Implements the EM algorithm for a parameterized Gaussian mixture model, starting with the maximization step.

meE(data, z, prior=NULL, control=emControl(), Vinv=NULL, warn=NULL, ...)
meV(data, z, prior=NULL, control=emControl(), Vinv=NULL, warn=NULL, ...)
meX(data, prior = NULL, warn = NULL, ...)
meEII(data, z, prior=NULL, control=emControl(), Vinv=NULL, warn=NULL, ...)
meVII(data, z, prior=NULL, control=emControl(), Vinv=NULL, warn=NULL, ...)
meEEI(data, z, prior=NULL, control=emControl(), Vinv=NULL, warn=NULL, ...)
meVEI(data, z, prior=NULL, control=emControl(), Vinv=NULL, warn=NULL, ...)
meEVI(data, z, prior=NULL, control=emControl(), Vinv=NULL, warn=NULL, ...)
meVVI(data, z, prior=NULL, control=emControl(), Vinv=NULL, warn=NULL, ...)
meEEE(data, z, prior=NULL, control=emControl(), Vinv=NULL, warn=NULL, ...)
meVEE(data, z, prior=NULL, control=emControl(), Vinv=NULL, warn=NULL, ...)
meEVE(data, z, prior=NULL, control=emControl(), Vinv=NULL, warn=NULL, ...)
meVVE(data, z, prior=NULL, control=emControl(), Vinv=NULL, warn=NULL, ...)
meEEV(data, z, prior=NULL, control=emControl(), Vinv=NULL, warn=NULL, ...)
meVEV(data, z, prior=NULL, control=emControl(), Vinv=NULL, warn=NULL, ...)
meEVV(data, z, prior=NULL, control=emControl(), Vinv=NULL, warn=NULL, ...)
meVVV(data, z, prior=NULL, control=emControl(), Vinv=NULL, warn=NULL, ...)
meXII(data, prior = NULL, warn = NULL, ...)
meXXI(data, prior = NULL, warn = NULL, ...)
meXXX(data, prior = NULL, warn = NULL, ...)

Arguments

data

A numeric vector, matrix, or data frame of observations. Categorical variables are not allowed. If a matrix or data frame, rows correspond to observations and columns correspond to variables.

z

A matrix whose [i,k]th entry is the conditional probability of the ith observation belonging to the kth component of the mixture.

prior

Specification of a conjugate prior on the means and variances. The default assumes no prior.

control

A list of control parameters for EM. The defaults are set by the call emControl().

Vinv

An estimate of the reciprocal hypervolume of the data region, when the model is to include a noise term. Set to a negative value or zero if a noise term is desired, but an estimate is unavailable --- in that case function hypvol will be used to obtain the estimate. The default is not to assume a noise term in the model through the setting Vinv=NULL.

warn

A logical value indicating whether or not certain warnings (usually related to singularity) should be issued when the estimation fails. The default is given by mclust.options("warn").

...

Catches unused arguments in indirect or list calls via do.call.

Value

A list including the following components:

modelName

A character string identifying the model (same as the input argument).

z

A matrix whose [i,k]th entry is the conditional probability of the ith observation belonging to the kth component of the mixture.

parameters

pro

A vector whose kth component is the mixing proportion for the kth component of the mixture model. If the model includes a Poisson term for noise, there should be one more mixing proportion than the number of Gaussian components.

mean

The mean for each component. If there is more than one component, this is a matrix whose kth column is the mean of the kth component of the mixture model.

variance

A list of variance parameters for the model. The components of this list depend on the model specification. See the help file for mclustVariance for details.

Vinv

The estimate of the reciprocal hypervolume of the data region used in the computation when the input indicates the addition of a noise component to the model.

loglik

The log likelihood for the data in the mixture model.

Attributes:

"info" Information on the iteration.
"WARNING" An appropriate warning if problems are encountered in the computations.

