Chi.square.compute.pvalues: Function to compute the stability indices and the p-values...

In mosclust: Model Order Selection for Clustering

Function to compute the stability indices and the p-values associated to a set of clusterings according to the chi-square test between multiple proportions.

Description

For a given similarity matrix a list of stability indices, sorted by descending order, from the most significant clustering to the least significant is given. Moreover the corresponding p-values, computed according to a chi-square based test are provided.

Usage

Chi.square.compute.pvalues(sim.matrix, s0 = 0.9)

Arguments

sim.matrix	a matrix that stores the similarity between pairs of clustering across multiple number of clusters and multiple clusterings. Rows correspond to the different clusterings; columns to the n repeated clusterings for each number of clusters. Row 1 corresponds to a 2-clustering, row 2 to a 3-clustering, ... row m to a m+1 clustering.
s0	threshold for the similarity value (default 0.9)

Details

The stability index for a given clustering is computed as the mean of the similarity indices between pairs of k-clusterings obtained from the perturbed data. The similarity matrix given as input can be obtained from the functions do.similarity.resampling, do.similarity.projection, do.similarity.noise. For each k-clustering the proportion of pairs of perturbed clusterings having similarity indices larger than a given threshold (the parameter s0) is computed. The p-values are obtained according the chi-square test between multiple proportions (each proportion corresponds to a different k-clustering). A low p-value means that there is a significant difference between the top sorted and the given k-clustering.

Value

a data frame with 4 components:

ordered.clusterings	a vector with the number of clusters ordered from the most significant to the least significant
p.value	a vector with the corresponding p-values computed according to chi-square test between multiple proportions in descending order (their values correspond to the clusterings of the vector ordered.clusterings)
means	vector with the stability index (mean similarity) for each k-clustering
variance	vector with the variance of the similarity for each k-clustering

Author(s)

Giorgio Valentini [e-mail]

References

A.Bertoni, G. Valentini, Model order selection for clustered bio-molecular data, In: Probabilistic Modeling and Machine Learning in Structural and Systems Biology, J. Rousu, S. Kaski and E. Ukkonen (Eds.), Tuusula, Finland, 17-18 June, 2006

See Also

Bernstein.compute.pvalues, Hypothesis.testing,

do.similarity.resampling, do.similarity.projection, do.similarity.noise

Examples

library("clusterv")
# Synthetic data set generation
M <- generate.sample6 (n=10, m=15, dim=800, d=3, s=0.2)
nsubsamples <- 10;  # number of pairs of clusterings to be evaluated
max.num.clust <- 6; # maximum number of cluster to be evaluated
fract.resampled <- 0.8; # fraction of samples to subsampled
# building a similarity matrix using resampling methods, considering clusterings 
# from 2 to 10 clusters with the k-means algorithm
Sr.Kmeans.sample6 <- do.similarity.resampling(M, c=max.num.clust, nsub=nsubsamples, 
                     f=fract.resampled, s=sFM, alg.clust.sim=Kmeans.sim.resampling);
# computing p-values according to the chi square-based test
dr.Kmeans.sample6 <- Chi.square.compute.pvalues(Sr.Kmeans.sample6);
# the same, using noise to perturbate the data and  hierarchical clustering algorithm
Sn.HC.sample6 <- do.similarity.noise(M, c=max.num.clust, nnoisy=nsubsamples, perc=0.5, 
                                 s=sFM, alg.clust.sim=Hierarchical.sim.noise);
dn.HC.sample6 <- Chi.square.compute.pvalues(Sn.HC.sample6);

mosclust documentation built on June 8, 2025, 11:23 a.m.