Analisis del discriminante lineal y cuadratico ejemplo introductorio
Jaime Isaac
30/5/2021
yes
Análisis discriminante lineal LDA
Cargar la librería MASS
##################################################################################################################
library(MASS)
##################################################################################################################Cargar los datos Iris
##################################################################################################################
# Cargar los datos Iris
##################################################################################################################
Z <- as.data.frame(iris)
ZDefinir la matriz de datos y la variable respuesta con las clasificaciones.
##################################################################################################################
# Definir la matriz de datos y la variable respuesta con las clasificaciones
##################################################################################################################
X <- Z[,1:4]
Xy <- Z[,5]
y## [1] setosa setosa setosa setosa setosa setosa
## [7] setosa setosa setosa setosa setosa setosa
## [13] setosa setosa setosa setosa setosa setosa
## [19] setosa setosa setosa setosa setosa setosa
## [25] setosa setosa setosa setosa setosa setosa
## [31] setosa setosa setosa setosa setosa setosa
## [37] setosa setosa setosa setosa setosa setosa
## [43] setosa setosa setosa setosa setosa setosa
## [49] setosa setosa versicolor versicolor versicolor versicolor
## [55] versicolor versicolor versicolor versicolor versicolor versicolor
## [61] versicolor versicolor versicolor versicolor versicolor versicolor
## [67] versicolor versicolor versicolor versicolor versicolor versicolor
## [73] versicolor versicolor versicolor versicolor versicolor versicolor
## [79] versicolor versicolor versicolor versicolor versicolor versicolor
## [85] versicolor versicolor versicolor versicolor versicolor versicolor
## [91] versicolor versicolor versicolor versicolor versicolor versicolor
## [97] versicolor versicolor versicolor versicolor virginica virginica
## [103] virginica virginica virginica virginica virginica virginica
## [109] virginica virginica virginica virginica virginica virginica
## [115] virginica virginica virginica virginica virginica virginica
## [121] virginica virginica virginica virginica virginica virginica
## [127] virginica virginica virginica virginica virginica virginica
## [133] virginica virginica virginica virginica virginica virginica
## [139] virginica virginica virginica virginica virginica virginica
## [145] virginica virginica virginica virginica virginica virginica
## Levels: setosa versicolor virginicaDefinir como n y p el número de flores y el número de variables
##################################################################################################################
# Definir como n y p el número de flores y el número de variables
##################################################################################################################
n <- nrow(X)
n## [1] 150p <- ncol(X)
p## [1] 4Código para el análisis del disriminante lineal LDA.
# LDA leave-one-out cross validation
lda.iris <- lda(y ~ .,data=X)
lda.iris## Call:
## lda(y ~ ., data = X)
##
## Prior probabilities of groups:
## setosa versicolor virginica
## 0.3333333 0.3333333 0.3333333
##
## Group means:
## Sepal.Length Sepal.Width Petal.Length Petal.Width
## setosa 5.006 3.428 1.462 0.246
## versicolor 5.936 2.770 4.260 1.326
## virginica 6.588 2.974 5.552 2.026
##
## Coefficients of linear discriminants:
## LD1 LD2
## Sepal.Length 0.8293776 0.02410215
## Sepal.Width 1.5344731 2.16452123
## Petal.Length -2.2012117 -0.93192121
## Petal.Width -2.8104603 2.83918785
##
## Proportion of trace:
## LD1 LD2
## 0.9912 0.0088# lda.iris$class contiene las clasificaciones hechas por CV usando LDA
#LDA leave-one-out cross validation
