This blog posts proclaims and describes the Raku package “ML::Clustering” that provides Machine Learning (ML) Clustering (or Cluster analysis) functions, [Wk1].
The Clustering framework includes:
- The algorithms K-means and K-medoids, and others
- The distance functions Euclidean, Cosine, Hamming, Manhattan, and others, and their corresponding similarity functions
The data in the examples below is generated and manipulated with the packages “Data::Generators”, “Data::Reshapers”, and “Data::Summarizers”, described in the article “Introduction to data wrangling with Raku”, [AA1].
The plots are made with the package “Text::Plot”, [AAp6].
Installation
Via zef-ecosystem:
zef install ML::ClusteringFrom GitHub:
zef install https://github.com/antononcube/Raku-ML-ClusteringUsage example
Here we derive a set of random points, and summarize it:
use Data::Generators;
use Data::Summarizers;
use Text::Plot;
my $n = 100;
my @data1 = (random-variate(NormalDistribution.new(5,1.5), $n) X random-variate(NormalDistribution.new(5,1), $n)).pick(30);
my @data2 = (random-variate(NormalDistribution.new(10,1), $n) X random-variate(NormalDistribution.new(10,1), $n)).pick(50);
my @data3 = [|@data1, |@data2].pick(*);
records-summary(@data3)# +------------------------------+-----------------------------+
# | 1 | 0 |
# +------------------------------+-----------------------------+
# | Min => 2.3898838030195453 | Min => 2.304900205776566 |
# | 1st-Qu => 5.706881157103716 | 1st-Qu => 5.736769825514594 |
# | Mean => 7.784565074436171 | Mean => 8.02083978767615 |
# | Median => 8.324205488000889 | Median => 9.333349983753054 |
# | 3rd-Qu => 9.667770938027495 | 3rd-Qu => 9.951571353489859 |
# | Max => 12.366646976770186 | Max => 11.87813636253523 |
# +------------------------------+-----------------------------+Here we plot the points:
use Text::Plot;
text-list-plot(@data3)# +-+----------+----------+---------+----------+----------+--+
# | |
# + * * + 12.00
# | **** * * |
# + * * *** ** * * + 10.00
# | * * * ** * ** |
# + * * **** * * + 8.00
# | * ** * |
# | * * * * |
# + * *** * * * + 6.00
# | * * ** * * * * * |
# + * * + 4.00
# | * * * |
# + + 2.00
# +-+----------+----------+---------+----------+----------+--+
# 2.00 4.00 6.00 8.00 10.00 12.00Problem: Group the points in such a way that each group has close (or similar) points.
Here is how we use the function find-clusters to give an answer:
use ML::Clustering;
my %res = find-clusters(@data3, 2, prop => 'All');
%res<Clusters>>>.elems# (31 49)Remark: The first argument is data points that is a list-of-numeric-lists. The second argument is a number of clusters to be found. (It is in the TODO list to have the number clusters automatically determined – currently they are not.)
Remark: The function find-clusters can return results of different types controlled with the named argument “prop”. Using prop => 'All' returns a hash with all properties of the cluster finding result.
Here are sample points from each found cluster:
.say for %res<Clusters>>>.pick(3);# ((7.739550750023431 7.869526528329702) (7.436113407675195 5.047068255152369) (3.137868648226576 6.18246060543501))
# ((10.196518357205878 10.291337792828818) (9.514778751211171 10.904815191998523) (10.118479992486252 8.418809517175601))Here are the centers of the clusters (the mean points):
%res<MeanPoints># [(10.013273073426063 9.513630351537644) (5.805077424361722 6.072817033230708)]We can verify the result by looking at the plot of the found clusters:
text-list-plot((|%res<Clusters>, %res<MeanPoints>), point-char => <▽ ☐ ●>, title => '▽ - 1st cluster; ☐ - 2nd cluster; ● - cluster centers')# ▽ - 1st cluster; ☐ - 2nd cluster; ● - cluster centers
# ++----------+-----------+----------+----------+-----------++
# | ☐ |
# + ☐ + 12.00
# | ☐☐☐☐ ☐ ☐ |
# + ☐ ☐ ☐☐☐☐☐ ☐ ☐ ☐ ☐ + 10.00
# | ☐☐ ☐ ☐ ●☐ ☐ ☐ |
# + ▽ ☐ ☐☐☐☐ ☐ ☐ + 8.00
# | ☐ ☐☐☐☐ |
# | ▽ ▽ ▽ ▽● |
# + ▽ ▽▽ ▽ ▽ ▽ + 6.00
# | ▽ ▽▽ ▽ ▽ ▽ ▽▽ ▽ |
# + ▽ ▽ ▽ ▽ + 4.00
# | ▽ ▽ |
# + ▽ + 2.00
# ++----------+-----------+----------+----------+-----------++
# 2.00 4.00 6.00 8.00 10.00 12.00Remark: By default find-clusters uses the K-means algorithm. The functions k-means and k-medoids call find-clusters with the option settings method=>'K-means' and method=>'K-medoids' respectively.
