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## ML::Clustering zef:antononcube last updated on 2022-08-04

```# Raku ML::Clustering

This repository has the code of a Raku package for
Machine Learning (ML)
[Clustering (or Cluster analysis)](https://en.wikipedia.org/wiki/Cluster_analysis)
functions, [Wk1].

The Clustering framework includes:

- The algorithms
[K-means](https://en.wikipedia.org/wiki/K-means_clustering)
and
[K-medoids](https://en.wikipedia.org/wiki/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"](https://raku.land/zef:antononcube/Data::Generators),
["Data::Reshapers"](https://raku.land/zef:antononcube/Data::Reshapers), and
["Data::Summarizers"](https://raku.land/zef:antononcube/Data::Summarizers), described in the article
["Introduction to data wrangling with Raku"](https://rakuforprediction.wordpress.com/2021/12/31/introduction-to-data-wrangling-with-raku/),
[AA1].

The plots are made with the package
["Text::Plot"](https://raku.land/zef:antononcube/Text::Plot), [AAp6].

-------

## Installation

Via zef-ecosystem:

```shell
zef install ML::Clustering
```

From GitHub:

```shell
zef install https://github.com/antononcube/Raku-ML-Clustering
```

-------

## Usage example

Here we derive a set of random points, and summarize it:

```perl6
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)
```

Here we plot the points:

```perl6
use Text::Plot;
text-list-plot(@data3)
```

**Problem:** 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:

```perl6
use ML::Clustering;
my %res = find-clusters(@data3, 2, prop => 'All');
%res<Clusters>>>.elems
```

**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:

```perl6
.say for %res<Clusters>>>.pick(3);
```

Here are the centers of the clusters (the mean points):

```perl6
%res<MeanPoints>
```

We can verify the result by looking at the plot of the found clusters:

```perl6
text-list-plot((|%res<Clusters>, %res<MeanPoints>), point-char => <▽ ☐ ●>, title => '▽ - 1st cluster; ☐ - 2nd cluster; ● - cluster centers')
```

**Remark:** 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`:

```perl6
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
```

Here is a plot of that data:

```perl6
text-list-plot(@data2D5)
```

Here we find clusters and plot them together with their mean points:

```perl6
srand(32);
my %clRes = find-clusters(@data2D5, 5, prop=>'All');
text-list-plot([|%clRes<Clusters>, %clRes<MeanPoints>], point-char=><1 2 3 4 5 ●>)
```

-------

## Detailed function pages

Detailed parameter explanations and usage examples for the functions provided by the package are given in:

- ["K-means function page"](./doc/K-means-function-page.md)

- ["K-medoids function page"]()

- ["Bi-sectional-K-means function page"]()

-------

## Implementation considerations

### UML diagram

Here is a UML diagram that shows package's structure:

![](./resources/class-diagram.png)

The
[PlantUML spec](./resources/class-diagram.puml)
and
[diagram](./resources/class-diagram.png)
were obtained with the CLI script `to-uml-spec` of the package "UML::Translators", [AAp6].

Here we get the [PlantUML spec](./resources/class-diagram.puml):

```shell
to-uml-spec ML::AssociationRuleLearning > ./resources/class-diagram.puml
```

Here get the [diagram](./resources/class-diagram.png):

```shell
to-uml-spec ML::Clustering | java -jar ~/PlantUML/plantuml-1.2022.5.jar -pipe > ./resources/class-diagram.png
```

**Remark:** 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.

-------

## TODO

- [ ] Implement Bi-sectional K-means algorithm, [AAp1].

- [ ] Implement K-medoids algorithm.

- [ ] Automatic determination of the number of clusters.

- [ ] Allow data points to be `Pair` objects the keys of which are point labels.

- Hence, the returned clusters consist of those labels, not points themselves.

- [ ] Implement Agglomerate algorithm.

- [ ] Factor-out the distance functions in a separate package.

-------

## References

### Articles

[Wk1] Wikipedia entry, ["Cluster Analysis"](https://en.wikipedia.org/wiki/Cluster_analysis).

[AA1] Anton Antonov,
["Introduction to data wrangling with Raku"](https://rakuforprediction.wordpress.com/2021/12/31/introduction-to-data-wrangling-with-raku/),
(2021),
[RakuForPrediction at WordPress](https://rakuforprediction.wordpress.com).

### Packages

[AAp1] Anton Antonov,
[Bi-sectional K-means algorithm in Mathematica](https://github.com/antononcube/MathematicaForPrediction/blob/master/BiSectionalKMeans.m),
(2020),
[MathematicaForPrediction at GitHub/antononcube](https://github.com/antononcube/MathematicaForPrediction/).

[AAp2] Anton Antonov,
[Data::Generators Raku package](https://github.com/antononcube/Raku-Data-Generators),
(2021),
[GitHub/antononcube](https://github.com/antononcube).

[AAp3] Anton Antonov,
[Data::Reshapers Raku package](https://github.com/antononcube/Raku-Data-Reshapers),
(2021),
[GitHub/antononcube](https://github.com/antononcube).

[AAp4] Anton Antonov,
[Data::Summarizers Raku package](https://github.com/antononcube/Raku-Data-Summarizers),
(2021),
[GitHub/antononcube](https://github.com/antononcube).

[AAp5] Anton Antonov,
[UML::Translators Raku package](https://github.com/antononcube/Raku-UML-Translators),
(2022),
[GitHub/antononcube](https://github.com/antononcube).

[AAp6] Anton Antonov,
[Text::Plot Raku package](https://raku.land/zef:antononcube/Text::Plot),
(2022),
[GitHub/antononcube](https://github.com/antononcube).
```