lda.iris <- lda(y ~ .,data=X,CV=TRUE)
# lda.iris$class contiene las clasificaciones hechas por CV usando LDA
lda.iris$class## [1] setosa setosa setosa setosa setosa setosa
## [7] setosa setosa setosa setosa setosa setosa
## [13] setosa setosa setosa setosa setosa setosa
## [19] setosa setosa setosa setosa setosa setosa
## [25] setosa setosa setosa setosa setosa setosa
## [31] setosa setosa setosa setosa setosa setosa
## [37] setosa setosa setosa setosa setosa setosa
## [43] setosa setosa setosa setosa setosa setosa
## [49] setosa setosa versicolor versicolor versicolor versicolor
## [55] versicolor versicolor versicolor versicolor versicolor versicolor
## [61] versicolor versicolor versicolor versicolor versicolor versicolor
## [67] versicolor versicolor versicolor versicolor virginica versicolor
## [73] versicolor versicolor versicolor versicolor versicolor versicolor
## [79] versicolor versicolor versicolor versicolor versicolor virginica
## [85] versicolor versicolor versicolor versicolor versicolor versicolor
## [91] versicolor versicolor versicolor versicolor versicolor versicolor
## [97] versicolor versicolor versicolor versicolor virginica virginica
## [103] virginica virginica virginica virginica virginica virginica
## [109] virginica virginica virginica virginica virginica virginica
## [115] virginica virginica virginica virginica virginica virginica
## [121] virginica virginica virginica virginica virginica virginica
## [127] virginica virginica virginica virginica virginica virginica
## [133] virginica versicolor virginica virginica virginica virginica
## [139] virginica virginica virginica virginica virginica virginica
## [145] virginica virginica virginica virginica virginica virginica
## Levels: setosa versicolor virginica#LDA leave-one-out cross validation
lda.iris <- lda(y ~ .,data=X,CV=TRUE)
# lda.iris$class contiene las clasificaciones hechas por CV usando LDA
lda.iris$class## [1] setosa setosa setosa setosa setosa setosa
## [7] setosa setosa setosa setosa setosa setosa
## [13] setosa setosa setosa setosa setosa setosa
## [19] setosa setosa setosa setosa setosa setosa
## [25] setosa setosa setosa setosa setosa setosa
## [31] setosa setosa setosa setosa setosa setosa
## [37] setosa setosa setosa setosa setosa setosa
## [43] setosa setosa setosa setosa setosa setosa
## [49] setosa setosa versicolor versicolor versicolor versicolor
## [55] versicolor versicolor versicolor versicolor versicolor versicolor
## [61] versicolor versicolor versicolor versicolor versicolor versicolor
## [67] versicolor versicolor versicolor versicolor virginica versicolor
## [73] versicolor versicolor versicolor versicolor versicolor versicolor
## [79] versicolor versicolor versicolor versicolor versicolor virginica
## [85] versicolor versicolor versicolor versicolor versicolor versicolor
## [91] versicolor versicolor versicolor versicolor versicolor versicolor
## [97] versicolor versicolor versicolor versicolor virginica virginica
## [103] virginica virginica virginica virginica virginica virginica
## [109] virginica virginica virginica virginica virginica virginica
## [115] virginica virginica virginica virginica virginica virginica
## [121] virginica virginica virginica virginica virginica virginica
## [127] virginica virginica virginica virginica virginica virginica
## [133] virginica versicolor virginica virginica virginica virginica
## [139] virginica virginica virginica virginica virginica virginica
## [145] virginica virginica virginica virginica virginica virginica
## Levels: setosa versicolor virginicaTabla con clasificaciones buenas y malas
# Tabla con clasificaciones buenas y malas
table.lda <- table(y,lda.iris$class)
