uclust (version 0.1.0)

uclust: U-statistic based significance clustering

Description

Partitions the sample into the two significant subgroups with the largest Bn statistic. If no significant partition exists, the test will return "homogeneous".

Usage

uclust(md = NULL, data = NULL, alpha = 0.05, rep = 15)

Arguments

md

Matrix of squared Euclidean distances between all data points.

data

Data matrix. Each row represents an observation.

alpha

Significance level.

rep

Number of times to repeat optimization procedures. Important for problems with multiple optima.

Value

Returns a list with the following elements:

cluster1

Elements in group 1 in the final partition. This is the significant partition with maximal Bn, if sample is heterogeneous.

cluster2

Elements in group 2 in the final partition.

p.value

P-value for the test that renders the final partition, if heterogeneous. Homogeneity test p-value, if homogeneous.

alpha_corrected

Bonferroni corrected significance level for the test that renders the final partition, if heterogeneous. Homogeneity test significance level, if homogeneous.

n1

Size of the smallest cluster

ishomo

Logical, returns TRUE when the sample is homogeneous.

Bn

Value of Bn statistic for the final partition, if heterogeneous. Value of Bn statistic for the maximal homogeneity test partition, if homogeneous.

varBn

Variance estimate for final partition, if heterogeneous. Variance estimate for the maximal homogeneity test partition, if homogeneous.

ishomoResult

Result of homogeneity test (see is_homo).

Details

This is the significance clustering procedure of Valk and Cybis (2018). The method first performs a homogeneity test to verify whether the data can be significantly partitioned. If the hypothesis of homogeneity is rejected, then the method will search, among all the significant partitions, for the partition that better separates the data, as measured by larger bn statistic. This function should be used in high dimension small sample size settings.

Either data or md should be provided. If data are entered directly, Bn will be computed considering the squared Euclidean distance. It is important that if a distance matrix is entered, it consists of squared Euclidean distances, otherwise test results are invalid.

Variance of bn is estimated through resampling, and thus, p-values may vary a bit in different runs.

For more detail see Cybis, Gabriela B., Marcio Valk, and S<U+00ED>lvia RC Lopes. "Clustering and classification problems in genetics through U-statistics." Journal of Statistical Computation and Simulation 88.10 (2018) and Valk, Marcio, and Gabriela Bettella Cybis. "U-statistical inference for hierarchical clustering." arXiv preprint arXiv:1805.12179 (2018). See also is_homo, uhclust, Utest_class.

Examples

# NOT RUN {
set.seed(17161)
x = matrix(rnorm(100000),nrow=50)  #creating homogeneous Gaussian dataset
res = uclust(data=x)

x[1:30,] = x[1:30,]+0.25   #Heterogeneous dataset (first 30 samples have different mean)
res = uclust(data=x)

md = as.matrix(dist(x)^2)   #squared Euclidean distances for the same data
res = uclust(md)

# Multidimensional scaling plot of distance matrix
fit <- cmdscale(md, eig = TRUE, k = 2)
x <- fit$points[, 1]
y <- fit$points[, 2]
col=rep(3,dim(md)[1])
col[res$cluster2]=2
plot(x,y, main=paste("Multidimensional scaling plot of data:
                    homogeneity p-value =",res$ishomoResult$p.MaxTest),col=col)


# }