Cluster multivariate observations by Gaussian finite mixture modeling

Cluster prediction for multivariate observations based on Gaussian finite mixture models estimated by Mclust.

Usage

# S3 method for Mclust
predict(object, newdata, ...)

Arguments

object

an object of class 'Mclust' resulting from a call to Mclust.

newdata

a data frame or matrix giving the data. If missing the clustering data obtained from the call to Mclust are classified.

...

further arguments passed to or from other methods.

Value

Returns a list of with the following components:

classification

a factor of predicted cluster labels for newdata.

z

a matrix whose [i,k]th entry is the probability that observation i in newdata belongs to the kth cluster.

Author

Luca Scrucca

See also

Mclust.

Examples

model <- Mclust(faithful)

# predict cluster for the observed data
pred <- predict(model) 
str(pred)
#> List of 2
#>  $ classification: int [1:272] 1 2 1 2 3 2 3 1 2 3 ...
#>  $ z             : num [1:272, 1:3] 9.72e-01 8.12e-13 9.97e-01 3.06e-07 1.17e-02 ...
#>   ..- attr(*, "dimnames")=List of 2
#>   .. ..$ : NULL
#>   .. ..$ : chr [1:3] "1" "2" "3"
pred$z              # equal to model$z
#>                   1            2            3
#>   [1,] 9.718934e-01 1.352740e-08 2.810657e-02
#>   [2,] 8.122644e-13 1.000000e+00 6.813886e-21
#>   [3,] 9.967828e-01 2.108920e-05 3.196126e-03
#>   [4,] 3.056090e-07 9.999997e-01 1.407759e-13
#>   [5,] 1.165923e-02 1.183305e-19 9.883408e-01
#>   [6,] 3.050001e-03 9.969497e-01 3.160044e-07
#>   [7,] 2.962193e-03 3.235046e-22 9.970378e-01
#>   [8,] 9.758494e-01 1.249199e-09 2.415062e-02
#>   [9,] 4.942048e-12 1.000000e+00 1.658458e-19
#>  [10,] 5.501578e-02 2.166813e-17 9.449842e-01
#>  [11,] 1.571164e-12 1.000000e+00 1.757682e-20
#>  [12,] 7.125339e-01 2.401096e-12 2.874661e-01
#>  [13,] 1.522898e-01 1.947418e-14 8.477102e-01
#>  [14,] 1.847134e-14 1.000000e+00 1.201399e-22
#>  [15,] 2.602557e-03 2.076298e-21 9.973974e-01
#>  [16,] 5.633073e-10 1.000000e+00 1.222865e-16
#>  [17,] 7.200548e-12 1.000000e+00 3.172820e-20
#>  [18,] 1.118067e-03 8.116665e-23 9.988819e-01
#>  [19,] 6.725706e-15 1.000000e+00 1.038195e-23
#>  [20,] 1.065036e-01 3.367444e-15 8.934964e-01
#>  [21,] 2.463338e-13 1.000000e+00 2.233795e-21
#>  [22,] 1.847134e-14 1.000000e+00 1.201399e-22
#>  [23,] 9.920432e-01 4.123192e-07 7.956377e-03
#>  [24,] 9.691025e-01 3.054996e-02 3.475489e-04
#>  [25,] 8.788529e-03 7.084549e-18 9.912115e-01
#>  [26,] 9.745951e-01 2.763897e-09 2.540491e-02
#>  [27,] 3.407283e-11 1.000000e+00 1.195405e-18
#>  [28,] 3.212497e-01 9.439276e-13 6.787503e-01
