Plots for model-based mixture discriminant analysis results, such as scatterplot of training and test data, classification of train and test data, and errors.

# S3 method for MclustDA
plot(x, what = c("scatterplot", "classification", "train&test", "error"), 
     newdata, newclass, dimens = NULL, 
     symbols, colors, main = NULL, ...)

Arguments

x

An object of class 'MclustDA' resulting from a call to MclustDA.

what

A string specifying the type of graph requested. Available choices are:

"scatterplot" =

a plot of training data with points marked based on the known classification. Ellipses corresponding to covariances of mixture components are also drawn.

"classification" =

a plot of data with points marked on based the predicted classification; if newdata is provided then the test set is shown otherwise the training set.

"train&test" =

a plot of training and test data with points marked according to the type of set.

"error" =

a plot of training set (or test set if newdata and newclass are provided) with misclassified points marked.

If not specified, in interactive sessions a menu of choices is proposed.

newdata

A data frame or matrix for test data.

newclass

A vector giving the class labels for the observations in the test data (if known).

dimens

A vector of integers giving the dimensions of the desired coordinate projections for multivariate data. The default is to take all the the available dimensions for plotting.

symbols

Either an integer or character vector assigning a plotting symbol to each unique class. Elements in colors correspond to classes in order of appearance in the sequence of observations (the order used by the function factor). The default is given by mclust.options("classPlotSymbols").

colors

Either an integer or character vector assigning a color to each unique class in classification. Elements in colors correspond to classes in order of appearance in the sequence of observations (the order used by the function factor). The default is given by mclust.options("classPlotColors").

main

A logical, a character string, or NULL (default) for the main title. If NULL or FALSE no title is added to a plot. If TRUE a default title is added identifying the type of plot drawn. If a character string is provided, this is used for the title.

...

further arguments passed to or from other methods.

Details

For more flexibility in plotting, use mclust1Dplot, mclust2Dplot, surfacePlot, coordProj, or randProj.

Author

Luca Scrucca

Examples

# \donttest{
odd <- seq(from = 1, to = nrow(iris), by = 2)
even <- odd + 1
X.train <- iris[odd,-5]
Class.train <- iris[odd,5]
X.test <- iris[even,-5]
Class.test <- iris[even,5]

# common EEE covariance structure (which is essentially equivalent to linear discriminant analysis)
irisMclustDA <- MclustDA(X.train, Class.train, modelType = "EDDA", modelNames = "EEE")
summary(irisMclustDA, parameters = TRUE)
#> ------------------------------------------------ 
#> Gaussian finite mixture model for classification 
#> ------------------------------------------------ 
#> 
#> EDDA model summary: 
#> 
#>  log-likelihood  n df       BIC
#>        -125.443 75 22 -345.8707
#>             
#> Classes       n     % Model G
#>   setosa     25 33.33   EEE 1
#>   versicolor 25 33.33   EEE 1
#>   virginica  25 33.33   EEE 1
#> 
#> Class prior probabilities:
#>     setosa versicolor  virginica 
#>  0.3333333  0.3333333  0.3333333 
#> 
#> Class = setosa
#> 
#> Means:
#>               [,1]
#> Sepal.Length 5.024
#> Sepal.Width  3.480
#> Petal.Length 1.456
#> Petal.Width  0.228
#> 
#> Variances:
#> [,,1]
#>              Sepal.Length Sepal.Width Petal.Length Petal.Width
#> Sepal.Length   0.26418133  0.06244800   0.15935467  0.03141333
#> Sepal.Width    0.06244800  0.09630933   0.03326933  0.03222400
#> Petal.Length   0.15935467  0.03326933   0.18236800  0.04091733
#> Petal.Width    0.03141333  0.03222400   0.04091733  0.03891200
#> 
#> Class = versicolor
#> 
#> Means:
#>               [,1]
#> Sepal.Length 5.992
#> Sepal.Width  2.776
#> Petal.Length 4.308
#> Petal.Width  1.352
#> 
#> Variances:
#> [,,1]
#>              Sepal.Length Sepal.Width Petal.Length Petal.Width
#> Sepal.Length   0.26418133  0.06244800   0.15935467  0.03141333
#> Sepal.Width    0.06244800  0.09630933   0.03326933  0.03222400
#> Petal.Length   0.15935467  0.03326933   0.18236800  0.04091733
#> Petal.Width    0.03141333  0.03222400   0.04091733  0.03891200
#> 
#> Class = virginica
#> 
#> Means:
#>               [,1]
#> Sepal.Length 6.504
#> Sepal.Width  2.936
#> Petal.Length 5.564
#> Petal.Width  2.076
#> 
#> Variances:
#> [,,1]
#>              Sepal.Length Sepal.Width Petal.Length Petal.Width
#> Sepal.Length   0.26418133  0.06244800   0.15935467  0.03141333
#> Sepal.Width    0.06244800  0.09630933   0.03326933  0.03222400
#> Petal.Length   0.15935467  0.03326933   0.18236800  0.04091733
#> Petal.Width    0.03141333  0.03222400   0.04091733  0.03891200
#> 
#> Training confusion matrix:
#>             Predicted
#> Class        setosa versicolor virginica
#>   setosa         25          0         0
#>   versicolor      0         24         1
#>   virginica       0          1        24
#> Classification error = 0.0267 
#> Brier score          = 0.0097 
summary(irisMclustDA, newdata = X.test, newclass = Class.test)
#> ------------------------------------------------ 
#> Gaussian finite mixture model for classification 
#> ------------------------------------------------ 
#> 
#> EDDA model summary: 
#> 
#>  log-likelihood  n df       BIC
#>        -125.443 75 22 -345.8707
#>             
#> Classes       n     % Model G
#>   setosa     25 33.33   EEE 1
#>   versicolor 25 33.33   EEE 1
#>   virginica  25 33.33   EEE 1
#> 
#> Training confusion matrix:
#>             Predicted
#> Class        setosa versicolor virginica
#>   setosa         25          0         0
#>   versicolor      0         24         1
#>   virginica       0          1        24
#> Classification error = 0.0267 
#> Brier score          = 0.0097 
#> 
#> Test confusion matrix:
#>             Predicted
#> Class        setosa versicolor virginica
#>   setosa         25          0         0
#>   versicolor      0         24         1
#>   virginica       0          2        23
#> Classification error = 0.04 
#> Brier score          = 0.0243 

