uclust: U-statistic based significance clustering
In uclust: Clustering and Classification Inference with U-Statistics

Description Usage Arguments Details Value Examples

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

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

`md`	Matrix of 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.

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.

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 Sílvia 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." Journal of Computational and Graphical Statistics 30(1) (2021). See also is_homo, uhclust, Utest_class.

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).

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)