E-step for parameterized Gaussian mixture models.
estep.RdImplements the expectation step of EM algorithm for parameterized Gaussian mixture models.
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.
- modelName
A character string indicating the model. The help file for
mclustModelNamesdescribes the available models.- parameters
A names list giving the parameters of the model. The components are as follows:
proMixing proportions for the components of the mixture. If the model includes a Poisson term for noise, there should be one more mixing proportion than the number of Gaussian components.
meanThe 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.
varianceA list of variance parameters for the model. The components of this list depend on the model specification. See the help file for
mclustVariancefor details.VinvAn estimate of the reciprocal hypervolume of the data region. If set to NULL or a negative value, the default is determined by applying function
hypvolto the data. Used only whenproincludes an additional mixing proportion for a noise component.
- warn
A logical value indicating whether or not a warning should be issued when computations fail. The default is
warn=FALSE.- ...
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
The input parameters.
- loglik
The log-likelihood for the data in the mixture model.
- Attributes
"WARNING": an appropriate warning if problems are encountered in the computations.
See also
estepE, ...,
estepVVV,
em,
mstep,
mclust.options
mclustVariance
Examples
# \donttest{
msEst <- mstep(modelName = "VVV", data = iris[,-5], z = unmap(iris[,5]))
names(msEst)
#> [1] "modelName" "prior" "n" "d" "G"
#> [6] "z" "parameters"
estep(modelName = msEst$modelName, data = iris[,-5],
parameters = msEst$parameters)# }
#> $modelName
#> [1] "VVV"
#>
#> $n
#> [1] 150
#>
#> $d
#> [1] 4
#>
#> $G
#> [1] 3
#>
#> $z
#> [,1] [,2] [,3]
#> [1,] 1.000000e+00 1.531298e-26 4.631660e-42
#> [2,] 1.000000e+00 3.341913e-19 2.782813e-35
#> [3,] 1.000000e+00 5.970550e-22 6.659211e-37
#> [4,] 1.000000e+00 3.629271e-19 2.069429e-32
#> [5,] 1.000000e+00 9.920165e-28 3.097629e-42
#> [6,] 1.000000e+00 4.473024e-27 2.035241e-41
#> [7,] 1.000000e+00 1.023721e-21 5.400089e-35
#> [8,] 1.000000e+00 3.951048e-24 1.188427e-38
#> [9,] 1.000000e+00 6.348304e-17 2.222620e-30
#> [10,] 1.000000e+00 3.282086e-21 1.202430e-35
#> [11,] 1.000000e+00 1.619962e-29 2.944164e-45
#> [12,] 1.000000e+00 7.891556e-23 2.286635e-35
#> [13,] 1.000000e+00 2.172110e-20 1.922311e-35
#> [14,] 1.000000e+00 1.830223e-20 8.325932e-35
#> [15,] 1.000000e+00 1.347076e-37 5.789535e-57
#> [16,] 1.000000e+00 2.707999e-38 1.150952e-53