table.lda##
## y setosa versicolor virginica
## setosa 50 0 0
## versicolor 0 48 2
## virginica 0 1 49Proporción de errores.
# Proporción de errores
mis.lda <- n - sum(y==lda.iris$class)
mis.lda/n## [1] 0.02# Buenas clasificaciones en rojo, malas en negro
col.lda.iris <- c("black","indianred1")[1*(y==lda.iris$class)+1]
pairs(X,main="Good (in red) and bad (in black) classifications for the Iris data set with LDA",pch=19,col=col.lda.iris)
# lda.iris$posterior son las probabilidades de pertenencia a uno de los tres grupos
lda.iris$posterior## setosa versicolor virginica
## 1 1.000000e+00 5.087494e-22 4.385241e-42
## 2 1.000000e+00 9.588256e-18 8.888069e-37
## 3 1.000000e+00 1.983745e-19 8.606982e-39
## 4 1.000000e+00 1.505573e-16 5.101765e-35
## 5 1.000000e+00 2.075670e-22 1.739832e-42
## 6 1.000000e+00 5.332271e-21 8.674906e-40
## 7 1.000000e+00 1.498839e-18 3.999205e-37
## 8 1.000000e+00 5.268133e-20 1.983027e-39
## 9 1.000000e+00 2.280729e-15 1.293376e-33
## 10 1.000000e+00 1.504085e-18 5.037348e-38
## 11 1.000000e+00 1.296140e-23 4.023338e-44
## 12 1.000000e+00 2.171874e-18 3.223111e-37
## 13 1.000000e+00 1.996136e-18 6.109118e-38
## 14 1.000000e+00 1.604055e-19 2.549802e-39
## 15 1.000000e+00 2.843397e-31 1.593594e-54
## 16 1.000000e+00 2.330545e-28 3.074132e-49
## 17 1.000000e+00 5.136116e-25 3.269819e-45
## 18 1.000000e+00 5.747697e-21 2.253825e-40
## 19 1.000000e+00 2.187125e-22 4.069438e-42
## 20 1.000000e+00 3.297882e-22 9.802494e-42
## 21 1.000000e+00 1.757286e-19 8.150916e-39
## 22 1.000000e+00 2.027767e-20 3.730752e-39
## 23 1.000000e+00 5.650696e-25 6.509776e-46
## 24 1.000000e+00 8.618517e-15 7.014744e-32
## 25 1.000000e+00 1.520334e-15 1.857885e-33
## 26 1.000000e+00 2.936141e-16 8.159510e-35
## 27 1.000000e+00 4.557392e-17 5.510803e-35
## 28 1.000000e+00 2.079675e-21 2.831513e-41
## 29 1.000000e+00 1.232321e-21 1.082692e-41
## 30 1.000000e+00 1.153050e-16 4.267126e-35
## 31 1.000000e+00 2.584595e-16 9.537258e-35
## 32 1.000000e+00 2.878754e-19 5.473623e-38
## 33 1.000000e+00 2.247070e-27 4.047137e-49
## 34 1.000000e+00 2.620949e-29 1.970538e-51
## 35 1.000000e+00 1.493279e-17 2.047516e-36
## 36 1.000000e+00 2.146308e-21 1.550216e-41
## 37 1.000000e+00 1.673983e-24 1.322398e-45
## 38 1.000000e+00 3.810942e-23 9.131835e-44
## 39 1.000000e+00 5.423320e-17 1.146137e-35
## 40 1.000000e+00 2.414191e-20 6.552342e-40
## 41 1.000000e+00 1.417602e-21 3.569675e-41
## 42 1.000000e+00 8.956712e-11 4.968454e-28
## 43 1.000000e+00 2.125837e-18 2.395462e-37
## 44 1.000000e+00 1.101293e-15 1.403899e-32
## 45 1.000000e+00 2.285363e-17 5.214629e-35
## 46 1.000000e+00 2.087086e-16 1.027948e-34
## 47 1.000000e+00 2.588201e-22 3.634491e-42
## 48 1.000000e+00 3.643000e-18 4.504970e-37
## 49 1.000000e+00 3.000767e-23 1.346233e-43
## 50 1.000000e+00 3.171862e-20 7.860312e-40
## 51 3.157725e-18 9.998716e-01 1.284247e-04
## 52 1.753919e-19 9.991816e-01 8.184018e-04
## 53 2.551962e-22 9.951044e-01 