# common covariance structure selected by BIC
irisMclustDA <- MclustDA(X.train, Class.train, modelType = "EDDA")
summary(irisMclustDA, parameters = TRUE)
#> ------------------------------------------------ 
#> Gaussian finite mixture model for classification 
#> ------------------------------------------------ 
#> 
#> EDDA model summary: 
#> 
#>  log-likelihood  n df       BIC
#>       -87.93758 75 36 -331.3047
#>             
#> Classes       n     % Model G
#>   setosa     25 33.33   VEV 1
#>   versicolor 25 33.33   VEV 1
#>   virginica  25 33.33   VEV 1
#> 
#> Class prior probabilities:
#>     setosa versicolor  virginica 
#>  0.3333333  0.3333333  0.3333333 
#> 
#> Class = setosa
#> 
#> Means:
#>               [,1]
#> Sepal.Length 5.024
#> Sepal.Width  3.480
#> Petal.Length 1.456
#> Petal.Width  0.228
#> 
#> Variances:
#> [,,1]
#>              Sepal.Length Sepal.Width Petal.Length Petal.Width
#> Sepal.Length  0.154450439 0.097646496  0.017347101 0.005327878
#> Sepal.Width   0.097646496 0.105230813  0.004066916 0.005599939
#> Petal.Length  0.017347101 0.004066916  0.041742267 0.003476241
#> Petal.Width   0.005327878 0.005599939  0.003476241 0.006454832
#> 
#> Class = versicolor
#> 
#> Means:
#>               [,1]
#> Sepal.Length 5.992
#> Sepal.Width  2.776
#> Petal.Length 4.308
#> Petal.Width  1.352
#> 
#> Variances:
#> [,,1]
#>              Sepal.Length Sepal.Width Petal.Length Petal.Width
#> Sepal.Length   0.26653496  0.06976610   0.17015657  0.04336127
#> Sepal.Width    0.06976610  0.09861066   0.07509657  0.03823057
#> Petal.Length   0.17015657  0.07509657   0.19799871  0.06126251
#> Petal.Width    0.04336127  0.03823057   0.06126251  0.03627058
#> 
#> Class = virginica
#> 
#> Means:
#>               [,1]
#> Sepal.Length 6.504
#> Sepal.Width  2.936
#> Petal.Length 5.564
#> Petal.Width  2.076
#> 
#> Variances:
#> [,,1]
#>              Sepal.Length Sepal.Width Petal.Length Petal.Width
#> Sepal.Length   0.37570480 0.025364426  0.280227270  0.03871029
#> Sepal.Width    0.02536443 0.080872957  0.006413281  0.05009229
#> Petal.Length   0.28022727 0.006413281  0.309059434  0.05805268
#> Petal.Width    0.03871029 0.050092291  0.058052679  0.07540425
#> 
#> Training confusion matrix:
#>             Predicted
#> Class        setosa versicolor virginica
#>   setosa         25          0         0
#>   versicolor      0         24         1
#>   virginica       0          0        25
#> Classification error = 0.0133 
#> Brier score          = 0.0054 
summary(irisMclustDA, newdata = X.test, newclass = Class.test)
#> ------------------------------------------------ 
#> Gaussian finite mixture model for classification 
#> ------------------------------------------------ 
#> 
#> EDDA model summary: 
#> 
#>  log-likelihood  n df       BIC
#>       -87.93758 75 36 -331.3047
#>             
#> Classes       n     % Model G
#>   setosa     25 33.33   VEV 1
#>   versicolor 25 33.33   VEV 1
#>   virginica  25 33.33   VEV 1
#> 
#> Training confusion matrix:
#>             Predicted
#> Class        setosa versicolor virginica
#>   setosa         25          0         0
#>   versicolor      0         24         1
#>   virginica       0          0        25
#> Classification error = 0.0133 
#> Brier score          = 0.0054 
#> 
#> Test confusion matrix:
#>             Predicted
#> Class        setosa versicolor virginica
#>   setosa         25          0         0
#>   versicolor      0         24         1
#>   virginica       0          2        23
#> Classification error = 0.04 
#> Brier score          = 0.0297 