#>  [29,] 7.919031e-01 1.107526e-10 2.080969e-01
#>  [30,] 2.358343e-02 1.921480e-17 9.764166e-01
#>  [31,] 6.186793e-02 7.827461e-15 9.381321e-01
#>  [32,] 1.675999e-02 1.533009e-17 9.832400e-01
#>  [33,] 9.944634e-01 2.568250e-04 5.279751e-03
#>  [34,] 4.481798e-01 7.290846e-13 5.518202e-01
#>  [35,] 7.991348e-01 7.705541e-10 2.008652e-01
#>  [36,] 2.807776e-11 1.000000e+00 1.647089e-18
#>  [37,] 2.851554e-13 1.000000e+00 5.014801e-21
#>  [38,] 7.559766e-04 1.392489e-22 9.992440e-01
#>  [39,] 1.147741e-11 1.000000e+00 1.127699e-19
#>  [40,] 1.514760e-03 1.420726e-23 9.984852e-01
#>  [41,] 4.864473e-02 1.399562e-16 9.513553e-01
#>  [42,] 2.095305e-11 1.000000e+00 3.268107e-19
#>  [43,] 8.471971e-03 6.485284e-20 9.915280e-01
#>  [44,] 1.467127e-12 1.000000e+00 7.172049e-21
#>  [45,] 8.565250e-03 1.027686e-17 9.914347e-01
#>  [46,] 9.977963e-01 8.107782e-07 2.202843e-03
#>  [47,] 7.542305e-01 3.880895e-08 2.457695e-01
#>  [48,] 2.196538e-10 1.000000e+00 2.589804e-17
#>  [49,] 4.540594e-03 2.058058e-20 9.954594e-01
#>  [50,] 3.234673e-10 1.000000e+00 1.364151e-17
#>  [51,] 8.853270e-04 2.304271e-21 9.991147e-01
#>  [52,] 2.714269e-03 9.717403e-23 9.972857e-01
#>  [53,] 1.571164e-12 1.000000e+00 1.757682e-20
#>  [54,] 7.559766e-04 1.392489e-22 9.992440e-01
#>  [55,] 2.127974e-13 1.000000e+00 9.950224e-22
#>  [56,] 5.284488e-04 1.086389e-23 9.994716e-01
#>  [57,] 9.101062e-01 2.941878e-08 8.989382e-02
#>  [58,] 3.035027e-12 1.000000e+00 6.155272e-21
#>  [59,] 7.074222e-03 8.763842e-19 9.929258e-01
#>  [60,] 6.540510e-02 2.445501e-16 9.345949e-01
#>  [61,] 3.410870e-08 1.000000e+00 1.098053e-14
#>  [62,] 1.509745e-02 4.411429e-19 9.849025e-01
#>  [63,] 2.749305e-14 1.000000e+00 1.742360e-22
#>  [64,] 1.061560e-03 1.707274e-22 9.989384e-01
#>  [65,] 1.240645e-11 1.000000e+00 1.033014e-19
#>  [66,] 4.318969e-02 3.868255e-19 9.568103e-01
#>  [67,] 1.932731e-01 4.780616e-14 8.067269e-01
#>  [68,] 2.286484e-03 1.332539e-20 9.977135e-01
#>  [69,] 1.342481e-08 1.000000e+00 8.692163e-16
#>  [70,] 2.008720e-03 8.551723e-20 9.979913e-01
#>  [71,] 4.610517e-01 3.385527e-13 5.389483e-01
#>  [72,] 5.071456e-11 1.000000e+00 1.733666e-18
#>  [73,] 1.328412e-02 2.835508e-18 9.867159e-01
#>  [74,] 4.616284e-01 5.207901e-11 5.383716e-01
#>  [75,] 7.592772e-10 1.000000e+00 2.553912e-17
#>  [76,] 8.854996e-05 7.441358e-25 9.999115e-01
#>  [77,] 6.763293e-10 1.000000e+00 3.223454e-17
#>  [78,] 7.258917e-03 6.041756e-19 9.927411e-01
#>  [79,] 7.303983e-01 1.169947e-10 2.696017e-01
#>  [80,] 9.745951e-01 2.763897e-09 2.540491e-02
#>  [81,] 2.296721e-01 3.696588e-13 7.703279e-01