4.895626e-03
## 54 2.742687e-22 9.995996e-01 4.004477e-04
## 55 4.854978e-23 9.951404e-01 4.859638e-03
## 56 9.575747e-23 9.982973e-01 1.702702e-03
## 57 4.467689e-22 9.838631e-01 1.613691e-02
## 58 5.922943e-14 9.999999e-01 8.584221e-08
## 59 8.088509e-20 9.998655e-01 1.344590e-04
## 60 1.767441e-20 9.994314e-01 5.686054e-04
## 61 3.330661e-18 9.999987e-01 1.314516e-06
## 62 8.331100e-20 9.991631e-01 8.369389e-04
## 63 4.614428e-18 9.999989e-01 1.117671e-06
## 64 1.290071e-23 9.939163e-01 6.083745e-03
## 65 5.229707e-14 9.999984e-01 1.593028e-06
## 66 3.393529e-17 9.999528e-01 4.721492e-05
## 67 7.983370e-24 9.763990e-01 2.360097e-02
## 68 3.119288e-16 9.999991e-01 8.659241e-07
## 69 3.847473e-28 9.390462e-01 6.095377e-02
## 70 1.678698e-17 9.999966e-01 3.360127e-06
## 71 1.302246e-28 1.772727e-01 8.227273e-01
## 72 1.113263e-16 9.999902e-01 9.801197e-06
## 73 1.634947e-29 7.868347e-01 2.131653e-01
## 74 3.331093e-22 9.995073e-01 4.926830e-04
## 75 1.013127e-17 9.999741e-01 2.594176e-05
## 76 2.949236e-18 9.999081e-01 9.193549e-05
## 77 7.224891e-23 9.979459e-01 2.054146e-03
## 78 2.386376e-27 6.569495e-01 3.430505e-01
## 79 4.473658e-23 9.922840e-01 7.716012e-03
## 80 7.145460e-12 1.000000e+00 1.241414e-08
## 81 1.333306e-17 9.999970e-01 3.044209e-06
## 82 1.119894e-15 9.999997e-01 2.916503e-07
## 83 1.748156e-16 9.999961e-01 3.876682e-06
## 84 1.125494e-33 9.924153e-02 9.007585e-01
## 85 1.191672e-24 9.474667e-01 5.253333e-02
## 86 1.983291e-20 9.924721e-01 7.527887e-03
## 87 4.531906e-21 9.980100e-01 1.989996e-03
## 88 2.035626e-23 9.993358e-01 6.642410e-04
## 89 7.813451e-18 9.999440e-01 5.603286e-05
## 90 8.212308e-21 9.998033e-01 1.967487e-04
## 91 6.631189e-23 9.992802e-01 7.197827e-04
## 92 7.049062e-22 9.979525e-01 2.047473e-03
## 93 4.490728e-18 9.999881e-01 1.188058e-05
## 94 2.600275e-14 9.999999e-01 8.745690e-08
## 95 6.422939e-21 9.996751e-01 3.248823e-04
## 96 2.159263e-17 9.999804e-01 1.956029e-05
## 97 3.823305e-19 9.998801e-01 1.199041e-04
## 98 2.089502e-18 9.999504e-01 4.963639e-05
## 99 9.013113e-11 1.000000e+00 9.943306e-09
## 100 6.167377e-19 9.999219e-01 7.813051e-05
## 101 1.335977e-53 3.188548e-09 1.000000e+00
## 102 9.949508e-38 1.209398e-03 9.987906e-01
## 103 1.950796e-42 2.774428e-05 9.999723e-01
## 104 3.081602e-38 1.232592e-03 9.987674e-01
## 105 5.411117e-46 1.807449e-06 9.999982e-01
## 106 5.887455e-50 5.662591e-07 9.999994e-01
## 107 1.203272e-32 8.794800e-02 9.120520e-01
## 108 1.774038e-42 1.735541e-04 9.998264e-01
## 109 1.924345e-42 2.617818e-04 9.997382e-01
## 110 1.851248e-46 1.352651e-07 9.999999e-01
## 111 4.379051e-32 1.446014e-02 9.855399e-01
## 112 2.052671e-37 1.776421e-03 9.982236e-01
## 113 9.704392e-39 2.172029e-04 9.997828e-01
## 114 2.386650e-40 2.251253e-04 9.997749e-01
## 115 8.048237e-46 8.410965e-07 9.999992e-01
## 116 1.008588e-39 2.840103e-05 9.999716e-01
## 117 2.811294e-35 6.595206e-03 9.934048e-01
## 118 7.282186e-45 1.296566e-06 