# general covariance structure selected by BIC
irisMclustDA <- MclustDA(X.train, Class.train)
summary(irisMclustDA, parameters = TRUE)
#> ------------------------------------------------ 
#> Gaussian finite mixture model for classification 
#> ------------------------------------------------ 
#> 
#> MclustDA model summary: 
#> 
#>  log-likelihood  n df       BIC
#>       -71.74193 75 48 -350.7233
#>             
#> Classes       n     % Model G
#>   setosa     25 33.33   VEI 2
#>   versicolor 25 33.33   VEE 2
#>   virginica  25 33.33   XXX 1
#> 
#> Class prior probabilities:
#>     setosa versicolor  virginica 
#>  0.3333333  0.3333333  0.3333333 
#> 
#> Class = setosa
#> 
#> Mixing probabilities: 0.7229143 0.2770857 
#> 
#> Means:
#>                   [,1]      [,2]
#> Sepal.Length 5.1761949 4.6269248
#> Sepal.Width  3.6366552 3.0712877
#> Petal.Length 1.4777585 1.3992323
#> Petal.Width  0.2441875 0.1857668
#> 
#> Variances:
#> [,,1]
#>              Sepal.Length Sepal.Width Petal.Length Petal.Width
#> Sepal.Length     0.120728    0.000000   0.00000000 0.000000000
#> Sepal.Width      0.000000    0.046461   0.00000000 0.000000000
#> Petal.Length     0.000000    0.000000   0.04892923 0.000000000
#> Petal.Width      0.000000    0.000000   0.00000000 0.006358681
#> [,,2]
#>              Sepal.Length Sepal.Width Petal.Length Petal.Width
#> Sepal.Length   0.03044364  0.00000000   0.00000000 0.000000000
#> Sepal.Width    0.00000000  0.01171594   0.00000000 0.000000000
#> Petal.Length   0.00000000  0.00000000   0.01233835 0.000000000
#> Petal.Width    0.00000000  0.00000000   0.00000000 0.001603451
#> 
#> Class = versicolor
#> 
#> Mixing probabilities: 0.2364317 0.7635683 
#> 
#> Means:
#>                  [,1]     [,2]
#> Sepal.Length 6.736465 5.761483
#> Sepal.Width  3.000982 2.706336
#> Petal.Length 4.669933 4.195931
#> Petal.Width  1.400893 1.336861
#> 
#> Variances:
#> [,,1]
#>              Sepal.Length Sepal.Width Petal.Length Petal.Width
#> Sepal.Length  0.030012918 0.008262520   0.02533959 0.008673053
#> Sepal.Width   0.008262520 0.020600060   0.01200205 0.008400168
#> Petal.Length  0.025339590 0.012002053   0.03924151 0.013788157
#> Petal.Width   0.008673053 0.008400168   0.01378816 0.007666627
#> [,,2]
#>              Sepal.Length Sepal.Width Petal.Length Petal.Width
#> Sepal.Length   0.16630011  0.04578222   0.14040543  0.04805696
#> Sepal.Width    0.04578222  0.11414392   0.06650279  0.04654492
#> Petal.Length   0.14040543  0.06650279   0.21743528  0.07639950
#> Petal.Width    0.04805696  0.04654492   0.07639950  0.04248041
#> 
#> Class = virginica
#> 
#> Mixing probabilities: 1 
#> 
#> Means:
#>               [,1]
#> Sepal.Length 6.504
#> Sepal.Width  2.936
#> Petal.Length 5.564
#> Petal.Width  2.076
#> 
#> Variances:
#> [,,1]
#>              Sepal.Length Sepal.Width Petal.Length Petal.Width
#> Sepal.Length     0.349184    0.019056     0.272144    0.040896
#> Sepal.Width      0.019056    0.079104     0.011296    0.048064
#> Petal.Length     0.272144    0.011296     0.285504    0.049536
#> Petal.Width      0.040896    0.048064     0.049536    0.074624
#> 
#> Training confusion matrix:
#>             Predicted
#> Class        setosa versicolor virginica
#>   setosa         25          0         0
#>   versicolor      0         25         0
#>   virginica       0          0        25
#> Classification error = 0 
#> Brier score          = 0.0041 
summary(irisMclustDA, newdata = X.test, newclass = Class.test)
#> ------------------------------------------------ 
#> Gaussian finite mixture model for classification 
#> ------------------------------------------------ 
#> 
#> MclustDA model summary: 
#> 
#>  log-likelihood  n df       BIC
#>       -71.74193 75 48 -350.7233
#>             
#> Classes       n     % Model G
#>   setosa     25 33.33   VEI 2
#>   versicolor 25 33.33   VEE 2
#>   virginica  25 33.33   XXX 1
#> 
#> Training confusion matrix:
#>             Predicted
#> Class        setosa versicolor virginica
#>   setosa         25          0         0
#>   versicolor      0         25         0
#>   virginica       0          0        25
#> Classification error = 0 
#> Brier score          = 0.0041 
#> 
#> Test confusion matrix:
#>             Predicted
#> Class        setosa versicolor virginica
#>   setosa         25          0         0
#>   versicolor      0         24         1
#>   virginica       0          1        24
#> Classification error = 0.0267 
#> Brier score          = 0.0159 