See also

Examples

meVVV(data = iris[,-5], z = unmap(iris[,5]))
#> $modelName #> [1] "VVV" #> #> $prior #> NULL #> #> $n #> [1] 150 #> #> $d #> [1] 4 #> #> $G #> [1] 3 #> #> $z #> [,1] [,2] [,3] #> [1,] 1.000000e+00 1.340380e-44 1.861339e-34 #> [2,] 1.000000e+00 2.201405e-31 6.676298e-28 #> [3,] 1.000000e+00 1.896748e-36 1.102178e-29 #> [4,] 1.000000e+00 3.488647e-32 6.409600e-26 #> [5,] 1.000000e+00 4.393475e-47 7.745885e-35 #> [6,] 1.000000e+00 1.278514e-45 9.141846e-35 #> [7,] 1.000000e+00 1.725033e-36 1.528128e-28 #> [8,] 1.000000e+00 1.013323e-40 1.687173e-31 #> [9,] 1.000000e+00 6.118503e-28 6.204452e-24 #> [10,] 1.000000e+00 3.941874e-36 2.494386e-28 #> [11,] 1.000000e+00 4.448705e-50 1.929162e-37 #> [12,] 1.000000e+00 3.292550e-39 7.578657e-29 #> [13,] 1.000000e+00 2.565267e-34 5.452124e-28 #> [14,] 1.000000e+00 9.106612e-35 1.909555e-27 #> [15,] 1.000000e+00 3.125165e-63 1.593148e-47 #> [16,] 1.000000e+00 1.896077e-64 4.876149e-46 #> [17,] 1.000000e+00 5.596191e-50 1.021588e-39 #> [18,] 1.000000e+00 6.308031e-41 2.149597e-33 #> [19,] 1.000000e+00 2.370660e-47 1.329559e-36 #> [20,] 1.000000e+00 4.052147e-48 1.898553e-35 #> [21,] 1.000000e+00 3.784797e-39 8.212299e-31 #> [22,] 1.000000e+00 2.257628e-41 6.202577e-33 #> [23,] 1.000000e+00 6.419874e-48 7.020340e-35 #> [24,] 1.000000e+00 6.639759e-26 1.443374e-24 #> [25,] 1.000000e+00 7.175865e-36 2.846195e-24 #> [26,] 1.000000e+00 1.227836e-29 6.692266e-26 #> [27,] 1.000000e+00 1.658055e-32 6.789689e-28 #> [28,] 1.000000e+00 6.872462e-44 7.516822e-34 #> [29,] 1.000000e+00 4.516919e-42 6.057310e-34 #> [30,] 1.000000e+00 6.438483e-34 2.970895e-26 #> [31,] 1.000000e+00 9.491263e-32 6.566490e-26 #> [32,] 1.000000e+00 1.359677e-34 1.377621e-31 #> [33,] 1.000000e+00 1.807081e-66 1.923514e-41 #> [34,] 1.000000e+00 2.640245e-67 1.082266e-45 #> [35,] 1.000000e+00 6.866910e-33 9.278292e-28 #> [36,] 1.000000e+00 5.302053e-38 1.312420e-32 #> [37,] 1.000000e+00 3.083368e-46 5.787644e-38 #> [38,] 1.000000e+00 1.102357e-50 7.771785e-35 #> [39,] 1.000000e+00 8.786404e-31 1.026566e-25 #> [40,] 1.000000e+00 6.077402e-41 4.042171e-32 #> [41,] 1.000000e+00 1.877063e-41 1.037298e-33 #> [42,] 1.000000e+00 3.904478e-15 2.495765e-19 #> [43,] 1.000000e+00 2.822962e-35 2.367557e-27 #> [44,] 1.000000e+00 1.608040e-27 5.055302e-25 #> [45,] 1.000000e+00 3.082923e-39 2.560673e-28 #> [46,] 1.000000e+00 4.000241e-28 2.471836e-26 #> [47,] 1.000000e+00 2.987492e-51 3.564570e-35 #> [48,] 1.000000e+00 2.344766e-35 6.084895e-28 #> [49,] 1.000000e+00 7.194407e-50 8.191014e-37 #> [50,] 1.000000e+00 5.327318e-39 1.230925e-31 #> [51,] 3.032539e-92 9.997227e-01 2.773164e-04 #> [52,] 1.150038e-83 9.986288e-01 1.371182e-03 #> [53,] 1.797174e-104 9.944941e-01 5.505859e-03 #> [54,] 1.115012e-63 9.320826e-01 6.791742e-02 #> [55,] 4.881945e-92 9.705411e-01 2.945894e-02 #> [56,] 2.954459e-79 9.685784e-01 3.142162e-02 #> [57,] 8.550867e-94 9.865626e-01 1.343744e-02 #> [58,] 3.765759e-34 9.998441e-01 1.558591e-04 #> [59,] 1.336478e-86 9.986175e-01 1.382503e-03 #> [60,] 1.747387e-60 9.669572e-01 3.304278e-02 #> [61,] 3.021885e-42 9.982058e-01 1.794178e-03 #> [62,] 1.635100e-72 9.927992e-01 7.200848e-03 #> [63,] 4.079064e-61 9.991369e-01 8.630789e-04 #> [64,] 1.012713e-90 9.670966e-01 3.290342e-02 #> [65,] 7.559543e-47 9.997995e-01 2.005120e-04 #> [66,] 3.050597e-79 9.998767e-01 1.232632e-04 #> [67,] 1.489175e-83 9.246757e-01 7.532431e-02 #> [68,] 8.933659e-58 9.965960e-01 3.404046e-03 #> [69,] 3.934648e-92 2.925580e-03 9.970744e-01 #> [70,] 7.242827e-55 9.995024e-01 4.975685e-04 #> [71,] 7.707744e-106 5.397566e-02 9.460243e-01 #> [72,] 3.850909e-62 9.998443e-01 1.556841e-04 #> [73,] 4.713812e-107 4.325311e-02 9.567469e-01 #> [74,] 3.438056e-86 9.136402e-01 8.635976e-02 #> [75,] 1.817276e-73 9.997824e-01 2.176209e-04 #> [76,] 6.615926e-80 9.997244e-01 2.755883e-04 #> [77,] 3.767869e-100 9.879246e-01 1.207544e-02 #> [78,] 1.254096e-114 3.361880e-01 6.638120e-01 #> [79,] 4.845433e-85 9.646654e-01 3.533460e-02 #> [80,] 2.507098e-39 9.999864e-01 1.363479e-05 #> [81,] 3.878089e-52 9.995100e-01 4.900484e-04 #> [82,] 8.943244e-47 9.998196e-01 1.803552e-04 #> [83,] 4.112093e-56 9.998282e-01 1.717912e-04 #> [84,] 1.761949e-116 6.973648e-03 9.930264e-01 #> [85,] 1.873570e-83 8.494274e-01 1.505726e-01 #> [86,] 4.330051e-84 9.873428e-01 1.265717e-02 #> [87,] 1.827651e-94 9.975530e-01 2.447044e-03 #> [88,] 2.149510e-82 9.204475e-01 7.955247e-02 #> [89,] 1.777598e-62 9.985437e-01 1.456316e-03 #> [90,] 1.223594e-62 9.899298e-01 1.007019e-02 #> [91,] 1.057937e-73 9.412283e-01 5.877173e-02 #> [92,] 1.119977e-85 9.910150e-01 8.985033e-03 #> [93,] 1.917546e-60 9.995110e-01 4.889726e-04 #> [94,] 5.809300e-35 9.998832e-01 1.168043e-04 #> [95,] 1.439348e-68 9.937569e-01 6.243104e-03 #> [96,] 4.058872e-63 9.973306e-01 2.669419e-03 #> [97,] 3.805944e-67 9.979620e-01 2.037953e-03 #> [98,] 1.658725e-72 9.994971e-01 5.028802e-04 #> [99,] 3.308948e-28 9.999418e-01 5.818736e-05 #> [100,] 1.884676e-64 9.986048e-01 1.395245e-03 #> [101,] 3.010949e-203 5.530199e-17 1.000000e+00 #> [102,] 1.753436e-128 