9.999987e-01
## 119 1.004644e-64 2.647509e-10 1.000000e+00
## 120 3.160887e-33 3.033047e-01 6.966953e-01
## 121 1.719583e-42 6.688965e-06 9.999933e-01
## 122 6.252717e-37 9.870164e-04 9.990130e-01
## 123 2.627103e-51 7.704580e-07 9.999992e-01
## 124 1.504499e-31 1.070121e-01 8.929879e-01
## 125 3.688147e-39 9.571422e-05 9.999043e-01
## 126 2.426533e-36 3.398007e-03 9.966020e-01
## 127 3.865436e-30 2.055755e-01 7.944245e-01
## 128 3.606381e-30 1.437670e-01 8.562330e-01
## 129 8.371636e-44 1.376281e-05 9.999862e-01
## 130 2.937738e-32 1.589920e-01 8.410080e-01
## 131 6.294581e-42 1.714027e-04 9.998286e-01
## 132 5.466934e-36 7.736441e-04 9.992264e-01
## 133 1.208158e-45 3.051435e-06 9.999969e-01
## 134 5.464475e-29 7.876238e-01 2.123762e-01
## 135 9.884011e-35 1.578198e-01 8.421802e-01
## 136 6.515088e-46 1.990735e-06 9.999980e-01
## 137 2.840394e-44 7.895048e-07 9.999992e-01
## 138 7.160822e-35 7.053731e-03 9.929463e-01
## 139 1.782247e-29 2.122042e-01 7.877958e-01
## 140 3.640914e-36 9.289807e-04 9.990710e-01
## 141 5.881132e-45 1.108009e-06 9.999989e-01
## 142 2.122304e-35 6.157433e-04 9.993843e-01
## 143 9.949508e-38 1.209398e-03 9.987906e-01
## 144 9.585800e-46 9.978596e-07 9.999990e-01
## 145 2.206003e-46 2.038879e-07 9.999998e-01
## 146 1.133074e-38 8.851900e-05 9.999115e-01
## 147 8.781586e-36 7.084468e-03 9.929155e-01
## 148 7.108984e-35 3.342993e-03 9.966570e-01
## 149 3.096565e-40 1.338572e-05 9.999866e-01
## 150 3.585667e-33 2.058806e-02 9.794119e-01plot(1:n,lda.iris$posterior[,1],main="Posterior probabilities (blue, group 1, green, group 2 and orange, group 3)",pch=20,col="blue",
xlab="Observation number",ylab="Probabilities")
points(1:n,lda.iris$posterior[,2],pch=20,col="green")
points(1:n,lda.iris$posterior[,3],pch=20,col="orange")
Análisis discriminante cuadrático QDA.
# QDA con leave-one-out cross validation
qda.iris <- qda(y ~ .,data=X,CV=TRUE)# qda.iris$class contiene las clasificaciones hechas por CV usando QDA
qda.iris$class## [1] setosa setosa setosa setosa setosa setosa
## [7] setosa setosa setosa setosa setosa setosa
## [13] setosa setosa setosa setosa setosa setosa
## [19] setosa setosa setosa setosa setosa setosa
## [25] setosa setosa setosa setosa setosa setosa
## [31] setosa setosa setosa setosa setosa setosa
## [37] setosa setosa setosa setosa setosa setosa
## [43] setosa setosa setosa setosa setosa setosa
## [49] setosa setosa versicolor versicolor versicolor versicolor
## [55] versicolor versicolor versicolor versicolor versicolor versicolor
## [61] versicolor versicolor versicolor versicolor versicolor versicolor
## [67] versicolor versicolor virginica versicolor virginica versicolor
## [73] versicolor versicolor versicolor versicolor versicolor versicolor
## [79] versicolor versicolor versicolor versicolor versicolor virginica
## [85] versicolor versicolor versicolor versicolor versicolor versicolor
## [91] versicolor versicolor versicolor versicolor versicolor