R Under development (unstable) (2024-05-07 r86527 ucrt) -- "Unsuffered Consequences" Copyright (C) 2024 The R Foundation for Statistical Computing Platform: x86_64-w64-mingw32/x64 R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > ## VT::11.10.2023 - this will render the output independent > ## from the version of the package > suppressPackageStartupMessages(library(tclust)) > > require(tclust) > require(MASS) Loading required package: MASS > #--- EXAMPLE 1 ------------------------------------------ > > set.seed(123) > sig <- diag (2) > cen <- rep (1,2) > x <- rbind(MASS::mvrnorm(360, cen * 0, sig), + MASS::mvrnorm(540, cen * 5, sig * 6 - 2), + MASS::mvrnorm(100, cen * 2.5, sig * 50) + ) > > # Two groups and 10% trimming level > (clus <- tclust(x, k = 2, alpha = 0.1, restr.fact = 8)) * Results for TCLUST algorithm: * trim = 0.1, k = 2 Classification (trimmed points are indicated by 0 ): [1] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [38] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [75] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [112] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [149] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [186] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [223] 2 2 2 2 2 2 2 2 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [260] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [297] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [334] 2 2 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 [371] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [408] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [445] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [482] 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 [519] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 [556] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [593] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [630] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [667] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [704] 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 [741] 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 [778] 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 [815] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [852] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [889] 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 2 0 2 0 1 0 0 0 0 0 1 [926] 0 0 0 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 [963] 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 2 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 2 2 2 [1000] 1 Means: C 1 C 2 X 1 4.984845 0.02269302 X 2 4.929012 0.03215462 Trimmed objective function: -3747.378 Selected restriction factor: 8 > > > # Three groups (one of them very scattered) and 0% trimming level > (clus <- tclust(x, k = 3, alpha=0.0, restr.fact = 100)) * Results for TCLUST algorithm: * trim = 0, k = 3 Classification (trimmed points are indicated by 0 ): [1] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [38] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [75] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [112] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [149] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [186] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [223] 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [260] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [297] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [334] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 [371] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [408] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [445] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [482] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [519] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [556] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [593] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [630] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [667] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [704] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [741] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [778] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [815] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [852] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [889] 