purity | R Documentation |

Calculate the purity of the clustering results. For example, see \insertCiteSchaeffer_etal_2016_trust;textualfuntimes.

```
purity(classes, clusters)
```

`classes` |
a vector with labels of true classes. |

`clusters` |
a vector with labels of assigned clusters for which purity is to
be tested. Should be of the same length as |

Following \insertCiteManning_etal_2008;textualfuntimes, each cluster is assigned to the class which is most frequent in the cluster, then

`Purity(\Omega,C) = \frac{1}{N}\sum_{k}\max_{j}|\omega_k\cap c_j|,`

where `\Omega=\{\omega_1,\ldots,\omega_K \}`

is the set of identified
clusters and `C=\{c_1,\ldots,c_J\}`

is the set of classes. That is, within
each class `j=1,\ldots,J`

find the size of the most populous cluster from
the `K-j`

unassigned clusters. Then, sum together the `\min(K,J)`

sizes
found and divide by `N`

,
where `N`

= `length(classes)`

= `length(clusters)`

.

If `\max_{j}|\omega_k\cap c_j|`

is not unique for some `j`

,
it is assigned to the class which the second maximum is the smallest, to
maximize the `Purity`

(see ‘Examples’).

The number of unique elements
in `classes`

and `clusters`

may differ.

A list with two elements:

`pur` |
purity value. |

`out` |
table with |

Vyacheslav Lyubchich

```
# Fix seed for reproducible simulations:
# RNGkind(sample.kind = "Rounding") #run this line to have same seed across R versions > R 3.6.0
set.seed(1)
##### Example 1
#Create some classes and cluster labels:
classes <- rep(LETTERS[1:3], each = 5)
clusters <- sample(letters[1:5], length(classes), replace = TRUE)
#From the table below:
# - cluster 'b' corresponds to class A;
# - either of the clusters 'd' and 'e' can correspond to class B,
# however, 'e' should be chosen, because cluster 'd' also highly
# intersects with Class C. Thus,
# - cluster 'd' corresponds to class C.
table(classes, clusters)
## clusters
##classes a b c d e
## A 0 3 1 0 1
## B 1 0 0 2 2
## C 1 2 0 2 0
#The function does this choice automatically:
purity(classes, clusters)
#Sample output:
##$pur
##[1] 0.4666667
##
##$out
## ClassLabels ClusterLabels ClusterSize
##1 A b 3
##2 B e 2
##3 C d 2
##### Example 2
#The labels can be also numeric:
classes <- rep(1:5, each = 3)
clusters <- sample(1:3, length(classes), replace = TRUE)
purity(classes, clusters)
```

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