versicolor
## [97] versicolor versicolor versicolor versicolor virginica virginica
## [103] virginica virginica virginica virginica virginica virginica
## [109] virginica virginica virginica virginica virginica virginica
## [115] virginica virginica virginica virginica virginica virginica
## [121] virginica virginica virginica virginica virginica virginica
## [127] virginica virginica virginica virginica virginica virginica
## [133] virginica versicolor virginica virginica virginica virginica
## [139] virginica virginica virginica virginica virginica virginica
## [145] virginica virginica virginica virginica virginica virginica
## Levels: setosa versicolor virginica# Tabla con clasificaciones buenas y malas
table.qda <- table(y,qda.iris$class)
table.qda##
## y setosa versicolor virginica
## setosa 50 0 0
## versicolor 0 47 3
## virginica 0 1 49# Proporción de errores
mis.qda <- n - sum(y==qda.iris$class)
mis.qda/n## [1] 0.02666667# Buenas clasificaciones en rojo, malas en negro
col.qda.iris <- c("black","indianred1")[1*(y==qda.iris$class)+1]
pairs(X,main="Good (in red) and bad (in black) classifications for the Iris data set with QDC",pch=19,col=col.qda.iris)
# qda.iris$posterior son las probabilidades de pertenencia a uno de los tres grupos
qda.iris$posterior## setosa versicolor virginica
## 1 1.000000e+00 5.135602e-26 3.113136e-41
## 2 1.000000e+00 8.359713e-19 1.431573e-34
## 3 1.000000e+00 1.645823e-21 3.584152e-36
## 4 1.000000e+00 8.922330e-19 9.181884e-32
## 5 1.000000e+00 3.527981e-27 2.107122e-41
## 6 1.000000e+00 1.792730e-26 1.548504e-40
## 7 1.000000e+00 3.128897e-21 2.983384e-34
## 8 1.000000e+00 1.184795e-23 6.821520e-38
## 9 1.000000e+00 1.507202e-16 9.616964e-30
## 10 1.000000e+00 9.632271e-21 6.728268e-35
## 11 1.000000e+00 6.461752e-29 2.377724e-44
## 12 1.000000e+00 2.325868e-22 1.177394e-34
## 13 1.000000e+00 6.029082e-20 1.046640e-34
## 14 1.000000e+00 8.504485e-20 7.344485e-34
## 15 1.000000e+00 3.018977e-36 3.104485e-55
## 16 1.000000e+00 3.230868e-37 2.733399e-52
## 17 1.000000e+00 7.143287e-30 2.219336e-46
## 18 1.000000e+00 2.163753e-24 6.490402e-40
## 19 1.000000e+00 2.698108e-27 4.575422e-43
## 20 1.000000e+00 7.761462e-28 1.383849e-41
## 21 1.000000e+00 2.956983e-22 3.124562e-37
## 22 1.000000e+00 1.704048e-24 7.695902e-39
## 23 1.000000e+00 1.481079e-26 3.836668e-41
## 24 1.000000e+00 1.991718e-15 1.060673e-29
## 25 1.000000e+00 4.395459e-19 7.006800e-29
## 26 1.000000e+00 2.481172e-17 3.585961e-32
## 27 1.000000e+00 2.109095e-19 1.564273e-33
## 28 1.000000e+00 1.722923e-25 1.564694e-40
## 29 1.000000e+00 9.579097e-25 6.085000e-41
## 30 1.000000e+00 1.638107e-19 5.711344e-32
## 31 1.000000e+00 1.832646e-18 7.862708e-32
## 32 1.000000e+00 4.036497e-21 4.686975e-38
## 33 1.000000e+00 1.987833e-36 7.492007e-48
## 34 1.000000e+00 3.933328e-38 1.102795e-52
## 35 1.000000e+00 2.081381e-19 4.057141e-34
## 36 1.000000e+00 9.711433e-23 7.170642e-40
## 37 1.000000e+00 