R Under development (unstable) (2023-12-04 r85659 ucrt) -- "Unsuffered Consequences" Copyright (C) 2023 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::03.09.2016 - this will render the output independent > ## from the version of the package > suppressPackageStartupMessages(library(tclust)) > > require(tclust) > require(mvtnorm) Loading required package: mvtnorm > #--- EXAMPLE 1 ------------------------------------------ > > set.seed(123) > sig <- diag (2) > cen <- rep (1,2) > x <- rbind(mvtnorm::rmvnorm(360, cen * 0, sig), + mvtnorm::rmvnorm(540, cen * 5, sig * 6 - 2), + mvtnorm::rmvnorm(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 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 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 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 0 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 0 [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 0 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 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 0 1 [408] 1 1 1 1 1 1 1 1 1 1 1 1 1 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 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 [482] 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 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 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 [556] 1 0 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 [593] 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 [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 0 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 0 1 1 1 1 1 0 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 0 1 1 1 1 1 1 0 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] 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 1 1 [889] 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 0 0 0 2 0 1 0 0 1 0 1 0 0 1 0 0 0 1 0 0 0 [926] 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 2 1 0 0 0 0 0 0 1 0 0 0 0 0 [963] 0 1 0 0 0 0 0 0 0 0 1 2 0 1 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 [1000] 0 Means: C 1 C 2 X 1 4.952001 0.08665503 X 2 5.153003 -0.08689752 Trimmed objective function: -3750.043 82% of iterations converged successfully. > > > # 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 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 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 3 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 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 1 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 3 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 3 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 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 1 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] 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 [889] 1 1 1 1 1 1 1 1 1 1 1 1 3 1 3 1 3 3 1 2 1 1 3 3 1 3 1 2 3 1 3 3 3 1 3 3 3 [926] 3 3 1 3 3 1 3 1 3 3 3 3 1 3 1 3 3 1 3 3 3 1 3 2 1 3 3 3 3 3 3 1 1 3 1 3 3 [963] 1 1 3 1 3 3 3 3 3 1 1 2 3 1 2 3 1 3 3 1 3 3 3 3 3 3 3 3 3 3 1 3 3 3 3 3 1 [1000] 1 Means: C 1 C 2 C 3 X 1 4.964561 0.08222926 2.240668 X 2 5.155258 -0.07771533 2.274133 Trimmed objective function: -4733.24 76% of iterations converged successfully. Warning message: In .tclust.warn(O, O$ret) : The result is artificially constrained due to restr.fact = 100. > > > #--- EXAMPLE 3 ------------------------------------------ > set.seed(123) > data (M5data) > x <- M5data[, 1:2] > > (clus.a <- tclust (x, k = 3, alpha = 0.1, restr.fact = 1, + restr = "eigen", equal.weights = TRUE, warnings = 1)) * 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 3 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 3 3 3 3 2 1 2 3 3 3 3 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 2 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 3 3 2 1 3 2 3 3 0 2 3 3 2 3 3 0 3 3 3 3 1 3 3 [593] 1 3 3 3 2 2 3 3 3 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 3 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 3 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 2 3 2 3 3 3 3 0 3 3 3 2 [926] 3 3 3 2 3 1 3 2 3 2 3 3 3 3 2 3 1 3 3 3 3 3 3 3 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 2 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 0 