#> [17,] 1.000000e+00 1.194101e-30 1.742225e-47
#> [18,] 1.000000e+00 6.948699e-25 1.025185e-40
#> [19,] 1.000000e+00 5.504880e-28 4.538366e-44
#> [20,] 1.000000e+00 2.069605e-28 1.972755e-42
#> [21,] 1.000000e+00 7.479277e-23 3.988370e-38
#> [22,] 1.000000e+00 5.032153e-25 1.181412e-39
#> [23,] 1.000000e+00 7.912651e-28 1.053516e-42
#> [24,] 1.000000e+00 5.071504e-16 1.408708e-30
#> [25,] 1.000000e+00 5.079161e-20 5.211806e-30
#> [26,] 1.000000e+00 9.462960e-18 6.946195e-33
#> [27,] 1.000000e+00 8.007503e-20 3.118746e-34
#> [28,] 1.000000e+00 5.238689e-26 2.393533e-41
#> [29,] 1.000000e+00 2.981616e-25 9.025368e-42
#> [30,] 1.000000e+00 6.305750e-20 1.248894e-32
#> [31,] 1.000000e+00 7.474435e-19 1.745401e-32
#> [32,] 1.000000e+00 1.143232e-21 6.109943e-39
#> [33,] 1.000000e+00 1.712290e-37 3.848459e-49
#> [34,] 1.000000e+00 4.783083e-39 6.903779e-54
#> [35,] 1.000000e+00 8.338572e-20 8.305829e-35
#> [36,] 1.000000e+00 2.989188e-23 1.006538e-40
#> [37,] 1.000000e+00 6.887941e-28 1.135265e-46
#> [38,] 1.000000e+00 3.867251e-29 2.455633e-42
#> [39,] 1.000000e+00 1.417061e-18 2.036480e-32
#> [40,] 1.000000e+00 2.473260e-24 1.859072e-39
#> [41,] 1.000000e+00 3.020988e-25 3.902559e-41
#> [42,] 1.000000e+00 2.560802e-10 2.997338e-26
#> [43,] 1.000000e+00 7.792261e-21 5.097178e-34
#> [44,] 1.000000e+00 4.049190e-17 8.149856e-31
#> [45,] 1.000000e+00 2.350953e-22 5.235460e-34
#> [46,] 1.000000e+00 1.246886e-17 3.033197e-33
#> [47,] 1.000000e+00 1.560647e-29 3.679695e-42
#> [48,] 1.000000e+00 4.767026e-21 1.084422e-34
#> [49,] 1.000000e+00 2.532098e-29 1.912018e-44
#> [50,] 1.000000e+00 1.942649e-23 4.162666e-39
#> [51,] 4.427741e-92 9.999635e-01 3.651562e-05
#> [52,] 1.492993e-83 9.996963e-01 3.036808e-04
#> [53,] 2.323794e-104 9.985558e-01 1.444189e-03
#> [54,] 3.820558e-64 9.974857e-01 2.514348e-03
#> [55,] 2.529967e-92 9.975986e-01 2.401407e-03
#> [56,] 3.438709e-79 9.895919e-01 1.040812e-02
#> [57,] 9.128977e-94 9.951481e-01 4.851888e-03
#> [58,] 5.148001e-34 9.999951e-01 4.872649e-06
#> [59,] 1.880560e-86 9.998169e-01 1.830687e-04
#> [60,] 1.542139e-60 9.941598e-01 5.840159e-03
#> [61,] 2.992578e-42 9.999480e-01 5.203024e-05
#> [62,] 1.708982e-72 9.987050e-01 1.295008e-03
#> [63,] 3.769219e-61 9.999887e-01 1.133958e-05
#> [64,] 1.085898e-90 9.892610e-01 1.073895e-02
#> [65,] 9.208897e-47 9.999914e-01 8.648146e-06
#> [66,] 4.247145e-79 9.999894e-01 1.063020e-05
#> [67,] 1.205637e-83 9.747235e-01 2.527649e-02
#> [68,] 6.402952e-58 9.998866e-01 1.133547e-04
#> [69,] 5.514687e-92 8.146259e-01 1.853741e-01
#> [70,] 9.644338e-55 9.999704e-01 2.957058e-05
#> [71,] 8.144832e-106 3.284513e-01 6.715487e-01
#> [72,] 5.073314e-62 9.999918e-01 8.225435e-06