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 3 3 3 3 1 1 3 3 1 3 2 2 3 2 3 1 3 3 3 3 3 1 [926] 3 3 3 2 3 1 3 3 3 2 3 3 3 3 3 3 3 3 1 1 3 1 3 1 3 3 3 3 3 3 1 3 1 1 3 3 3 [963] 3 3 3 3 3 3 3 1 3 3 1 3 3 3 3 3 1 3 2 3 1 3 3 1 1 3 1 3 3 3 1 1 3 3 2 2 2 [1000] 1 Means: C 1 C 2 C 3 X 1 4.889052 0.02676419 1.229842 X 2 5.055564 0.04517830 2.340643 Trimmed objective function: -4731.715 Selected restriction factor: 100 > > > #--- EXAMPLE 2 ------------------------------------------ > data(geyser2) > set.seed(123) > (clus <- tclust(geyser2, k=3, alpha=0.03)) * Results for TCLUST algorithm: * trim = 0.03, k = 3 Classification (trimmed points are indicated by 0 ): [1] 1 0 1 3 2 2 2 1 3 1 3 2 1 3 1 0 3 1 3 1 0 0 0 2 2 1 3 2 2 2 2 2 2 2 1 0 3 [38] 1 3 2 1 3 1 3 2 2 1 3 1 3 2 1 3 1 3 2 1 3 2 1 3 1 3 1 3 2 2 1 3 2 1 3 2 1 [75] 3 1 3 2 2 2 2 2 1 3 2 2 2 1 3 1 3 1 3 1 3 2 2 1 3 1 3 1 3 2 1 3 1 3 2 2 1 [112] 3 2 1 3 1 3 1 3 1 3 2 1 3 2 1 3 1 3 1 3 1 2 1 3 1 3 1 3 2 1 3 2 2 1 3 1 3 [149] 1 3 2 1 3 2 2 2 2 1 3 1 3 1 3 2 2 1 3 1 3 1 0 3 2 2 2 2 1 3 2 1 3 2 2 1 3 [186] 2 1 3 1 3 1 3 2 2 2 2 2 1 3 1 3 2 1 3 1 3 2 1 3 1 3 1 3 2 2 1 3 1 3 1 3 1 [223] 3 2 2 2 2 2 2 2 1 3 1 3 1 0 3 2 1 3 1 3 2 2 2 1 3 1 3 1 3 2 2 2 2 2 2 1 3 [260] 2 2 1 3 1 0 3 2 1 3 1 3 Means: C 1 C 2 C 3 Eruption length 4.340629 4.199207 2.020919 Previous eruption length 2.026584 4.093862 4.501721 Trimmed objective function: -441.7624 Selected restriction factor: 12 > plot(clus) > > #--- EXAMPLE 3 ------------------------------------------ > data (M5data) > set.seed(123) > x <- M5data[, 1:2] > > (clus.a <- tclust(x, k=3, alpha=0.1, restr.fact=1, + restr = "eigen", equal.weights=TRUE)) * Results for TCLUST algorithm: * trim = 0.1, k = 3 Classification (trimmed points are indicated by 0 ): [1] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [38] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [75] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [112] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [149] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [186] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [223] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [260] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [297] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [334] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 2 3 1 2 3 3 1 [371] 3 3 0 3 3 3 3 3 3 2 2 3 3 3 3 3 1 2 3 3 3 3 3 3 0 3 2 3 3 3 3 3 2 0 3 3 3 [408] 3 3 2 3 3 3 3 3 2 2 3 1 3 3 1 2 3 3 3 3 3 2 3 2 3 1 2 1 3 3 3 3 2 3 3 2 1 [445] 2 0 1 3 3 3 3 1 3 0 3 3 2 3 3 3 3 2 3 3 2 2 2 3 3 3 2 3 3 2 2 2 3 2 3 3 2 [482] 2 3 3 3 3 3 3 3 2 3 3 3 2 1 2 3 3 3 2 3 3 3 3 3 1 3 3 2 2 3 3 3 0 0 2 3 3 [519] 3 3 3 3 1 3 3 1 3 2 3 3 1 3 3 3 3 2 2 1 2 3 2 2 3 2 3 2 3 3 3 3 3 3 3 3 3 [556] 3 3 3 2 3 3 3 1 3 3 3 2 1 3 0 3 2 1 3 2 3 3 0 2 3 3 2 3 3 0 3 3 3 3 1 0 3 [593] 1 3 3 3 2 2 3 3 1 3 3 3 3 2 3 2 3 3 3 3 1 3 3 3 3 3 3 2 2 1 3 3 3 3 3 1 3 [630] 3 3 2 3 3 2 3 3 3 3 2 3 0 3 3 3 2 2 3 3 3 2 0 1 3 3 3 3 3 3 2 3 3 0 3 3 3 [667] 3 3 3 3 3 3 0 3 0 3 2 3 2 1 3 1 3 3 3 3 3 3 2 3 3 0 2 2 2 3 3 3 2 3 3 3 2 [704] 3 2 1 3 2 3 3 0 3 3 2 3 2 3 2 3 3 3 2 3 0 2 2 3 2 0 3 3 3 3 2 3 3 3 2 2 1 [741] 2 3 3 2 0 3 3 3 3 3 3 3 3 3 3 1 3 3 2 3 2 3 3 3 2 3 3 3 3 3 3 3 3 3 2 2 3 [778] 3 3 3 2 3 3 2 3 3 3 0 3 3 2 1 3 3 2 3 3 2 3 1 2 3 0 3 2 3 2 3 3 2 3 0 3 3 [815] 3 3 3 3 3 3 3 3 3 0 0 3 3 2 3 3 2 3 2 2 1 3 2 3 3 2 2 3 3 2 2 2 2 3 3 3 3 [852] 3 3 3 3 0 2 3 3 3 3 3 2 0 1 3 2 2 3 3 3 3 3 2 3 3 3 3 3 3 2 2 3 2 3 3 1 3 [889] 3 3 2 3 3 2 3 3 3 3 3 2 3 3 3 2 3 2 3 2 2 0 3 2 2 1 3 2 3 3 3 3 0 3 3 3 2 [926] 3 3 3 2 1 1 3 2 3 2 3 3 3 3 2 3 1 3 3 3 3 3 3 2 2 3 3 0 2 2 3 2 2 3 1 3 2 [963] 3 2 2 3 3 3 2 3 3 3 3 0 3 3 3 2 3 3 0 0 2 0 0 3 1 3 3 3 3 2 2 3 3 3 3 1 3 [1000] 2 3 3 3 1 2 3 2 3 2 3 2 1 1 3 3 3 3 3 3 3 3 2 3 2 3 3 3 2 3 3 3 3 3 2 2 2 [1037] 2 3 3 2 1 3 3 3 3 2 3 3 1 3 2 3 3 3 0 1 3 3 2 3 3 3 3 3 3 3 3 0 3 3 3 3 3 [1074] 2 3 2 3 3 3 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1111] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1148] 