More interesting looking data
Here is more interesting looking two-dimensional data, data2D2:
use Data::Reshapers;
my $pointsPerCluster = 200;
my @data2D5 = [[10,20,4],[20,60,6],[40,10,6],[-30,0,4],[100,100,8]].map({
random-variate(NormalDistribution.new($_[0], $_[2]), $pointsPerCluster) Z random-variate(NormalDistribution.new($_[1], $_[2]), $pointsPerCluster)
}).Array;
@data2D5 = flatten(@data2D5, max-level=>1).pick(*);
@data2D5.elems# 1000Here is a plot of that data:
text-list-plot(@data2D5)# ++---------------+--------------+---------------+----------+
# | |
# | * ** ** |
# | * ************* |
# + ************** + 100.00
# | * * ** * *** |
# | ********* * |
# | *********** |
# + **** + 50.00
# | ******* ** |
# | ****************** |
# + ****** ** ********** + 0.00
# | ******* * ** |
# | |
# ++---------------+--------------+---------------+----------+
# -50.00 0.00 50.00 100.00Here we find clusters and plot them together with their mean points:
srand(32);
my %clRes = find-clusters(@data2D5, 5, prop=>'All');
text-list-plot([|%clRes<Clusters>, %clRes<MeanPoints>], point-char=><1 2 3 4 5 ●>)# +---------------+---------------+----------------+---------+
# | 4 |
# | 4 44444 44 |
# + 4 444444●44444444 + 100.00
# | 444444444444 |
# | 3 4 444 4 |
# | 3333333333 |
# | 33333●33333 |
# + 333333 + 50.00
# | 22222 1 |
# | 2222●222221 111111 |
# | 555555 22222222 1111●1111 |
# + 5555●555 11111111 1 + 0.00
# |5 5 555 |
# +---------------+---------------+----------------+---------+
# 0.00 50.00 100.00Detailed function pages
Detailed parameter explanations and usage examples for the functions provided by the package are given in:
Implementation considerations
UML diagram
Here is a UML diagram that shows package’s structure:
The PlantUML spec and diagram were obtained with the CLI script to-uml-spec of the package “UML::Translators”, [AAp6].
Here we get the PlantUML spec:
to-uml-spec ML::AssociationRuleLearning > ./resources/class-diagram.pumlHere get the diagram:
to-uml-spec ML::Clustering | java -jar ~/PlantUML/plantuml-1.2022.5.jar -pipe > ./resources/class-diagram.pngRemark: Maybe it is a good idea to have an abstract class named, say, ML::Clustering::AbstractFinder that is a parent of ML::Clustering::KMeans, ML::Clustering::KMedoids, ML::Clustering::BiSectionalKMeans, etc., but I have not found to be necessary. (At this point of development.)
Remark: It seems it is better to have a separate package for the distance functions, named, say, “ML::DistanceFunctions”. (Although distance functions are not just for ML…) After thinking over package and function names I will make such a package.
References
Articles
[Wk1] Wikipedia entry, “Cluster Analysis”.
[AA1] Anton Antonov, “Introduction to data wrangling with Raku”, (2021), RakuForPrediction at WordPress.
Packages
[AAp1] Anton Antonov, Bi-sectional K-means algorithm in Mathematica, (2020), MathematicaForPrediction at GitHub/antononcube.
[AAp2] Anton Antonov, Data::Generators Raku package, (2021), GitHub/antononcube.
[AAp3] Anton Antonov, Data::Reshapers Raku package, (2021), GitHub/antononcube.
[AAp4] Anton Antonov, Data::Summarizers Raku package, (2021), GitHub/antononcube.
[AAp5] Anton Antonov, UML::Translators Raku package, (2022), GitHub/antononcube.
[AAp6] Anton Antonov, Text::Plot Raku package, (2022), GitHub/antononcube.
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