticfind the number of clusters automatically
    nfind exactly n clusters
    UpTo[n]find at most n clusters
  • The following options can be given:
  • CriterionFunction Automaticcriterion for selecting a method
    DistanceFunction Automaticthe distance function to use
    FeatureExtractor Identityhow to extract features from which to learn
    FeatureNames Automaticfeature names to assign for input data
    FeatureTypes Automaticfeature types to assume for input data
    Method Automaticwhat method to use
    MissingValueSynthesisAutomatichow to synthesize missing values
    PerformanceGoal Automaticaspect of performance to optimize
    RandomSeeding 1234what seeding of pseudorandom generators should be done internally
    Weights Automaticwhat weight to give to each example
  • By default, FindClusters will preprocess the data automatically unless a DistanceFunction is specified.
  • The setting for DistanceFunction can be any distance or dissimilarity function, or a function f defining a distance between two values.
  • Possible settings for PerformanceGoal include:
  • Automaticautomatic tradeoff among speed, accuracy, and memory
    "Quality"maximize the accuracy of the classifier
    "Speed"maximize the speed of the classifier
  • Possible settings for Method include:
  • Automaticautomatically select a method
    "Agglomerate"single-linkage clustering algorithm
    "DBSCAN"density-based spatial clustering of applications with noise
    "GaussianMixture"variational Gaussian mixture algorithm
    "JarvisPatrick"Jarvis–Patrick clustering algorithm
    "KMeans"k-means clustering algorithm
    "KMedoids"partitioning around medoids
    "MeanShift"mean-shift clustering algorithm
    "NeighborhoodContraction"shift data points toward high-density regions
    "SpanningTree"minimum spanning tree-based clustering algorithm
    "Spectral"spectral clustering algorithm
  • The methods "KMeans" and "KMedoids" can only be used when the number of clusters is specified.
  • The methods "DBSCAN", "GaussianMixture", "JarvisPatrick", "MeanShift" and "NeighborhoodContraction" can only be used when the number of clusters is Automatic.
  • The following plots show results of common methods on toy datasets:
    • ✖
    https://wolfram.com/xid/0b0kmgigs1w-kdgqdj
  • Possible settings for CriterionFunction include:
  • "StandardDeviation"root-mean-square standard deviation
    "RSquared"R-squared
    "Dunn"Dunn index
    "CalinskiHarabasz"Calinski–Harabasz index
    "DaviesBouldin"Davies–Bouldin index
    "Silhouette"Silhouette score
    Automaticinternal index
  • Possible settings for RandomSeeding include:
  • Automaticautomatically reseed every time the function is called
    Inheriteduse externally seeded random numbers
    seeduse an explicit integer or strings as a seed

Examples

open allclose all

Basic Examples  (4)Summary of the most common use cases

Find clusters of nearby values:

In[1]:=1
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https://wolfram.com/xid/0b0kmgigs1w-jpdaco
Out[1]=1

Find exactly four clusters:

In[1]:=1
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https://wolfram.com/xid/0b0kmgigs1w-dzpf7o
Out[1]=1

Represent clustered elements with the right-hand sides of each rule:

In[1]:=1
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https://wolfram.com/xid/0b0kmgigs1w-h9jjdw
Out[1]=1

Represent clustered elements with the keys of the association:

In[1]:=1
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https://wolfram.com/xid/0b0kmgigs1w-gabdcd
Out[1]=1

Scope  (6)Survey of the scope of standard use cases

Cluster vectors of real values:

In[1]:=1
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https://wolfram.com/xid/0b0kmgigs1w-icwhxs
Out[1]=1

Cluster data of any precision:

In[1]:=1
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https://wolfram.com/xid/0b0kmgigs1w-ndtrw
In[2]:=2
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https://wolfram.com/xid/0b0kmgigs1w-iaczwq
Out[2]=2

Cluster Boolean True, False data:

In[1]:=1
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https://wolfram.com/xid/0b0kmgigs1w-grm7nn
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0b0kmgigs1w-bwu8u
Out[2]=2

