balanced_clustering {anticlust} | R Documentation |

Create balanced clusters of equal size

```
balanced_clustering(x, K, method = "centroid")
```

`x` |
The data input. Can be one of two structures: (1) A feature
matrix where rows correspond to elements and columns correspond
to variables (a single numeric variable can be passed as a
vector). (2) An N x N matrix dissimilarity matrix; can be an
object of class |

`K` |
How many clusters should be created. |

`method` |
One of "centroid" or "ilp". See Details. |

This function partitions a set of elements into `K`

equal-sized clusters. The function offers two methods: a heuristic
and an exact method. The heuristic (`method = "centroid"`

)
first computes the centroid of all data points. If the input is a
feature matrix, the centroid is defined as the mean vector of all
columns. If the input is a dissimilarity matrix, the most central
element acts as the centroid; the most central element is defined
as the element having the minimum maximal distance to all other
elements. After identifying the centroid, the algorithm proceeds as
follows: The element having the highest distance from the centroid
is clustered with its `(N/K) - 1`

nearest neighbours
(neighbourhood is defined according to the Euclidean distance if
the data input is a feature matrix). From the remaining elements,
again the element farthest to the centroid is selected and
clustered with its `(N/K) - 1`

neighbours; the procedure is
repeated until all elements are part of a cluster.

An exact method (`method = "ilp"`

) can be used to solve
equal-sized weighted cluster editing optimally (implements the
integer linear program described in Papenberg and Klau, 2020;
(8) - (10), (12) - (13)). The cluster editing objective is the
sum of pairwise distances
within clusters; clustering is accomplished by minimizing this
objective. If the argument `x`

is a features matrix, the
Euclidean distance is computed as the basic unit of the cluster
editing objective. If another distance measure is preferred, users
may pass a self-computed dissimiliarity matrix via the argument
`x`

. The optimal cluster editing objective can be found via
integer linear programming. To obtain an optimal solution, the open
source GNU linear programming kit (available from
https://www.gnu.org/software/glpk/glpk.html) and the R package
`Rglpk`

must be installed.

An integer vector representing the cluster affiliation of each data point

Martin Papenberg martin.papenberg@hhu.de

Meik Michalke meik.michalke@hhu.de

The centroid method was originally developed and contributed by Meik Michalke. It was later rewritten by Martin Papenberg, who also implemented the integer linear programming method.

Grötschel, M., & Wakabayashi, Y. (1989). A cutting plane algorithm for a clustering problem. Mathematical Programming, 45, 59–96.

Papenberg, M., & Klau, G. W. (2021). Using anticlustering to partition data sets into equivalent parts. Psychological Methods, 26(2), 161–174. https://doi.org/10.1037/met0000301.

```
# Cluster a data set and visualize results
N <- 1000
lds <- data.frame(f1 = rnorm(N), f2 = rnorm(N))
cl <- balanced_clustering(lds, K = 10)
plot_clusters(lds, clusters = cl)
# Repeat using a distance matrix as input
cl2 <- balanced_clustering(dist(lds), K = 10)
plot_clusters(lds, clusters = cl2)
```

[Package *anticlust* version 0.8.1 Index]