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 0 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 -7.777440 0.3887642 10.46422 y -8.496549 7.3181737 -1.10711 Trimmed objective function: -9899.122 98% of iterations converged successfully. > (clus.b <- tclust (x, k = 3, alpha = 0.1, restr.fact = 1, + equal.weights = TRUE, warnings = 1)) * 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 3 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 3 3 3 3 2 1 2 3 3 3 3 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 2 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 3 3 2 1 3 2 3 3 0 2 3 3 2 3 3 0 3 3 3 3 1 3 3 [593] 1 3 3 3 2 2 3 3 3 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 3 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 3 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 2 3 2 3 3 3 3 0 3 3 3 2 [926] 3 3 3 2 3 1 3 2 3 2 3 3 3 3 2 3 1 3 3 3 3 3 3 3 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 2 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 0 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 0 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 -7.777440 0.3887642 10.46422 y -8.496549 7.3181737 -1.10711 Trimmed objective function: -9899.122 94% of iterations converged successfully. > (clus.c <- tclust (x, k = 3, alpha = 0.1, restr.fact = 1, + restr = "deter", equal.weights = TRUE, iter.max = 100, + warnings = 1)) * 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 3 [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 3 3 3 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 3 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 3 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 3 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 3 2 3 3 1 3 3 3 3 3 2 2 3 3 0 3 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 3 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 3 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 3 2 0 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 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 3 3 2 3 3 3 3 2 3 2 3 2 3 2 2 3 2 2 3 1 0 2 [963] 3 2 2 3 3 3 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 3 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 3 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 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 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 0 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 0 Means: C 1 C 2 C 3 x -7.953569 1.038084 9.960540 y -8.346524 7.294284 -1.867793 Trimmed objective function: -9718.277 100% of iterations converged successfully. > (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 1 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 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 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 -8.007264 8.6605632 0.04397704 y -8.364590 -0.1056621 7.92670007 Trimmed objective function: -11200.97 66% of iterations converged successfully. > > #--- EXAMPLE 4 ------------------------------------------ > set.seed(123) > data (swissbank) > # 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 92% of iterations converged successfully. > > # 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] 1 1 1 1 1 1 1 1 1 1 1 1 1 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 2 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 214.969697 214.78000 215.05625 Ht_Left 129.940404 130.26706 130.46875 Ht_Right 129.715152 130.18353 130.24375 IF_Lower 8.308081 10.84588 8.69375 IF_Upper 10.157576 11.09882 11.31875 Diagonal 141.536364 139.62941 138.50625 Trimmed objective function: -628.3746 96% of iterations converged successfully. > > > ##### Discriminant Factor Analysis for tclust Objects ############################ > sig <- diag (2) > cen <- rep (1, 2) > x <- rbind(mvtnorm::rmvnorm(360, cen * 0, sig), + mvtnorm::rmvnorm(540, cen * 5, sig * 6 - 2), + mvtnorm::rmvnorm(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 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] 0 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 1 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 0 2 2 2 0 2 2 2 2 2 2 2 2 2 2 2 [186] 2 2 2 0 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 [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 1 1 1 1 1 1 