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Tutorial: hierarchical clustering

Source: vignettes/articles/Tutorials_hier.Rmd
Tutorials_hier.Rmd

For hierarchical clustering, set clustering = "hclust". By default the package uses average linkage on squared Euclidean distances and cuts the tree into K clusters; hclust_method chooses another linkage.

set.seed(123)
Sigma <- matrix(c(1, 0.6, 0.6, 1), 2, 2)
X <- rbind(matrix(rnorm(100), ncol = 2), matrix(rnorm(100), ncol = 2) + 4) %*% chol(Sigma)
res <- selective_hotelling_test(X, k1 = 1, k2 = 2, K = 2, clustering = "hclust", M = 1000)
res
#> Selective Hotelling T^2 test (unknown covariance)
#>   Clusters tested : 1 vs 2 (of K = 2)
#>   Sampler         : besag-clifford
#>   Conditioning    : pair-preserved
#>   Observed T^2    : 842.1
#>   Selective p-val : 0.002837 (MC s.e. ~ 0.002)
table(res$cluster)
#> 
#>  1  2 
#> 50 50

The two clusters come from two different groups, and the test rejects. With a single group, it does not:

set.seed(321)
X0 <- matrix(rnorm(200), ncol = 2) %*% chol(Sigma)
res0 <- selective_hotelling_test(X0, k1 = 1, k2 = 2, K = 2, clustering = "hclust",
                                 M = 1000)
res0$pval
#> [1] 0.4715096

With complete linkage:

selective_hotelling_test(X, k1 = 1, k2 = 2, K = 2, clustering = "hclust",
                         hclust_method = "complete", M = 1000)$pval
#> [1] 0.0002489197

Average-linkage hierarchical clustering is sensitive to outliers. The technical details discuss when the tests rely on Gaussian data.