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1185] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1222] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1259] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1296] 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1333] 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1370] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1407] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1444] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1481] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 [1518] 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1555] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1592] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1629] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1666] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1703] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1740] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1777] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 2 0 1 0 0 0 0 0 0 [1814] 0 2 0 0 1 0 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 1 1 2 0 0 0 2 0 0 2 0 0 0 0 [1851] 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 [1888] 2 1 2 0 0 0 0 0 0 1 0 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 2 0 0 0 0 1 1 2 0 0 0 [1925] 0 1 1 1 0 1 1 1 0 0 0 1 0 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 0 1 0 0 [1962] 0 0 2 0 0 0 0 0 0 2 0 1 0 0 0 0 0 1 0 0 0 0 0 2 0 1 0 0 0 0 0 0 0 0 0 0 0 [1999] 0 0 Means: C 1 C 2 C 3 x -7.721913 0.429590 10.530402 y -8.457188 7.342434 -1.075651 Trimmed objective function: -11834.43 Selected restriction factor: 1 > (clus.b <- tclust(x, k=3, alpha=0.1, restr.fact=50, + restr="eigen", equal.weights=TRUE)) * Results for TCLUST algorithm: * trim = 0.1, k = 3 Classification (trimmed points are indicated by 0 ): [1] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 [38] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 [75] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 [112] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 [149] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 [186] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 [223] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 [260] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 [297] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 [334] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 [371] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [408] 2 2 2 2 2 2 2 2 2 3 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 1 3 2 2 2 2 2 2 2 2 2 1 [445] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [482] 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 [519] 2 2 2 2 1 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 0 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [556] 2 2 2 3 2 2 2 1 2 2 2 2 2 2 2 2 2 1 2 2 2 2 0 2 2 2 2 2 2 0 2 2 2 2 2 2 2 [593] 1 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 [630] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [667] 2 2 2 2 2 2 2 2 0 2 2 2 3 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 [704] 2 2 1 2 2 2 2 0 2 2 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 2 2 2 2 2 1 [741] 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 0 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 [778] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 0 2 2 [815] 2 2 2 2 2 2 2 2 2 0 0 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [852] 2 2 2 2 2 3 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 [889] 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 0 2 2 2 3 [926] 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 [963] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 [1000] 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 0 2 2 2 2 2 2 2 2 2 0 2 2 [1037] 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 2 2 2 2 2 [1074] 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1111] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1148] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1185] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1222] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1259] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1296] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1333] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1370] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1407] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1444] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1481] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 [1518] 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1555] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1592] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1629] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1666] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1703] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 [1740] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1777] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 [1814] 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 2 0 0 0 0 0 0 [1851] 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 [1888] 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 [1925] 0 1 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 2 0 0 0 0 0 0 0 0 0 0 1 0 0 [1962] 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 2 0 0 0 0 0 [1999] 0 0 Means: C 1 C 2 C 3 x -7.979638 8.7127651 0.04397704 y -8.393728 -0.1162452 7.92670007 Trimmed objective function: -11201.95 Selected restriction factor: 50 > (clus.c <- tclust(x, k=3, alpha=0.1, restr.fact=1, + restr="deter", equal.weights=TRUE)) * Results for TCLUST algorithm: * trim = 0.1, k = 3 Classification (trimmed points are indicated by 0 ): [1] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [38] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [75] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [112] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [149] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [186] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [223] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [260] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [297] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [334] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 3 2 3 3 2 3 3 1 [371] 3 3 0 3 3 3 3 2 3 2 2 3 3 3 3 3 1 2 3 3 3 3 3 3 0 3 2 3 3 3 3 3 2 0 3 3 3 [408] 3 3 2 3 3 3 3 3 3 2 3 3 3 3 1 2 3 3 3 3 3 2 3 2 3 1 2 3 3 3 3 3 2 3 2 2 1 [445] 2 0 3 3 3 3 3 1 3 0 3 3 2 3 2 2 3 2 3 3 2 2 2 3 3 2 2 3 3 2 2 2 3 2 2 3 2 [482] 2 3 3 3 3 3 3 0 2 3 3 3 2 3 2 3 3 3 2 3 3 3 3 3 3 3 3 2 2 3 3 3 0 3 2 3 3 [519] 3 3 3 3 1 3 3 1 3 3 3 3 3 3 3 3 3 2 2 3 2 3 2 2 3 2 3 2 3 2 3 3 3 2 3 3 2 [556] 3 2 3 2 3 3 3 1 3 3 3 2 3 3 0 3 2 1 3 2 3 3 0 2 3 3 2 3 2 0 3 3 3 0 3 3 2 [593] 1 3 3 2 2 2 3 3 3 3 3 2 3 2 3 2 3 3 3 3 1 3 3 3 3 3 3 2 3 1 3 3 3 3 3 3 3 [630] 3 3 2 3 3 2 3 3 3 3 2 3 0 3 0 3 2 2 3 3 3 3 0 3 3 3 3 3 3 3 3 3 3 0 3 3 3 [667] 3 3 3 3 3 3 0 2 0 3 2 2 2 3 3 1 3 3 3 3 3 2 2 3 3 0 2 2 2 3 3 2 2 3 3 3 2 [704] 2 2 1 3 2 2 3 0 3 3 2 3 2 3 2 3 3 3 2 3 0 2 2 3 2 0 3 3 2 3 2 3 2 2 2 2 1 [741] 2 3 3 2 0 3 3 3 3 3 3 3 3 3 3 1 3 3 2 3 2 3 3 3 2 3 3 2 3 3 3 3 3 3 2 2 3 [778] 3 3 0 2 3 3 2 3 3 3 0 3 3 2 1 3 2 2 3 3 2 3 3 2 2 3 3 2 3 2 3 3 2 3 0 0 3 [815] 3 2 3 3 3 3 2 3 3 0 0 2 3 2 3 3 3 3 2 2 1 3 2 3 2 2 2 3 2 2 0 2 2 3 3 3 3 [852] 3 3 2 3 1 2 3 3 3 3 3 2 0 1 3 2 2 3 3 3 3 3 2 3 3 3 3 3 2 2 2 3 2 3 3 3 3 [889] 3 3 2 2 3 2 3 3 2 0 3 2 3 3 2 2 3 2 3 2 2 0 3 2 2 3 3 2 3 3 3 3 0 3 3 3 2 [926] 2 3 2 2 3 1 3 2 3 2 3 3 3 3 2 0 3 2 3 3 3 3 2 2 2 3 2 3 2 2 3 2 2 3 1 0 2 [963] 3 2 2 3 3 2 2 3 3 3 3 0 3 3 3 2 3 0 0 0 3 1 0 3 1 3 3 2 3 2 2 3 3 3 3 3 3 [1000] 2 3 3 3 1 2 3 2 2 2 3 2 1 1 3 3 3 3 3 2 3 3 2 3 2 3 2 3 2 3 3 3 3 3 2 2 2 [1037] 2 3 3 2 3 3 3 3 2 2 3 2 1 3 2 3 3 3 0 2 3 2 2 3 3 3 3 3 2 3 3 0 3 3 2 3 3 [1074] 2 3 2 2 2 3 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1111] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1148] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1185] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1222] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1259] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1296] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1333] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1370] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1407] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1444] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1481] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 [1518] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1555] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1592] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1629] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1666] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1703] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 [1740] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1777] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 2 0 0 0 1 0 0 0 0 0 0 [1814] 0 0 0 0 1 0 0 0 0 0 0 0 2 0 1 0 0 0 1 2 0 0 0 0 0 2 0 1 0 2 0 0 2 0 0 0 0 [1851] 0 1 0 1 0 1 0 0 0 2 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 2 0 0 1 0 0 [1888] 0 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 1 0 2 0 0 0 0 0 1 2 0 0 2 [1925] 0 1 1 1 0 0 0 1 0 0 0 1 0 2 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 2 0 0 1 0 0 [1962] 0 0 2 0 0 0 0 0 0 2 0 0 0 1 0 0 0 1 0 0 0 0 0 2 0 1 0 0 0 0 0 0 0 0 0 0 0 [1999] 0 1 Means: C 1 C 2 C 3 x -7.965219 1.168752 10.076689 y -8.306009 7.206464 -1.901498 Trimmed objective function: -11651.92 Selected restriction factor: 1 > (clus.d <- tclust(x, k=3, alpha=0.1, restr.fact=50, + restr="eigen", equal.weights=FALSE)) * Results for TCLUST algorithm: * trim = 0.1, k = 3 Classification (trimmed points are indicated by 0 ): [1] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 [38] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 [75] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 [112] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 [149] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 [186] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 [223] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 [260] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 [297] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 [334] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 [371] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [408] 2 2 2 2 2 2 2 2 2 3 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 1 3 2 2 2 2 2 2 2 2 2 1 [445] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [482] 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 [519] 2 2 2 2 1 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 0 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [556] 2 2 2 3 2 2 2 1 2 2 2 2 2 2 2 2 2 1 2 2 2 2 0 2 2 2 2 2 2 0 2 2 2 2 2 2 2 [593] 1 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 [630] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [667] 2 2 2 2 2 2 2 2 0 2 2 2 3 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 [704] 2 2 1 2 2 2 2 0 2 2 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 2 2 2 2 2 1 [741] 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 0 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 [778] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 0 2 2 [815] 2 2 2 2 2 2 2 2 2 0 0 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [852] 2 2 2 2 2 3 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 [889] 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 0 2 2 2 3 [926] 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 [963] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 [1000] 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 0 2 2 2 2 2 2 2 2 2 0 2 2 [1037] 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 2 2 2 2 2 [1074] 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1111] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1148] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1185] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1222] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1259] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1296] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1333] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1370] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1407] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1444] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1481] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 [1518] 