Validity.indices {clusterv} | R Documentation |
Function to compute the validity index of each cluster.
Description
It computes the validity index (e.g. the stability index) for each individual cluster.
This function is called by Cluster.validity
and Cluster.validity.from.similarity
Usage
Validity.indices(cluster, c, Sim.M)
Arguments
cluster |
list of clusters representing a clustering in the original space. Each element of the list is a vector whose elements are the examples belonging to the cluster. |
c |
number of clusters |
Sim.M |
the pairwise similarity matrix |
Details
Using the similarity matrix M, the stability index s for a cluster A is:
s(A) = \frac{1}{|A|(|A|-1)} \sum_{(i,j) \in A \times A, i\neq j} M_{ij}
The index s(A)
estimates the stability of a cluster A
by measuring how much the projections
of the pairs (i,j) \in A \times A
occur together in the same cluster in the projected subspaces.
The stability index has values between 0 and 1: low values indicate no reliable clusters,
high values denote stable clusters.
Value
vector of the validity indices. Each element corresponds to validity index of each cluster.
Author(s)
Giorgio Valentini valentini@di.unimi.it
See Also
Cluster.validity
, Cluster.validity.from.similarity
,
Do.similarity.matrix.partition
, Do.similarity.matrix
Examples
# Computation of the stability indices found out by a hierarchical clustering algorithm
M <- generate.sample0(n=10, m=2, sigma=2, dim=800)
d <- dist (t(M));
tree <- hclust(d, method = "average");
plot(tree, main="");
cl.orig <- rect.hclust(tree, k = 3);
l.norm <- Multiple.Random.hclustering (M, dim=100, pmethod="Norm",
c=3, hmethod="average", n=20)
Sim <- Do.similarity.matrix.partition(l.norm);
val.indices <- Validity.indices(cl.orig, c=3, Sim)