3.617342e-27 1.388674e-45
## 38 1.000000e+00 1.621581e-28 1.854333e-41
## 39 1.000000e+00 3.702994e-18 9.872742e-32
## 40 1.000000e+00 7.503909e-24 1.110035e-38
## 41 1.000000e+00 9.818747e-25 2.585685e-40
## 42 1.000000e+00 3.473021e-09 8.303154e-25
## 43 1.000000e+00 2.453421e-20 2.888472e-33
## 44 1.000000e+00 7.457607e-16 2.765978e-29
## 45 1.000000e+00 1.668579e-21 6.232274e-33
## 46 1.000000e+00 2.917024e-17 1.428353e-32
## 47 1.000000e+00 6.517907e-29 2.695927e-41
## 48 1.000000e+00 1.268355e-20 5.303904e-34
## 49 1.000000e+00 9.793198e-29 1.455187e-43
## 50 1.000000e+00 5.650031e-23 2.443158e-38
## 51 4.939440e-90 9.999286e-01 7.139489e-05
## 52 7.676333e-82 9.996115e-01 3.884766e-04
## 53 3.373285e-102 9.980608e-01 1.939232e-03
## 54 8.976327e-63 9.965561e-01 3.443898e-03
## 55 1.953436e-90 9.970446e-01 2.955439e-03
## 56 1.524298e-77 9.869249e-01 1.307513e-02
## 57 7.851457e-92 9.938631e-01 6.136886e-03
## 58 3.293224e-33 9.999918e-01 8.246015e-06
## 59 1.139916e-84 9.997560e-01 2.440350e-04
## 60 3.207247e-59 9.917797e-01 8.220276e-03
## 61 3.555186e-41 9.998933e-01 1.067302e-04
## 62 5.357381e-71 9.983673e-01 1.632735e-03
## 63 1.023107e-59 9.999771e-01 2.294662e-05
## 64 7.519232e-89 9.875989e-01 1.240115e-02
## 65 1.174534e-45 9.999840e-01 1.603784e-05
## 66 2.059636e-77 9.999832e-01 1.683778e-05
## 67 6.677398e-82 9.682535e-01 3.174653e-02
## 68 1.590680e-56 9.997674e-01 2.326482e-04
## 69 1.376175e-89 3.134218e-01 6.865782e-01
## 70 1.262083e-53 9.999620e-01 3.801566e-05
## 71 1.329043e-103 1.616423e-01 8.383577e-01
## 72 9.469839e-61 9.999889e-01 1.106703e-05
## 73 7.690827e-105 5.895851e-01 4.104149e-01
## 74 4.743472e-84 9.470645e-01 5.293553e-02
## 75 7.636284e-72 9.999778e-01 2.217696e-05
## 76 4.048679e-78 9.999631e-01 3.689607e-05
## 77 4.039192e-98 9.981226e-01 1.877389e-03
## 78 1.552432e-112 8.209927e-01 1.790073e-01
## 79 1.893043e-83 9.917377e-01 8.262263e-03
## 80 1.455398e-38 9.999999e-01 1.165082e-07
## 81 5.889664e-51 9.999680e-01 3.202996e-05
## 82 1.075672e-45 9.999933e-01 6.685904e-06
## 83 7.399197e-55 9.999880e-01 1.198434e-05
## 84 4.504693e-114 7.133282e-02 9.286672e-01
## 85 1.002250e-81 9.135265e-01 8.647346e-02
## 86 2.875383e-82 9.939806e-01 6.019439e-03
## 87 1.982274e-92 9.993237e-01 6.763186e-04
## 88 3.092010e-81 9.982980e-01 1.702014e-03
## 89 3.532313e-61 9.997400e-01 2.600160e-04
## 90 1.831894e-61 9.988687e-01 1.131340e-03
## 91 5.391793e-72 9.719023e-01 2.809769e-02
## 92 7.374366e-84 9.967873e-01 3.212691e-03
## 93 4.126904e-59 9.999577e-01 4.233169e-05
## 94 5.622536e-34 9.999951e-01 4.945718e-06
## 95 3.965708e-67 9.985726e-01 1.427361e-03
## 96 6.996659e-62 9.996513e-01 3.486541e-04
## 97 1.063207e-65 9.995516e-01 4.483507e-04
## 98 6.430539e-71 9.999294e-01 7.063526e-05
## 99 7.195471e-27 9.999970e-01 2.979928e-06
## 100 4.822963e-63 9.997492e-01 2.507665e-04
## 101 1.769562e-198 9.456673e-09 1.000000e+00
## 102 6.663736e-126 4.940560e-04 