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1555] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1592] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1629] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1666] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1703] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 [1740] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [1777] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 [1814] 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 [1851] 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 [1888] 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 [1925] 0 1 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 [1962] 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 2 0 0 0 0 0 [1999] 0 0 Means: C 1 C 2 C 3 x -8.001393 8.6605632 0.04397704 y -8.360821 -0.1056621 7.92670007 Trimmed objective function: -11200.97 Selected restriction factor: 50 > > #--- EXAMPLE 4 ------------------------------------------ > data (swissbank) > set.seed(123) > # Two clusters and 8% trimming level > (clus <- tclust(swissbank, k = 2, alpha = 0.08, restr.fact = 50)) * Results for TCLUST algorithm: * trim = 0.08, k = 2 Classification (trimmed points are indicated by 0 ): [1] 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [38] 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 [75] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 1 [112] 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 2 2 2 2 2 2 2 2 2 0 [149] 2 2 2 2 2 2 2 2 2 2 2 0 0 0 2 2 2 2 0 0 2 2 0 2 2 2 2 2 2 2 2 0 2 0 2 2 2 [186] 2 0 2 2 2 2 0 2 0 2 2 2 2 2 2 Means: C 1 C 2 Length 215.001010 214.78000 Ht_Left 129.939394 130.26706 Ht_Right 129.724242 130.18353 IF_Lower 8.294949 10.84588 IF_Upper 10.191919 11.09882 Diagonal 141.483838 139.62941 Trimmed objective function: -542.7962 Selected restriction factor: 50 > > # Three clusters and 0% trimming level > (clus <- tclust(swissbank, k = 3, alpha = 0.0, restr.fact = 110)) * Results for TCLUST algorithm: * trim = 0, k = 3 Classification (trimmed points are indicated by 0 ): [1] 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [38] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 [75] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 [112] 2 2 2 2 3 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 3 [149] 2 2 2 2 2 2 2 2 2 2 2 3 3 3 2 2 2 2 3 3 2 2 3 2 2 2 2 2 2 2 2 3 2 3 2 2 2 [186] 2 3 2 2 2 2 3 2 3 2 2 2 2 2 2 Means: C 1 C 2 C 3 Length 214.97143 214.78095 215.022222 Ht_Left 129.92959 130.26429 130.500000 Ht_Right 129.70102 130.17976 130.305556 IF_Lower 8.30102 10.85714 8.777778 IF_Upper 10.16224 11.10833 11.172222 Diagonal 141.54184 139.62381 138.733333 Trimmed objective function: -627.1889 Selected restriction factor: 110 > > ##### Discriminant Factor Analysis for tclust Objects #################### > sig <- diag (2) > cen <- rep (1, 2) > x <- rbind(MASS::mvrnorm(360, cen * 0, sig), + MASS::mvrnorm(540, cen * 5, sig * 6 - 2), + MASS::mvrnorm(100, cen * 2.5, sig * 50) + ) > (clus.1 <- tclust(x, k = 2, alpha = 0.1, restr.fact = 12)) * Results for TCLUST algorithm: * trim = 0.1, k = 2 Classification (trimmed points are indicated by 0 ): [1] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 0 2 2 [38] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [75] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [112] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [149] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [186] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [223] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [260] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [297] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [334] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 0 1 [371] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [408] 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [445] 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 [482] 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [519] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [556] 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 [593] 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 [630] 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [667] 