#> [73,] 4.134551e-107 6.987624e-01 3.012376e-01
#> [74,] 4.817238e-86 9.735004e-01 2.649958e-02
#> [75,] 2.448343e-73 9.999831e-01 1.685110e-05
#> [76,] 9.080831e-80 9.999734e-01 2.661419e-05
#> [77,] 3.308249e-100 9.986285e-01 1.371485e-03
#> [78,] 6.162406e-115 8.630616e-01 1.369384e-01
#> [79,] 3.606949e-85 9.927366e-01 7.263396e-03
#> [80,] 1.827587e-39 9.999999e-01 6.520517e-08
#> [81,] 5.062737e-52 9.999754e-01 2.463634e-05
#> [82,] 1.118752e-46 9.999953e-01 4.706239e-06
#> [83,] 5.410273e-56 9.999908e-01 9.231469e-06
#> [84,] 1.930587e-116 1.473576e-01 8.526424e-01
#> [85,] 1.417725e-83 9.454001e-01 5.459993e-02
#> [86,] 4.017430e-84 9.963529e-01 3.647118e-03
#> [87,] 2.333373e-94 9.994678e-01 5.322498e-04
#> [88,] 4.416063e-83 9.990213e-01 9.787027e-04
#> [89,] 1.824762e-62 9.997972e-01 2.027893e-04
#> [90,] 9.617210e-63 9.990635e-01 9.364656e-04
#> [91,] 1.267274e-73 9.817631e-01 1.823689e-02
#> [92,] 1.366483e-85 9.972534e-01 2.746587e-03
#> [93,] 2.483385e-60 9.999664e-01 3.362787e-05
#> [94,] 8.736184e-35 9.999970e-01 2.980291e-06
#> [95,] 1.632088e-68 9.987856e-01 1.214423e-03
#> [96,] 3.007660e-63 9.997647e-01 2.352778e-04
#> [97,] 4.649893e-67 9.996298e-01 3.702063e-04
#> [98,] 2.213572e-72 9.999435e-01 5.649197e-05
#> [99,] 4.667070e-28 9.999995e-01 5.312475e-07
#> [100,] 2.415298e-64 9.997932e-01 2.068042e-04
#> [101,] 5.431127e-203 2.210439e-09 1.000000e+00
#> [102,] 1.642385e-128 3.822927e-04 9.996177e-01
#> [103,] 2.935239e-181 4.340914e-05 9.999566e-01
#> [104,] 1.281149e-148 5.160913e-03 9.948391e-01
#> [105,] 8.739248e-178 1.967500e-06 9.999980e-01
#> [106,] 1.169524e-228 1.454416e-06 9.999985e-01
#> [107,] 3.059959e-95 3.396516e-03 9.966035e-01
#> [108,] 1.199215e-196 3.541718e-05 9.999646e-01
#> [109,] 1.063382e-166 1.059411e-04 9.998941e-01
#> [110,] 1.856330e-207 4.601010e-08 1.000000e+00
#> [111,] 1.697668e-129 5.349751e-03 9.946502e-01
#> [112,] 8.800846e-140 8.088253e-04 9.991912e-01
#> [113,] 9.146951e-158 5.195774e-05 9.999480e-01
#> [114,] 1.691089e-130 1.177827e-06 9.999988e-01
#> [115,] 1.529536e-156 1.686232e-13 1.000000e+00
#> [116,] 8.247834e-156 4.558397e-08 1.000000e+00
#> [117,] 6.788928e-143 3.037798e-02 9.696220e-01
#> [118,] 2.930198e-228 2.149645e-04 9.997850e-01
#> [119,] 9.079687e-265 8.879452e-11 1.000000e+00
#> [120,] 2.303150e-113 3.790989e-02 9.620901e-01
#> [121,] 3.843003e-177 3.783066e-07 9.999996e-01
#> [122,] 9.595809e-124 1.976052e-05 9.999802e-01
#> [123,] 9.581470e-236 2.100380e-07 9.999998e-01
#> [124,] 1.065022e-115 2.567755e-02 9.743225e-01
#> [125,] 1.850244e-164 7.609181e-04 9.992391e-01
#> [126,] 1.221324e-172 6.521046e-03 9.934790e-01