#>  [82,] 5.879368e-02 1.072609e-16 9.412063e-01
#>  [83,] 2.588245e-01 5.886331e-12 7.411755e-01
#>  [84,] 1.100918e-03 9.988991e-01 9.937520e-09
#>  [85,] 3.348483e-01 4.467229e-12 6.651517e-01
#>  [86,] 3.890515e-04 4.029390e-25 9.996109e-01
#>  [87,] 6.016098e-01 2.524587e-11 3.983902e-01
#>  [88,] 1.177245e-02 1.201813e-18 9.882276e-01
#>  [89,] 1.147751e-10 1.000000e+00 2.764243e-17
#>  [90,] 5.586289e-01 1.616689e-13 4.413711e-01
#>  [91,] 2.624614e-08 1.000000e+00 6.173453e-15
#>  [92,] 7.139508e-02 5.407336e-18 9.286049e-01
#>  [93,] 6.317286e-13 1.000000e+00 1.054763e-20
#>  [94,] 8.251763e-04 4.636603e-22 9.991748e-01
#>  [95,] 5.633028e-11 1.000000e+00 4.988789e-19
#>  [96,] 6.037828e-02 1.137000e-14 9.396217e-01
#>  [97,] 3.558599e-03 3.689506e-21 9.964414e-01
#>  [98,] 8.938701e-01 3.043581e-09 1.061299e-01
#>  [99,] 9.402753e-13 1.000000e+00 1.529697e-20
#> [100,] 4.439774e-04 9.670839e-24 9.995560e-01
#> [101,] 1.665979e-05 9.999833e-01 4.392748e-11
#> [102,] 5.146737e-02 4.376120e-18 9.485326e-01
#> [103,] 4.475494e-11 1.000000e+00 5.854163e-18
#> [104,] 1.471627e-02 6.400264e-19 9.852837e-01
#> [105,] 4.181515e-01 3.253355e-13 5.818485e-01
#> [106,] 1.915831e-13 1.000000e+00 3.457826e-21
#> [107,] 2.670820e-03 1.431560e-21 9.973292e-01
#> [108,] 2.610027e-13 1.000000e+00 1.988317e-21
#> [109,] 7.616311e-04 9.184970e-24 9.992384e-01
#> [110,] 9.464002e-01 1.131278e-09 5.359983e-02
#> [111,] 1.587192e-03 1.576850e-20 9.984128e-01
#> [112,] 1.301956e-07 9.999999e-01 7.519433e-14
#> [113,] 5.324023e-04 7.165921e-25 9.994676e-01
#> [114,] 2.702041e-02 3.031389e-17 9.729796e-01
#> [115,] 8.036454e-13 1.000000e+00 2.474800e-21
#> [116,] 4.424756e-03 2.985099e-20 9.955752e-01
#> [117,] 5.101283e-09 1.000000e+00 4.316568e-15
#> [118,] 6.532596e-03 1.736927e-20 9.934674e-01
#> [119,] 8.335337e-12 1.000000e+00 7.122883e-20
#> [120,] 3.305090e-02 1.539350e-18 9.669491e-01
#> [121,] 6.770422e-06 9.999932e-01 7.257881e-11
#> [122,] 3.121312e-01 2.043738e-11 6.878688e-01
#> [123,] 1.016630e-01 7.121113e-15 8.983370e-01
#> [124,] 5.071456e-11 1.000000e+00 1.733666e-18
#> [125,] 7.057939e-03 5.691153e-21 9.929421e-01
#> [126,] 8.945755e-01 1.994239e-10 1.054245e-01
#> [127,] 2.349827e-13 1.000000e+00 6.909647e-21
#> [128,] 1.434458e-02 9.285648e-19 9.856554e-01
#> [129,] 1.371431e-08 1.000000e+00 6.589274e-15
#> [130,] 4.817023e-03 6.452448e-22 9.951830e-01
#> [131,] 8.647851e-14 1.000000e+00 1.644001e-21
#> [132,] 2.143190e-01 7.256895e-15 7.856810e-01
#> [133,] 8.656118e-04 9.991343e-01 4.236381e-08
#> [134,] 6.969308e-02 7.856501e-18 9.303069e-01