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [704] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [741] 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [778] 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 [815] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 [852] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [889] 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 [926] 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 1 2 0 0 1 0 1 0 0 0 0 [963] 2 0 2 0 1 1 2 0 0 1 1 0 0 2 0 0 0 2 0 2 0 0 0 0 1 0 0 0 1 0 0 0 0 0 2 0 0 [1000] 0 Means: C 1 C 2 X 1 4.944642 -0.04331001 X 2 5.125260 0.07786115 Trimmed objective function: -3764.373 Selected restriction factor: 12 > > (clus.2 <- tclust(x, k = 3, alpha = 0.1, restr.fact = 1)) * Results for TCLUST algorithm: * trim = 0.1, k = 3 Classification (trimmed points are indicated by 0 ): [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [38] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [75] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [112] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [149] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [186] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [223] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [260] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [297] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [334] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 3 3 2 3 3 3 2 0 2 [371] 3 3 3 2 3 3 2 3 2 2 3 2 3 2 3 2 2 3 0 2 3 3 2 2 3 2 3 2 3 2 2 3 3 2 2 2 3 [408] 2 3 3 3 2 3 2 2 3 3 3 0 3 2 2 3 2 2 3 3 3 2 3 2 3 3 2 3 2 3 3 3 3 3 3 2 2 [445] 2 2 0 0 3 3 2 3 2 3 2 3 2 3 2 3 2 3 2 2 2 2 3 3 2 2 3 2 3 3 3 0 2 3 2 2 3 [482] 2 3 1 3 2 2 3 2 2 2 0 3 2 2 3 3 2 2 3 3 3 2 2 3 0 3 3 3 3 3 2 3 3 3 2 3 2 [519] 3 2 3 3 2 2 2 3 0 3 2 2 2 2 3 3 3 2 2 3 2 2 2 3 2 0 3 3 2 2 2 2 3 2 2 3 3 [556] 3 0 3 3 0 0 2 3 3 3 2 3 2 3 3 3 2 2 2 3 3 2 2 0 3 3 3 2 3 2 3 2 0 3 2 2 3 [593] 2 3 0 2 3 3 2 2 2 3 3 2 2 2 2 2 3 2 3 2 2 3 2 3 0 3 3 3 2 3 3 2 2 3 2 0 2 [630] 2 2 2 2 3 3 3 3 3 2 0 2 3 2 3 2 2 2 3 3 3 3 3 2 3 2 2 3 2 2 2 2 2 2 3 2 2 [667] 2 3 2 3 3 3 3 3 0 2 3 0 3 2 2 2 2 3 3 2 3 2 2 3 3 2 2 2 3 3 2 3 3 3 3 3 3 [704] 3 3 0 2 2 3 3 3 2 2 3 3 3 3 2 3 3 2 3 2 3 3 2 1 3 3 2 3 3 3 2 3 2 2 2 2 3 [741] 2 3 2 2 3 2 2 2 2 3 2 2 0 2 2 2 3 2 3 2 2 3 2 2 3 3 3 3 3 3 2 2 3 3 2 2 0 [778] 2 3 2 2 2 3 2 3 1 3 3 3 2 2 3 3 3 3 2 3 3 2 2 2 2 2 3 2 2 3 0 2 2 2 2 3 2 [815] 2 2 2 0 2 2 2 2 2 2 2 3 3 2 2 2 3 3 3 2 2 3 2 2 2 3 3 2 2 2 2 2 3 1 2 2 3 [852] 2 2 2 3 2 2 3 0 2 2 2 2 3 3 2 3 2 3 2 2 2 3 2 3 3 3 2 3 2 2 3 3 3 2 3 2 3 [889] 3 2 2 3 2 2 3 3 2 2 2 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 2 0 0 3 0 0 0 0 0 0 [926] 0 0 0 0 0 0 0 0 0 0 0 2 0 0 2 0 0 3 0 0 0 2 2 0 0 0 2 1 0 0 2 0 1 1 0 0 0 [963] 1 0 1 0 2 2 1 0 0 2 3 0 0 1 0 0 0 1 0 1 0 0 0 0 2 0 0 0 2 0 0 0 1 0 1 0 0 [1000] 0 Means: C 1 C 2 C 3 X 1 -0.03094984 3.834955 6.218532 X 2 0.13148330 6.408800 3.631850 Trimmed objective function: -3852.612 Selected restriction factor: 1 > ## restr.fact and k are chosen improperly for pointing out the > ## difference in the plot of DiscrFact > > (dsc.1 <- DiscrFact(clus.1)) Mean overall discriminant factor: -21.96625 Mean discriminant factor per cluster: O 1 2 -16.01511 -29.03675 -13.27628 38 decisions are considered as doubtful > (dsc.2 <- DiscrFact(clus.2)) Mean overall discriminant factor: -10.89956 Mean discriminant factor per cluster: O 1 2 3 -18.330737 -17.615898 -4.741228 -4.521998 159 decisions are considered as doubtful > > > ########## Classification Trimmed Likelihood Curves ################### > > ## Do not run - it takes too long and can show differences on some > ## architectures due to the random numbers. > ## > #--- EXAMPLE 1 ------------------------------------------ > > if(FALSE) { + sig <- diag (2) + cen <- rep (1, 2) + x <- rbind(MASS::mvrnorm(108, cen * 0, sig), + MASS::mvrnorm(162, cen * 5, sig * 6 - 2), + MASS::mvrnorm(30, cen * 2.5, sig * 50) + ) + + (ctl <- ctlcurves(x, k = 1:4)) + } > > #--- EXAMPLE 2 ------------------------------------------ > if(FALSE) { + data (geyser2) + (ctl <- ctlcurves(geyser2, k = 1:5)) + } > > proc.time() user system elapsed 9.12 0.32 7.86