1.077534e-07 9.999999e-01 #> [103,] 3.185553e-181 2.653929e-09 1.000000e+00 #> [104,] 1.348868e-148 4.312002e-05 9.999569e-01 #> [105,] 9.131952e-178 7.830553e-12 1.000000e+00 #> [106,] 1.376312e-228 2.727688e-11 1.000000e+00 #> [107,] 3.275601e-95 1.168041e-05 9.999883e-01 #> [108,] 1.485822e-196 1.996513e-07 9.999998e-01 #> [109,] 1.096470e-166 5.615666e-09 1.000000e+00 #> [110,] 1.838986e-207 5.153929e-13 1.000000e+00 #> [111,] 1.407473e-129 6.017637e-05 9.999398e-01 #> [112,] 7.916908e-140 1.650636e-07 9.999998e-01 #> [113,] 9.136916e-158 5.957065e-09 1.000000e+00 #> [114,] 1.956477e-130 2.233857e-12 1.000000e+00 #> [115,] 2.022253e-156 3.404704e-22 1.000000e+00 #> [116,] 9.392240e-156 1.026315e-12 1.000000e+00 #> [117,] 6.602144e-143 7.801735e-04 9.992198e-01 #> [118,] 2.748870e-228 5.421043e-06 9.999946e-01 #> [119,] 7.429637e-265 3.265440e-22 1.000000e+00 #> [120,] 1.370738e-113 5.282640e-05 9.999472e-01 #> [121,] 4.351788e-177 4.577282e-12 1.000000e+00 #> [122,] 1.054301e-123 3.279642e-09 1.000000e+00 #> [123,] 1.162139e-235 1.885723e-12 1.000000e+00 #> [124,] 6.201270e-116 5.216528e-05 9.999478e-01 #> [125,] 1.891890e-164 2.001713e-06 9.999980e-01 #> [126,] 1.323823e-172 7.420387e-04 9.992580e-01 #> [127,] 4.617100e-110 3.526679e-04 9.996473e-01 #> [128,] 2.794272e-112 5.946968e-03 9.940530e-01 #> [129,] 1.280855e-163 1.922717e-11 1.000000e+00 #> [130,] 3.061896e-157 4.726577e-03 9.952734e-01 #> [131,] 6.533587e-190 3.218376e-08 1.000000e+00 #> [132,] 4.771065e-201 6.006480e-03 9.939935e-01 #> [133,] 6.908783e-169 3.468057e-14 1.000000e+00 #> [134,] 2.744809e-113 2.199157e-01 7.800843e-01 #> [135,] 3.663047e-138 3.079362e-05 9.999692e-01 #> [136,] 2.609736e-207 1.978334e-14 1.000000e+00 #> [137,] 7.627542e-175 3.636807e-13 1.000000e+00 #> [138,] 2.136992e-141 2.459565e-03 9.975404e-01 #> [139,] 1.018504e-107 5.760480e-03 9.942395e-01 #> [140,] 8.410204e-152 7.863015e-08 9.999999e-01 #> [141,] 2.436458e-178 1.184065e-16 1.000000e+00 #> [142,] 2.086983e-148 3.695558e-14 1.000000e+00 #> [143,] 1.753436e-128 1.077534e-07 9.999999e-01 #> [144,] 1.276099e-187 4.205111e-12 1.000000e+00 #> [145,] 9.196112e-188 2.313054e-17 1.000000e+00 #> [146,] 1.126391e-153 3.179633e-15 1.000000e+00 #> [147,] 3.395534e-127 2.310806e-09 1.000000e+00 #> [148,] 1.300448e-136 1.192490e-06 9.999988e-01 #> [149,] 1.141901e-158 1.374617e-10 1.000000e+00 #> [150,] 2.488135e-121 1.722216e-03 9.982778e-01 #> #> $parameters #> $parameters$pro #> [1] 0.3333333 0.2995864 0.3670803 #> #> $parameters$mean #> [,1] [,2] [,3] #> Sepal.Length 5.006 5.915306 6.544949 #> Sepal.Width 3.428 2.777875 2.948818 #> Petal.Length 1.462 4.202227 5.480372 #> Petal.Width 0.246 1.297229 1.985127 #> #> $parameters$variance #> $parameters$variance$modelName #> [1] "VVV" #> #> $parameters$variance$d #> [1] 4 #> #> $parameters$variance$G #> [1] 3 #> #> $parameters$variance$sigma #> , , 1 #> #> Sepal.Length Sepal.Width Petal.Length Petal.Width #> Sepal.Length 0.121764 0.097232 0.016028 0.010124 #> Sepal.Width 0.097232 0.140816 0.011464 0.009112 #> Petal.Length 0.016028 0.011464 0.029556 0.005948 #> Petal.Width 0.010124 0.009112 0.005948 0.010884 #> #> , , 2 #> #> Sepal.Length Sepal.Width Petal.Length Petal.Width #> Sepal.Length 0.27533588 0.09687192 0.18477153 0.05444692 #> Sepal.Width 0.09687192 0.09262785 0.09111654 0.04299505 #> Petal.Length 0.18477153 0.09111654 0.20089896 0.06109388 #> Petal.Width 0.05444692 0.04299505 0.06109388 0.03205203 #> #> , , 3 #> #> Sepal.Length Sepal.Width Petal.Length Petal.Width #> Sepal.Length 0.38707068 0.09220736 0.30268373 0.06147257 #> Sepal.Width 0.09220736 0.11034902 0.08419484 0.05595573 #> Petal.Length 0.30268373 0.08419484 0.32736949 0.07416052 #> Petal.Width 0.06147257 0.05595573 0.07416052 0.08559833 #> #> #> $parameters$variance$cholsigma #> , , 1 #> #> Sepal.Length Sepal.Width Petal.Length Petal.Width #> Sepal.Length -0.348947 -0.2786440 -0.045932479 -0.029013003 #> Sepal.Width 0.000000 0.2513434 -0.005310709 0.004088826 #> Petal.Length 0.000000 0.0000000 -0.165583827 -0.028004398 #> Petal.Width 0.000000 0.0000000 0.000000000 0.096131581 #> #> , , 2 #> #> Sepal.Length Sepal.Width Petal.Length Petal.Width #> Sepal.Length 0.5247246 0.1846148 0.3521305 0.10376286 #> Sepal.Width 0.0000000 -0.2419612 -0.1079018 -0.09852359 #> Petal.Length 0.0000000 0.0000000 0.2554609 0.05450909 #> Petal.Width 0.0000000 0.0000000 0.0000000 -0.09277479 #> #> , , 3 #> #> Sepal.Length Sepal.Width Petal.Length Petal.Width #> Sepal.Length -0.62215 -0.1482076 -0.48651244 -0.09880666 #> Sepal.Width 0.00000 -0.2972937 -0.04066688 -0.13895968 #> Petal.Length 0.00000 0.0000000 -0.29836444 -0.06850276 #> Petal.Width 0.00000 0.0000000 0.00000000 -0.22766895 #> #> #> #> $parameters$Vinv #> NULL #> #> #> $control #> $control$eps #> [1] 2.220446e-16 #> #> $control$tol #> [1] 1.000000e-05 1.490116e-08 #> #> $control$itmax #> [1] 2147483647 2147483647 #> #> $control$equalPro #> [1] FALSE #> #> #> $loglik #> [1] -180.1859 #> #> attr(,"info") #> iterations error #> 1.100000e+01 4.438788e-06 #> attr(,"returnCode") #> [1] 0