#> [135,] 6.522677e-14 1.000000e+00 8.981236e-22
#> [136,] 3.881733e-02 2.606207e-17 9.611827e-01
#> [137,] 1.294720e-12 1.000000e+00 2.421824e-20
#> [138,] 3.693752e-04 8.475181e-25 9.996306e-01
#> [139,] 5.754502e-11 1.000000e+00 3.781855e-18
#> [140,] 9.155242e-01 8.922485e-10 8.447583e-02
#> [141,] 1.271110e-01 2.548436e-15 8.728890e-01
#> [142,] 5.076795e-08 9.999999e-01 1.592479e-14
#> [143,] 1.079512e-02 3.612667e-19 9.892049e-01
#> [144,] 8.040481e-04 6.724494e-22 9.991960e-01
#> [145,] 5.074409e-02 1.006568e-15 9.492559e-01
#> [146,] 2.302645e-10 1.000000e+00 8.372484e-18
#> [147,] 4.311859e-03 4.329707e-20 9.956881e-01
#> [148,] 8.515086e-12 1.000000e+00 5.399649e-19
#> [149,] 1.115927e-04 1.702496e-28 9.998884e-01
#> [150,] 5.457239e-13 1.000000e+00 4.698339e-21
#> [151,] 1.222524e-04 1.362083e-24 9.998777e-01
#> [152,] 5.004916e-01 5.193022e-12 4.995084e-01
#> [153,] 1.045187e-05 9.999895e-01 1.235923e-11
#> [154,] 5.892098e-03 7.688890e-20 9.941079e-01
#> [155,] 9.740026e-01 6.316488e-07 2.599678e-02
#> [156,] 4.551836e-01 7.643306e-11 5.448164e-01
#> [157,] 1.398213e-02 1.347170e-18 9.860179e-01
#> [158,] 4.239136e-01 1.442305e-15 5.760864e-01
#> [159,] 5.457239e-13 1.000000e+00 4.698339e-21
#> [160,] 6.459649e-01 1.096637e-13 3.540351e-01
#> [161,] 6.732841e-11 1.000000e+00 2.337600e-17
#> [162,] 2.548501e-01 3.676249e-15 7.451499e-01
#> [163,] 2.173231e-10 1.000000e+00 9.406154e-18
#> [164,] 8.152864e-01 1.601752e-10 1.847136e-01
#> [165,] 9.833253e-01 1.778141e-05 1.665694e-02
#> [166,] 6.001466e-03 8.036682e-19 9.939985e-01
#> [167,] 2.439069e-06 9.999976e-01 2.277971e-12
#> [168,] 2.168957e-04 5.885076e-26 9.997831e-01
#> [169,] 5.236342e-12 1.000000e+00 1.476206e-19
#> [170,] 6.929452e-03 5.444971e-22 9.930705e-01
#> [171,] 1.153277e-12 1.000000e+00 3.056737e-20
#> [172,] 7.674203e-10 1.000000e+00 7.031707e-17
#> [173,] 6.158327e-03 5.540612e-19 9.938417e-01
#> [174,] 9.960389e-01 2.291304e-04 3.732014e-03
#> [175,] 2.057063e-01 1.543074e-14 7.942937e-01
#> [176,] 5.737352e-02 1.557926e-16 9.426265e-01
#> [177,] 1.138996e-02 2.643425e-17 9.886100e-01
#> [178,] 3.766471e-08 1.000000e+00 7.625111e-14
#> [179,] 5.522189e-01 2.378695e-13 4.477811e-01
#> [180,] 1.775964e-01 2.155979e-13 8.224036e-01
#> [181,] 6.354389e-12 1.000000e+00 1.071383e-19
#> [182,] 6.158327e-03 5.540612e-19 9.938417e-01
#> [183,] 1.167960e-01 7.524305e-16 8.832040e-01
#> [184,] 8.993726e-01 9.050050e-11 1.006274e-01
#> [185,] 2.597520e-11 1.000000e+00 1.798058e-18
#> [186,] 2.299299e-02 2.788361e-17 9.770070e-01
#> [187,] 3.681036e-01 4.490247e-14 6.318964e-01