plot(irisMclustDA)




plot(irisMclustDA, dimens = 3:4)




plot(irisMclustDA, dimens = 4)





plot(irisMclustDA, what = "classification")

plot(irisMclustDA, what = "classification", newdata = X.test)

plot(irisMclustDA, what = "classification", dimens = 3:4)

plot(irisMclustDA, what = "classification", newdata = X.test, dimens = 3:4)

plot(irisMclustDA, what = "classification", dimens = 4)

plot(irisMclustDA, what = "classification", dimens = 4, newdata = X.test)


plot(irisMclustDA, what = "train&test", newdata = X.test)

plot(irisMclustDA, what = "train&test", newdata = X.test, dimens = 3:4)

plot(irisMclustDA, what = "train&test", newdata = X.test, dimens = 4)


plot(irisMclustDA, what = "error")

plot(irisMclustDA, what = "error", dimens = 3:4)

plot(irisMclustDA, what = "error", dimens = 4)

plot(irisMclustDA, what = "error", newdata = X.test, newclass = Class.test)

plot(irisMclustDA, what = "error", newdata = X.test, newclass = Class.test, dimens = 3:4)

plot(irisMclustDA, what = "error", newdata = X.test, newclass = Class.test, dimens = 4)


# simulated 1D data
n <- 250 
set.seed(1)
triModal <- c(rnorm(n,-5), rnorm(n,0), rnorm(n,5))
triClass <- c(rep(1,n), rep(2,n), rep(3,n))
odd <- seq(from = 1, to = length(triModal), by = 2)
even <- odd + 1
triMclustDA <- MclustDA(triModal[odd], triClass[odd])
summary(triMclustDA, parameters = TRUE)
#> ------------------------------------------------ 
#> Gaussian finite mixture model for classification 
#> ------------------------------------------------ 
#> 
#> MclustDA model summary: 
#> 
#>  log-likelihood   n df       BIC
#>       -942.4306 375  6 -1920.423
#>        
#> Classes   n     % Model G
#>       1 125 33.33     X 1
#>       2 125 33.33     X 1
#>       3 125 33.33     X 1
#> 
#> Class prior probabilities:
#>         1         2         3 
#> 0.3333333 0.3333333 0.3333333 
#> 
#> Class = 1
#> 
#> Mixing probabilities: 1 
#> 
#> Means:
#> [1] -4.951981
#> 
#> Variances:
#> [1] 0.8268339
#> 
#> Class = 2
#> 
#> Mixing probabilities: 1 
#> 
#> Means:
#> [1] -0.01814707
#> 
#> Variances:
#> [1] 1.201987
#> 
#> Class = 3
#> 
#> Mixing probabilities: 1 
#> 
#> Means:
#> [1] 4.875429
#> 
#> Variances:
#> [1] 1.200321
#> 
#> Training confusion matrix:
#>      Predicted
#> Class   1   2   3
#>     1 124   1   0
#>     2   0 124   1
#>     3   0   0 125
#> Classification error = 0.0053 
#> Brier score          = 0.0073 
summary(triMclustDA, newdata = triModal[even], newclass = triClass[even])
#> ------------------------------------------------ 
#> Gaussian finite mixture model for classification 
#> ------------------------------------------------ 
#> 
#> MclustDA model summary: 
#> 
#>  log-likelihood   n df       BIC
#>       -942.4306 375  6 -1920.423
#>        
#> Classes   n     % Model G
#>       1 125 33.33     X 1
#>       2 125 33.33     X 1
#>       3 125 33.33     X 1
#> 
#> Training confusion matrix:
#>      Predicted
#> Class   1   2   3
