funtimes (version 5.0)

purity: Clustering Purity

Description

Calculate purity of the clustering results.

Usage

purity(classes, clusters)

Arguments

classes, clusters

vectors of equal lengths, with labels of underlying true classes and assigned clusters. Number of unique elements in classes and clusters may differ.

Value

A list with two elements:

pur

purity value.

out

table with \(\min(K,J)\) = min(length(unique(classes)), length(unique(clusters))) rows and the following columns: ClassLabels, ClusterLabels, and ClusterSize.

Details

Following Manning et al. (2008), 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 second maximum is the smallest, to maximize the \(Purity\) (see `Examples').

References

Manning, C. D., Raghavan, P., and Schutze, H. (2008). Introduction to Information Retrieval. New York: Cambridge University Press.

Schaeffer, E. D., Testa, J. M., Gel, Y. R., and Lyubchich, V. (2016). On information criteria for dynamic spatio-temporal clustering. In A. Banerjee et al. (Eds.) Proceedings of the 6th International Workshop on Climate Informatics: CI 2016. NCAR Technical Note NCAR/TN-529+PROC, September 2016, pages 5--8. DOI: 10.5065/D6K072N6

Examples

# NOT RUN {
# Fix seed for reproducible simulations:
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)
# }