#> [188,] 6.522677e-14 1.000000e+00 8.981236e-22
#> [189,] 2.988859e-02 6.832150e-18 9.701114e-01
#> [190,] 2.557641e-09 1.000000e+00 5.905644e-16
#> [191,] 1.034386e-03 2.476085e-22 9.989656e-01
#> [192,] 5.180779e-12 1.000000e+00 5.361570e-20
#> [193,] 9.085891e-04 1.588814e-21 9.990914e-01
#> [194,] 3.343315e-01 2.903181e-14 6.656685e-01
#> [195,] 5.740909e-01 1.175468e-11 4.259091e-01
#> [196,] 1.271110e-01 2.548436e-15 8.728890e-01
#> [197,] 9.902747e-01 4.224845e-09 9.725258e-03
#> [198,] 3.951356e-02 2.722420e-16 9.604864e-01
#> [199,] 1.989174e-09 1.000000e+00 9.141704e-16
#> [200,] 3.046901e-03 3.434744e-20 9.969531e-01
#> [201,] 3.554759e-09 1.000000e+00 3.494787e-16
#> [202,] 5.110452e-02 6.636923e-17 9.488955e-01
#> [203,] 3.111355e-01 8.630793e-16 6.888645e-01
#> [204,] 2.083071e-12 1.000000e+00 3.217410e-20
#> [205,] 5.453055e-03 2.346427e-19 9.945469e-01
#> [206,] 2.400481e-14 1.000000e+00 2.136891e-22
#> [207,] 3.918381e-02 2.646264e-16 9.608162e-01
#> [208,] 8.164068e-01 1.050126e-11 1.835932e-01
#> [209,] 1.588015e-12 1.000000e+00 4.839441e-20
#> [210,] 1.471627e-02 6.400264e-19 9.852837e-01
#> [211,] 8.089220e-05 9.999191e-01 7.057578e-11
#> [212,] 2.408037e-03 6.334700e-21 9.975920e-01
#> [213,] 4.244300e-13 1.000000e+00 7.272844e-21
#> [214,] 8.032694e-01 5.203791e-10 1.967306e-01
#> [215,] 9.912176e-01 2.087079e-04 8.573687e-03
#> [216,] 1.133928e-01 1.660728e-14 8.866072e-01
#> [217,] 8.841066e-08 9.999999e-01 1.427544e-13
#> [218,] 1.448983e-03 1.971190e-24 9.985510e-01
#> [219,] 6.590714e-11 1.000000e+00 3.083617e-18
#> [220,] 2.087458e-01 1.606877e-13 7.912542e-01
#> [221,] 6.317286e-13 1.000000e+00 1.054763e-20
#> [222,] 9.998566e-02 6.824912e-16 9.000143e-01
#> [223,] 2.989302e-13 1.000000e+00 1.621217e-21
#> [224,] 1.387969e-02 2.042580e-17 9.861203e-01
#> [225,] 5.069810e-01 3.534195e-12 4.930190e-01
#> [226,] 2.755283e-01 1.244176e-13 7.244717e-01
#> [227,] 3.326739e-01 4.412307e-13 6.673261e-01
#> [228,] 9.102191e-02 3.049321e-15 9.089781e-01
#> [229,] 6.328107e-01 5.584964e-10 3.671893e-01
#> [230,] 8.628811e-03 6.778307e-19 9.913712e-01
#> [231,] 2.882723e-01 9.209705e-12 7.117277e-01
#> [232,] 1.848555e-07 9.999998e-01 3.373248e-13
#> [233,] 2.041132e-01 1.522184e-15 7.958868e-01
#> [234,] 6.909142e-10 1.000000e+00 2.443606e-16
#> [235,] 2.695946e-02 1.968646e-19 9.730405e-01
#> [236,] 4.269228e-12 1.000000e+00 7.387443e-20
#> [237,] 2.207115e-12 1.000000e+00 2.863839e-20
#> [238,] 7.822194e-02 2.832627e-15 9.217781e-01
#> [239,] 6.201193e-01 7.891822e-12 3.798807e-01
#> [240,] 1.839679e-06 9.999982e-01 1.244465e-12