#>     1 124   1   0
#>     2   0 124   1
#>     3   0   0 125
#> Classification error = 0.0053 
#> Brier score          = 0.0073 
#> 
#> Test confusion matrix:
#>      Predicted
#> Class   1   2   3
#>     1 124   1   0
#>     2   1 122   2
#>     3   0   1 124
#> Classification error = 0.0133 
#> Brier score          = 0.0089 
plot(triMclustDA)




plot(triMclustDA, what = "classification")

plot(triMclustDA, what = "classification", newdata = triModal[even])

plot(triMclustDA, what = "train&test", newdata = triModal[even])

plot(triMclustDA, what = "error")

plot(triMclustDA, what = "error", newdata = triModal[even], newclass = triClass[even])


# simulated 2D cross data
data(cross)
odd <- seq(from = 1, to = nrow(cross), by = 2)
even <- odd + 1
crossMclustDA <- MclustDA(cross[odd,-1], cross[odd,1])
summary(crossMclustDA, parameters = TRUE)
#> ------------------------------------------------ 
#> Gaussian finite mixture model for classification 
#> ------------------------------------------------ 
#> 
#> MclustDA model summary: 
#> 
#>  log-likelihood   n df     BIC
#>       -1381.404 250  9 -2812.5
#>        
#> Classes   n  % Model G
#>       1 125 50   XXX 1
#>       2 125 50   XXI 1
#> 
#> Class prior probabilities:
#>   1   2 
#> 0.5 0.5 
#> 
#> Class = 1
#> 
#> Mixing probabilities: 1 
#> 
#> Means:
#>           [,1]
#> X1  0.03982835
#> X2 -0.55982893
#> 
#> Variances:
#> [,,1]
#>          X1       X2
#> X1 1.030302  1.81975
#> X2 1.819750 72.90428
#> 
#> Class = 2
#> 
#> Mixing probabilities: 1 
#> 
#> Means:
#>          [,1]
#> X1  0.2877120
#> X2 -0.1231171
#> 
#> Variances:
#> [,,1]
#>         X1        X2
#> X1 87.3583 0.0000000
#> X2  0.0000 0.8995777
#> 
#> Training confusion matrix:
#>      Predicted
#> Class   1   2
#>     1 112  13
#>     2  13 112
#> Classification error = 0.104 
#> Brier score          = 0.0563 
summary(crossMclustDA, newdata = cross[even,-1], newclass = cross[even,1])
#> ------------------------------------------------ 
#> Gaussian finite mixture model for classification 
#> ------------------------------------------------ 
#> 
#> MclustDA model summary: 
#> 
#>  log-likelihood   n df     BIC
#>       -1381.404 250  9 -2812.5
#>        
#> Classes   n  % Model G
#>       1 125 50   XXX 1
#>       2 125 50   XXI 1
#> 
#> Training confusion matrix:
#>      Predicted
#> Class   1   2
#>     1 112  13
#>     2  13 112
#> Classification error = 0.104 
#> Brier score          = 0.0563 
#> 
#> Test confusion matrix:
#>      Predicted
#> Class   1   2
#>     1 118   7
#>     2   5 120
#> Classification error = 0.048 
#> Brier score          = 0.0298 
plot(crossMclustDA)




plot(crossMclustDA, what = "classification")

plot(crossMclustDA, what = "classification", newdata = cross[even,-1])

plot(crossMclustDA, what = "train&test", newdata = cross[even,-1])

plot(crossMclustDA, what = "error")

plot(crossMclustDA, what = "error", newdata =cross[even,-1], newclass = cross[even,1])

# }