Cluster colors:

In[1]:=1
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https://wolfram.com/xid/0b0kmgigs1w-wdy3pa
In[2]:=2
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https://wolfram.com/xid/0b0kmgigs1w-01rtjz
Out[2]=2

Cluster images:

In[1]:=1
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https://wolfram.com/xid/0b0kmgigs1w-s75f1y
In[2]:=2
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https://wolfram.com/xid/0b0kmgigs1w-lsioch
Out[2]=2

Clustering of 3D images:

In[1]:=1
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https://wolfram.com/xid/0b0kmgigs1w-4q05d0
In[2]:=2
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https://wolfram.com/xid/0b0kmgigs1w-b5l05p
Out[2]=2

Options  (15)Common values & functionality for each option

CriterionFunction  (1)

Generate some separated data and visualize it:

In[19]:=19
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https://wolfram.com/xid/0b0kmgigs1w-00c176
Out[22]=22

Cluster the data using different settings for CriterionFunction:

In[23]:=23
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https://wolfram.com/xid/0b0kmgigs1w-ys32xz
In[24]:=24
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https://wolfram.com/xid/0b0kmgigs1w-33iqa5

Compare the two clusterings of the data:

In[28]:=28
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https://wolfram.com/xid/0b0kmgigs1w-0u8j8j
Out[28]=28
In[29]:=29
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https://wolfram.com/xid/0b0kmgigs1w-60ogcx
Out[29]=29

DistanceFunction  (4)

Use CanberraDistance as the measure of distance for continuous data:

In[1]:=1
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https://wolfram.com/xid/0b0kmgigs1w-c1lu32
Out[1]=1

Clusters obtained with the default SquaredEuclideanDistance:

In[2]:=2
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https://wolfram.com/xid/0b0kmgigs1w-m1mdnd
Out[2]=2

Use DiceDissimilarity as the measure of distance for Boolean data:

In[1]:=1
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https://wolfram.com/xid/0b0kmgigs1w-rza4n
In[2]:=2
✖
https://wolfram.com/xid/0b0kmgigs1w-w1nomf
Out[2]=2

Use MatchingDissimilarity as the measure of distance for Boolean data:

In[3]:=3
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https://wolfram.com/xid/0b0kmgigs1w-2srsmp
Out[3]=3

Use HammingDistance as the measure of distance for string data:

In[1]:=1
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https://wolfram.com/xid/0b0kmgigs1w-xjylmz
In[2]:=2
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https://wolfram.com/xid/0b0kmgigs1w-frdmbi
Out[2]=2

Define a distance function as a pure function:

In[1]:=1
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https://wolfram.com/xid/0b0kmgigs1w-gdyy3i
In[2]:=2
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https://wolfram.com/xid/0b0kmgigs1w-bl8xio
Out[2]=2

FeatureExtractor  (1)

Find clusters for a list of images:

In[1]:=1
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https://wolfram.com/xid/0b0kmgigs1w-dfdw4g
In[2]:=2
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https://wolfram.com/xid/0b0kmgigs1w-zzmk1z
Out[2]=2

Create a custom FeatureExtractor to extract features:

In[3]:=3
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https://wolfram.com/xid/0b0kmgigs1w-ip44vf
Out[3]=3
In[4]:=4
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https://wolfram.com/xid/0b0kmgigs1w-s0sgf5
Out[4]=4

FeatureNames  (1)

Use FeatureNames to name features, and refer to their names in further specifications:

In[1]:=1
✖
https://wolfram.com/xid/0b0kmgigs1w-48k90i
Out[1]=1

FeatureTypes  (1)

Use FeatureTypes to enforce the interpretation of the features:

In[1]:=1
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https://wolfram.com/xid/0b0kmgigs1w-1cc459
Out[1]=1

Compare it to the result obtained by assuming nominal features:

In[2]:=2
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https://wolfram.com/xid/0b0kmgigs1w-jbdp7r
Out[2]=2