9.995059e-01
## 103 1.309935e-177 5.678904e-05 9.999432e-01
## 104 1.323191e-145 6.384441e-03 9.936156e-01
## 105 3.389341e-174 2.792434e-06 9.999972e-01
## 106 5.604406e-224 2.464853e-06 9.999975e-01
## 107 5.730859e-93 8.976504e-03 9.910235e-01
## 108 1.256200e-192 5.375826e-05 9.999462e-01
## 109 2.761801e-163 1.549088e-04 9.998451e-01
## 110 3.451213e-203 8.605211e-08 9.999999e-01
## 111 7.552253e-127 6.871689e-03 9.931283e-01
## 112 5.820268e-137 9.988090e-04 9.990012e-01
## 113 1.384008e-154 6.774866e-05 9.999323e-01
## 114 8.404018e-128 1.909940e-06 9.999981e-01
## 115 3.152326e-153 4.684004e-13 1.000000e+00
## 116 1.175690e-152 7.053284e-08 9.999999e-01
## 117 5.183491e-140 3.490122e-02 9.650988e-01
## 118 3.656159e-223 8.743017e-04 9.991257e-01
## 119 2.924821e-258 2.328542e-09 1.000000e+00
## 120 7.123246e-111 6.843139e-02 9.315686e-01
## 121 1.432654e-173 5.494482e-07 9.999995e-01
## 122 3.242236e-121 2.810365e-05 9.999719e-01
## 123 8.940697e-231 5.198710e-07 9.999995e-01
## 124 2.561265e-113 3.261982e-02 9.673802e-01
## 125 3.849104e-161 9.498652e-04 9.990501e-01
## 126 4.066148e-169 8.562406e-03 9.914376e-01
## 127 1.423627e-107 6.602421e-02 9.339758e-01
## 128 6.595751e-110 1.662081e-01 8.337919e-01
## 129 2.297544e-160 6.287451e-06 9.999937e-01
## 130 7.199198e-154 2.752552e-02 9.724745e-01
## 131 4.834630e-186 1.790728e-04 9.998209e-01
## 132 1.945822e-196 4.535880e-02 9.546412e-01
## 133 1.598435e-165 1.975729e-07 9.999998e-01
## 134 4.988739e-111 6.631976e-01 3.368024e-01
## 135 5.362532e-135 6.046378e-04 9.993954e-01
## 136 6.099393e-203 2.039287e-07 9.999998e-01
## 137 3.597064e-171 7.063359e-08 9.999999e-01
## 138 1.607777e-138 5.476922e-02 9.452308e-01
## 139 2.102568e-105 1.592660e-01 8.407340e-01
## 140 1.103719e-148 2.087213e-04 9.997913e-01
## 141 8.580626e-175 1.143856e-09 1.000000e+00
## 142 5.534645e-145 1.523893e-08 1.000000e+00
## 143 6.663736e-126 4.940560e-04 9.995059e-01
## 144 7.416113e-184 9.918438e-07 9.999990e-01
## 145 5.617297e-184 2.144889e-10 1.000000e+00
## 146 1.736727e-150 4.189019e-09 1.000000e+00
## 147 2.245608e-124 2.073773e-04 9.997926e-01
## 148 8.437198e-134 1.127230e-03 9.988728e-01
## 149 2.255147e-155 1.456774e-06 9.999985e-01
## 150 8.000997e-119 6.809620e-02 9.319038e-01# Gráfico de probabilidades
plot(1:n,qda.iris$posterior[,1],main="Posterior probabilities (blue, group 1, green, group 2 and orange, group 3)",pch=20,col="blue",
xlab="Observation number",ylab="Probabilities")
points(1:n,qda.iris$posterior[,2],pch=20,col="green")
points(1:n,qda.iris$posterior[,3],pch=20,col="orange")
qda.iris <- qda(y ~ .,data=X)
qda.iris## Call:
## qda(y ~ ., data = X)
##
## Prior probabilities of groups:
## setosa versicolor virginica
## 0.3333333 0.3333333 0.3333333
##
## Group means:
## Sepal.Length Sepal.Width Petal.Length Petal.Width
## setosa 5.006 3.428 1.462 0.246
## versicolor 5.936 2.770 4.260 1.326
## virginica 6.588 2.974 5.552 2.026