1 1 1 1 [371] 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 1 1 0 1 1 1 1 [408] 1 1 1 1 1 1 1 1 1 1 1 1 1 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 1 1 1 1 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 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 0 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 0 0 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 0 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 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 [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 1 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 0 1 0 1 1 1 1 0 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 0 0 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 2 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 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0 [926] 0 1 0 0 0 2 1 0 1 0 0 0 0 0 0 0 0 1 2 0 0 2 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 [963] 1 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 2 0 0 1 0 0 0 0 0 1 0 0 0 1 [1000] 0 Means: C 1 C 2 X 1 5.042155 -0.0003362897 X 2 4.898478 0.0403511802 Trimmed objective function: -3779.935 82% of iterations converged successfully. > > (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] 2 2 2 2 2 2 2 2 2 2 2 2 2 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 1 1 1 1 1 1 3 1 1 1 [371] 1 1 3 1 3 1 0 1 1 1 1 1 1 1 1 1 1 1 3 1 1 0 1 1 3 3 3 1 1 1 1 1 0 1 3 1 1 [408] 3 1 3 1 1 1 1 1 3 1 1 1 1 1 3 1 3 3 3 3 0 3 3 1 1 3 1 3 1 1 3 0 1 1 1 1 1 [445] 1 1 1 3 3 1 1 3 1 1 3 1 1 3 3 1 1 1 2 3 1 1 3 3 3 0 1 1 3 1 1 3 1 3 1 3 1 [482] 1 1 1 3 1 3 1 1 3 1 1 3 1 1 3 0 1 3 1 1 1 1 3 3 1 1 1 3 1 1 1 1 3 1 3 1 1 [519] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 3 3 1 0 1 1 1 0 1 3 1 1 3 1 1 1 3 3 3 1 [556] 1 1 1 1 1 1 3 1 3 3 1 1 1 1 1 3 1 1 0 2 1 1 1 1 1 3 1 1 1 1 3 1 3 1 1 3 1 [593] 1 1 1 3 3 1 1 1 1 3 1 1 1 3 1 1 3 1 1 1 1 1 1 3 3 1 3 1 3 1 3 1 1 1 1 1 1 [630] 1 2 3 3 1 1 3 3 1 3 1 1 1 1 3 0 1 1 3 1 1 1 1 1 3 1 3 1 1 1 1 3 1 1 1 1 1 [667] 1 1 1 1 3 1 0 1 0 1 3 1 1 3 1 1 0 1 1 1 1 1 3 1 1 1 1 1 1 1 1 3 1 1 1 1 1 [704] 1 1 1 3 1 1 1 1 3 1 1 3 0 1 3 3 1 1 1 1 1 1 1 0 1 3 1 3 1 1 1 1 3 1 1 1 1 [741] 1 1 1 1 3 1 3 1 1 1 1 1 3 1 3 1 1 3 1 1 1 1 1 3 1 1 1 1 3 1 1 1 1 3 3 1 1 [778] 1 3 1 1 1 1 3 3 3 0 1 1 1 1 1 1 0 1 3 1 3 0 3 0 3 1 3 1 0 1 2 3 1 3 0 1 3 [815] 3 3 1 3 3 3 1 1 1 1 1 3 1 1 1 1 1 3 1 0 3 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 [852] 1 1 1 1 1 1 1 1 3 1 1 1 1 3 1 3 1 1 1 1 1 1 2 1 1 0 1 1 1 3 3 1 1 1 1 1 1 [889] 3 1 3 3 1 3 1 1 1 1 1 1 0 0 0 0 0 0 3 0 0 0 0 0 0 1 0 3 0 0 0 0 0 3 0 3 0 [926] 0 2 0 0 0 2 3 0 3 0 0 0 0 0 0 0 0 3 2 0 0 2 0 0 0 0 0 1 0 2 3 0 0 0 0 0 0 [963] 3 2 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 2 0 0 3 0 0 0 0 0 1 0 0 0 1 [1000] 0 Means: C 1 C 2 C 3 X 1 4.384051 0.04308565 7.070885 X 2 5.691407 0.06814548 2.632401 Trimmed objective function: -3887.154 86% of iterations converged successfully. Warning message: In .tclust.warn(O, O$ret) : The result is artificially constrained due to restr.fact = 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: -23.02189 Mean discriminant factor per cluster: O 1 2 -14.22857 -31.63610 -12.43650 28 decisions are considered as doubtful > (dsc.2 <- DiscrFact (clus.2)) Mean overall discriminant factor: -10.54408 Mean discriminant factor per cluster: O 1 2 3 -17.802437 -6.045219 -15.682364 -4.226602 133 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. > ## > if(FALSE) + { + #--- EXAMPLE 1 ------------------------------------------ + + sig <- diag (2) + cen <- rep (1, 2) + x <- rbind(mvtnorm::rmvnorm(108, cen * 0, sig), + mvtnorm::rmvnorm(162, cen * 5, sig * 6 - 2), + mvtnorm::rmvnorm(30, cen * 2.5, sig * 50) + ) + + (ctl <- ctlcurves (x, k = 1:4)) + + } > > #--- EXAMPLE 2 ------------------------------------------ > > data (geyser2) > (ctl <- ctlcurves (geyser2, k = 1:5)) Depending on arguments x, k and alpha, this function needs some time to compute. (Remove this message by setting "trace = 0") Computed 30 solutions (chosen restr.fact = 50). alpha k 0 0.04 0.08 0.12 0.16 0.2 1 2 3 4 * 5 k *k *k (*) Identified 3 artificially restricted solutions. (k) Identified 3 solutions with very small/dropped clusters. > > proc.time() user system elapsed 3.92 0.06 3.96