Linear Discriminant Analysis in R

data("iris")
head(iris)

str(iris)

'data.frame':   150 obs. of  5 variables:
 $ Sepal.Length: num  5.1 4.9 4.7 4.6 5 5.4 4.6 5 4.4 4.9 ...
 $ Sepal.Width : num  3.5 3 3.2 3.1 3.6 3.9 3.4 3.4 2.9 3.1 ...
 $ Petal.Length: num  1.4 1.4 1.3 1.5 1.4 1.7 1.4 1.5 1.4 1.5 ...
 $ Petal.Width : num  0.2 0.2 0.2 0.2 0.2 0.4 0.3 0.2 0.2 0.1 ...
 $ Species     : Factor w/ 3 levels "setosa","versicolor",..: 1 1 1 1 1 1 1 1 1 1 ...

any(is.na(iris))

[1] FALSE

summary(iris)

  Sepal.Length    Sepal.Width     Petal.Length    Petal.Width   
 Min.   :4.300   Min.   :2.000   Min.   :1.000   Min.   :0.100  
 1st Qu.:5.100   1st Qu.:2.800   1st Qu.:1.600   1st Qu.:0.300  
 Median :5.800   Median :3.000   Median :4.350   Median :1.300  
 Mean   :5.843   Mean   :3.057   Mean   :3.758   Mean   :1.199  
 3rd Qu.:6.400   3rd Qu.:3.300   3rd Qu.:5.100   3rd Qu.:1.800  
 Max.   :7.900   Max.   :4.400   Max.   :6.900   Max.   :2.500  
       Species  
 setosa    :50  
 versicolor:50  
 virginica :50  
                
                
                

library(psych)
pairs.panels(iris[1:4], gap=0,bg= c("blue", "green", "red")[iris$Species],pch=21)

data partition

set.seed(345)
ir<- sample(2,nrow(iris),replace = TRUE, prob = c(0.75,0.25))
train <- iris[ir == 1,]
test <- iris[ir == 2,]

Linear discriminant analysis

library(MASS)
lnr <- lda(Species~., train)
lnr

Call:
lda(Species ~ ., data = train)

Prior probabilities of groups:
    setosa versicolor  virginica 
 0.3008850  0.3451327  0.3539823 

Group means:
           Sepal.Length Sepal.Width Petal.Length Petal.Width
setosa         4.947059    3.391176     1.455882   0.2441176
versicolor     5.943590    2.797436     4.282051   1.3487179
virginica      6.630000    2.975000     5.592500   2.0375000

Coefficients of linear discriminants:
                    LD1        LD2
Sepal.Length  0.9525357  0.4570886
Sepal.Width   1.6182574  2.1122989
Petal.Length -2.3789015 -1.2138097
Petal.Width  -2.5903620  2.9972039

Proportion of trace:
   LD1    LD2 
0.9917 0.0083 

percentage seprations achived by the first discriminant function is 99.04% i.e; very high.

attributes(lnr)

$names
 [1] "prior"   "counts"  "means"   "scaling" "lev"     "svd"     "N"      
 [8] "call"    "terms"   "xlevels"

$class
[1] "lda"

lnr$prior

    setosa versicolor  virginica 
 0.3008850  0.3451327  0.3539823 

lnr$counts

    setosa versicolor  virginica 
        34         39         40 

lnr$scaling

                    LD1        LD2
Sepal.Length  0.9525357  0.4570886
Sepal.Width   1.6182574  2.1122989
Petal.Length -2.3789015 -1.2138097
Petal.Width  -2.5903620  2.9972039

Stacked Histogram of discriminanr function values

prd <- predict(lnr, train)
ldahist(data = prd$x[,1], g = train$Species)

#install.packages("devtools")
library(devtools)
#install_github("fawda123/ggord")
library(ggord)
ggord(lnr, train$Species, ylim = c(-5, 5 ))

confusion matrix and accuracy on train data

p.train <- predict(lnr, train)$class
table1 <-  table(predicted = p.train, Actual = train$Species)
table1

            Actual
predicted    setosa versicolor virginica
  setosa         34          0         0
  versicolor      0         37         1
  virginica       0          2        39

sum(diag(table1)/sum(table1))

[1] 0.9734513

confusion matrix and accuracy on test data

p.test <- predict(lnr, test)$class
table2 <- table(predicted = p.test, Actual = test$Species)
table2

            Actual
predicted    setosa versicolor virginica
  setosa         16          0         0
  versicolor      0         11         0
  virginica       0          0        10

sum(diag(table2)/sum(table2))

[1] 1