#> [127,] 7.743971e-110 5.265561e-02 9.473444e-01
#> [128,] 3.432568e-112 1.442112e-01 8.557888e-01
#> [129,] 1.151967e-163 4.572452e-06 9.999954e-01
#> [130,] 3.706143e-157 1.797263e-02 9.820274e-01
#> [131,] 6.470511e-190 1.243961e-04 9.998756e-01
#> [132,] 3.730831e-201 8.236967e-03 9.917630e-01
#> [133,] 6.157428e-169 1.310745e-07 9.999999e-01
#> [134,] 2.506178e-113 6.022880e-01 3.977120e-01
#> [135,] 3.266558e-138 1.780195e-04 9.998220e-01
#> [136,] 2.569119e-207 8.589823e-08 9.999999e-01
#> [137,] 8.687854e-175 3.751507e-08 1.000000e+00
#> [138,] 2.183741e-141 4.651619e-02 9.534838e-01
#> [139,] 1.312185e-107 1.339905e-01 8.660095e-01
#> [140,] 9.141262e-152 1.555449e-04 9.998445e-01
#> [141,] 2.098453e-178 6.704480e-10 1.000000e+00
#> [142,] 2.368114e-148 4.059502e-09 1.000000e+00
#> [143,] 1.642385e-128 3.822927e-04 9.996177e-01
#> [144,] 1.224376e-187 6.897983e-07 9.999993e-01
#> [145,] 8.404700e-188 1.144473e-10 1.000000e+00
#> [146,] 1.099698e-153 2.083183e-09 1.000000e+00
#> [147,] 5.133200e-127 1.360843e-04 9.998639e-01
#> [148,] 1.472988e-136 9.106700e-04 9.990893e-01
#> [149,] 1.208779e-158 8.694131e-07 9.999991e-01
#> [150,] 2.673436e-121 5.663609e-02 9.433639e-01
#>
#> $parameters
#> $parameters$pro
#> [1] 0.3333333 0.3333333 0.3333333
#>
#> $parameters$mean
#> [,1] [,2] [,3]
#> Sepal.Length 5.006 5.936 6.588
#> Sepal.Width 3.428 2.770 2.974
#> Petal.Length 1.462 4.260 5.552
#> Petal.Width 0.246 1.326 2.026
#>
#> $parameters$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 0.261104 0.08348 0.17924 0.054664
#> Sepal.Width 0.083480 0.09650 0.08100 0.040380
#> Petal.Length 0.179240 0.08100 0.21640 0.071640
#> Petal.Width 0.054664 0.04038 0.07164 0.038324
#>
#> , , 3
#>
#> Sepal.Length Sepal.Width Petal.Length Petal.Width
#> Sepal.Length 0.396256 0.091888 0.297224 0.048112
#> Sepal.Width 0.091888 0.101924 0.069952 0.046676
#> Petal.Length 0.297224 0.069952 0.298496 0.047848
#> Petal.Width 0.048112 0.046676 0.047848 0.073924
#>
#>
#> $parameters$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 0.5109834 0.1633713 0.35077463 0.10697804
#> Sepal.Width 0.0000000 -0.2642155 -0.08967492 -0.08668251
#> Petal.Length 0.0000000 0.0000000 0.29208829 0.09018359
#> Petal.Width 0.0000000 0.0000000 0.00000000 -0.10598473
#>
#> , , 3
#>
#> Sepal.Length Sepal.Width Petal.Length Petal.Width
#> Sepal.Length -0.6294887 -0.1459724 -0.472167346 -0.07643029
#> Sepal.Width 0.0000000 -0.2839297 -0.003622656 -0.12509889
#> Petal.Length 0.0000000 0.0000000 0.274847001 0.04113898
#> Petal.Width 0.0000000 0.0000000 0.000000000 -0.22525600
#>
#>
#>
#>
#> $loglik
#> [1] -182.9208
#>
#> attr(,"returnCode")
#> [1] 0