#> [241,] 2.044905e-01 2.342947e-13 7.955095e-01
#> [242,] 2.992473e-09 1.000000e+00 3.650333e-15
#> [243,] 3.693752e-04 8.475181e-25 9.996306e-01
#> [244,] 9.380836e-02 9.061825e-01 9.159001e-06
#> [245,] 7.568981e-03 2.827070e-20 9.924310e-01
#> [246,] 8.304147e-01 3.324163e-11 1.695853e-01
#> [247,] 7.674203e-10 1.000000e+00 7.031707e-17
#> [248,] 4.437355e-02 4.102308e-17 9.556264e-01
#> [249,] 1.112770e-07 9.999999e-01 1.216522e-14
#> [250,] 4.192277e-02 1.311454e-15 9.580772e-01
#> [251,] 2.413896e-09 1.000000e+00 6.634756e-16
#> [252,] 2.258101e-02 2.668524e-18 9.774190e-01
#> [253,] 9.752857e-01 2.854950e-07 2.471402e-02
#> [254,] 1.138996e-02 2.643425e-17 9.886100e-01
#> [255,] 2.648343e-01 1.724430e-15 7.351657e-01
#> [256,] 8.424041e-01 1.028674e-10 1.575959e-01
#> [257,] 6.388216e-01 3.787927e-10 3.611784e-01
#> [258,] 2.258101e-02 2.668524e-18 9.774190e-01
#> [259,] 9.809727e-11 1.000000e+00 4.472095e-18
#> [260,] 8.204836e-02 1.341164e-15 9.179516e-01
#> [261,] 1.275783e-03 1.947860e-21 9.987242e-01
#> [262,] 1.136386e-02 1.716631e-19 9.886361e-01
#> [263,] 1.083236e-11 1.000000e+00 1.266925e-19
#> [264,] 1.167960e-01 7.524305e-16 8.832040e-01
#> [265,] 3.968583e-13 1.000000e+00 2.185978e-20
#> [266,] 7.131699e-08 9.999999e-01 2.594669e-14
#> [267,] 1.368736e-03 9.680041e-21 9.986313e-01
#> [268,] 2.860117e-01 5.829758e-14 7.139883e-01
#> [269,] 3.688036e-11 1.000000e+00 8.066162e-18
#> [270,] 3.563232e-02 5.032974e-19 9.643677e-01
#> [271,] 4.737018e-14 1.000000e+00 5.672819e-22
#> [272,] 1.552378e-02 4.682115e-17 9.844762e-01
pred$classification # equal to 
#>   [1] 1 2 1 2 3 2 3 1 2 3 2 1 3 2 3 2 2 3 2 3 2 2 1 1 3 1 2 3 1 3 3 3 1 3 1 2 2
#>  [38] 3 2 3 3 2 3 2 3 1 1 2 3 2 3 3 2 3 2 3 1 2 3 3 2 3 2 3 2 3 3 3 2 3 3 2 3 3
#>  [75] 2 3 2 3 1 1 3 3 3 2 3 3 1 3 2 1 2 3 2 3 2 3 3 1 2 3 2 3 2 3 3 2 3 2 3 1 3
#> [112] 2 3 3 2 3 2 3 2 3 2 3 3 2 3 1 2 3 2 3 2 3 2 3 2 3 2 3 2 1 3 2 3 3 3 2 3 2
#> [149] 3 2 3 1 2 3 1 3 3 3 2 1 2 3 2 1 1 3 2 3 2 3 2 2 3 1 3 3 3 2 1 3 2 3 3 1 2
#> [186] 3 3 2 3 2 3 2 3 3 1 3 1 3 2 3 2 3 3 2 3 2 3 1 2 3 2 3 2 1 1 3 2 3 2 3 2 3
#> [223] 2 3 1 3 3 3 1 3 3 2 3 2 3 2 2 3 1 2 3 2 3 2 3 1 2 3 2 3 2 3 1 3 3 1 1 3 2
#> [260] 3 3 3 2 3 2 2 3 3 2 3 2 3
plot(faithful, col = pred$classification, pch = pred$classification)


# predict cluster over a grid
grid <- apply(faithful, 2, function(x) seq(min(x), max(x), length = 50))
grid <- expand.grid(eruptions = grid[,1], waiting = grid[,2])
pred <- predict(model, grid)
plot(grid, col = mclust.options("classPlotColors")[pred$classification], pch = 15, cex = 0.5)
points(faithful, pch = model$classification)