Method  (4)

Cluster the data hierarchically:

In[26]:=26
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https://wolfram.com/xid/0b0kmgigs1w-be97pa
Out[26]=26

Clusters obtained with the default method:

In[27]:=27
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https://wolfram.com/xid/0b0kmgigs1w-cjvdme
Out[27]=27

Generate normally distributed data and visualize it:

In[1]:=1
✖
https://wolfram.com/xid/0b0kmgigs1w-7zq5le
Out[1]=1

Cluster the data in 4 clusters by using the k-means method:

In[2]:=2
✖
https://wolfram.com/xid/0b0kmgigs1w-zxidkh
Out[2]=2

Cluster the data using the "GaussianMixture" method without specifying the number of clusters:

In[3]:=3
✖
https://wolfram.com/xid/0b0kmgigs1w-i8o6wm
Out[3]=3

Generate some uniformly distributed data:

In[1]:=1
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https://wolfram.com/xid/0b0kmgigs1w-r9oe37
Out[1]=1

Cluster the data in 2 clusters by using the k-means method:

In[2]:=2
✖
https://wolfram.com/xid/0b0kmgigs1w-mugba9
Out[2]=2

Cluster the data using the "DBSCAN" method without specifying the number of clusters:

In[3]:=3
✖
https://wolfram.com/xid/0b0kmgigs1w-j7we1l
Out[3]=3

Generate a list of colors:

In[1]:=1
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https://wolfram.com/xid/0b0kmgigs1w-pys8nc

Cluster the colors in 5 clusters using the k-medoids method:

In[2]:=2
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https://wolfram.com/xid/0b0kmgigs1w-jg6ym
Out[2]=2

Cluster the colors without specifying the number of clusters using the "MeanShift" method:

In[3]:=3
✖
https://wolfram.com/xid/0b0kmgigs1w-9dkbzy
Out[3]=3

Cluster the colors without specifying the number of clusters using the "NeighborhoodContraction" method:

In[4]:=4
✖
https://wolfram.com/xid/0b0kmgigs1w-517ims
Out[4]=4

Cluster the colors using the "NeighborhoodContraction" method and its suboptions:

In[5]:=5
✖
https://wolfram.com/xid/0b0kmgigs1w-iekjlh
Out[5]=5

PerformanceGoal  (1)

Generate 500 random numerical vectors of length 1000:

In[1]:=1
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https://wolfram.com/xid/0b0kmgigs1w-0wf5h1

Compute their clustering and benchmark the operation:

In[2]:=2
✖
https://wolfram.com/xid/0b0kmgigs1w-2bg62
Out[2]=2

Perform the same operation with PerformanceGoal set to "Speed":

In[3]:=3
✖
https://wolfram.com/xid/0b0kmgigs1w-h39zsa
Out[3]=3

RandomSeeding  (1)

Generate 500 random numerical vectors in two dimensions:

In[1]:=1
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https://wolfram.com/xid/0b0kmgigs1w-sos7z

Compute their clustering several times and compare the results:

In[2]:=2
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https://wolfram.com/xid/0b0kmgigs1w-8soype
In[3]:=3
✖
https://wolfram.com/xid/0b0kmgigs1w-rd8neb
Out[3]=3

Compute their clustering several times by changing the RandomSeeding option, and compare the results:

In[4]:=4
✖
https://wolfram.com/xid/0b0kmgigs1w-l9zh33
In[5]:=5
✖
https://wolfram.com/xid/0b0kmgigs1w-3rsarn
Out[5]=5

Weights  (1)

Obtain cluster assignment for some numerical data:

In[1]:=1
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https://wolfram.com/xid/0b0kmgigs1w-0o8jn4
In[2]:=2
✖
https://wolfram.com/xid/0b0kmgigs1w-cypgbu
Out[2]=2

Look at the cluster assignment when changing the weight given to each number:

In[3]:=3
✖
https://wolfram.com/xid/0b0kmgigs1w-5ywa78
Out[3]=3

Applications  (3)Sample problems that can be solved with this function

Find and visualize clusters in bivariate data:

In[1]:=1
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https://wolfram.com/xid/0b0kmgigs1w-c7x5qf
In[2]:=2
✖
https://wolfram.com/xid/0b0kmgigs1w-bhb9o7
Out[2]=2

Find clusters in five‐dimensional vectors:

In[1]:=1
✖
https://wolfram.com/xid/0b0kmgigs1w-bl1803
In[2]:=2
✖
https://wolfram.com/xid/0b0kmgigs1w-eu3bg
Out[2]=2

Cluster genomic sequences based on the number of element‐wise differences:

In[1]:=1
✖
https://wolfram.com/xid/0b0kmgigs1w-cs39oi
In[2]:=2
✖
https://wolfram.com/xid/0b0kmgigs1w-c43z2h
Out[2]=2

Properties & Relations  (2)Properties of the function, and connections to other functions

FindClusters returns the list of clusters, while ClusteringComponents gives an array of cluster indices:

In[1]:=1
✖
https://wolfram.com/xid/0b0kmgigs1w-ms4t02
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0b0kmgigs1w-8qq15k
Out[2]=2

FindClusters groups data, while Nearest gives the elements closest to a given value:

In[1]:=1
✖
https://wolfram.com/xid/0b0kmgigs1w-c7sf87
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0b0kmgigs1w-l2hip
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0b0kmgigs1w-d07drv
Out[3]=3

Neat Examples  (2)Surprising or curious use cases

Divide a square into n segments by clustering uniformly distributed random points:

In[1]:=1
✖
https://wolfram.com/xid/0b0kmgigs1w-eu1jod
In[2]:=2
✖
https://wolfram.com/xid/0b0kmgigs1w-xce5j
In[3]:=3
✖
https://wolfram.com/xid/0b0kmgigs1w-dg5vim
Out[3]=3

Cluster words beginning with "agg" in the English dictionary:

In[1]:=1
✖
https://wolfram.com/xid/0b0kmgigs1w-ed67pg
Out[1]=1
Wolfram Research (2007), FindClusters, Wolfram Language function, https://reference.wolfram.com/language/ref/FindClusters.html (updated 2020).
✖
Wolfram Research (2007), FindClusters, Wolfram Language function, https://reference.wolfram.com/language/ref/FindClusters.html (updated 2020).

Text

Wolfram Research (2007), FindClusters, Wolfram Language function, https://reference.wolfram.com/language/ref/FindClusters.html (updated 2020).

✖
Wolfram Research (2007), FindClusters, Wolfram Language function, https://reference.wolfram.com/language/ref/FindClusters.html (updated 2020).

CMS

Wolfram Language. 2007. "FindClusters." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2020. https://reference.wolfram.com/language/ref/FindClusters.html.

✖
Wolfram Language. 2007. "FindClusters." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2020. https://reference.wolfram.com/language/ref/FindClusters.html.

APA

Wolfram Language. (2007). FindClusters. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FindClusters.html

✖
Wolfram Language. (2007). FindClusters. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FindClusters.html

BibTeX

@misc{reference.wolfram_2025_findclusters, author="Wolfram Research", title="{FindClusters}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/FindClusters.html}", note=[Accessed: 29-March-2025 ]}

✖
@misc{reference.wolfram_2025_findclusters, author="Wolfram Research", title="{FindClusters}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/FindClusters.html}", note=[Accessed: 29-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_findclusters, organization={Wolfram Research}, title={FindClusters}, year={2020}, url={https://reference.wolfram.com/language/ref/FindClusters.html}, note=[Accessed: 29-March-2025 ]}

✖
@online{reference.wolfram_2025_findclusters, organization={Wolfram Research}, title={FindClusters}, year={2020}, url={https://reference.wolfram.com/language/ref/FindClusters.html}, note=[Accessed: 29-March-2025 ]}