LDA Learning

Loading required R packages

# Install the two packages as follow
#install.packages(c("tidyverse", "caret"))
library(tidyverse)
library(caret)
theme_set(theme_classic())

We will use Credit Card Default data for this

library(ISLR)
data("Default")
head(Default)

##   default student   balance    income
## 1      No      No  729.5265 44361.625
## 2      No     Yes  817.1804 12106.135
## 3      No      No 1073.5492 31767.139
## 4      No      No  529.2506 35704.494
## 5      No      No  785.6559 38463.496
## 6      No     Yes  919.5885  7491.559

Split the data into training (80%) and test set (20%)

set.seed(123)
training.samples <- Default$default %>%
  createDataPartition(p = 0.8, list = FALSE)
train.data <- Default[training.samples, ]
test.data <- Default[-training.samples, ]
dim(train.data)

## [1] 8001    4

dim(test.data)

## [1] 1999    4

Normalize the data. (Categorical variables are automatically ignored)

# Estimate preprocessing parameters
preproc.param <- train.data %>% 
  preProcess(method = c("center", "scale"))
# Transform the data using the estimated parameters
train.transformed <- preproc.param %>% predict(train.data)
test.transformed <- preproc.param %>% predict(test.data)

Linear discriminant analysis - LDA

library(MASS)

## 
## Attaching package: 'MASS'

## The following object is masked from 'package:dplyr':
## 
##     select

# Fit the model
model <- lda(default~., data = train.transformed)
model

## Call:
## lda(default ~ ., data = train.transformed)
## 
## Prior probabilities of groups:
##         No        Yes 
## 0.96662917 0.03337083 
## 
## Group means:
##     studentYes     balance      income
## No   0.2940264 -0.06531569  0.00265296
## Yes  0.3782772  1.89195341 -0.07684642
## 
## Coefficients of linear discriminants:
##                    LD1
## studentYes -0.12703805
## balance     1.08587918
## income      0.08175247

plot(model)

Make predictions

predictions <- model %>% predict(test.transformed)
names(predictions)

## [1] "class"     "posterior" "x"

Understanding Outputs

# Predicted classes
head(predictions$class, 6)

## [1] No No No No No No
## Levels: No Yes

# Predicted probabilities of class memebership.
head(predictions$posterior, 6) 

##           No         Yes
## 6  0.9962229 0.003777134
## 19 0.9987222 0.001277790
## 23 0.9836605 0.016339509
## 24 0.9982105 0.001789493
## 34 0.9920594 0.007940607
## 37 0.9971680 0.002831959

# Linear discriminants
head(predictions$x, 3) 

##            LD1
## 6  -0.06404822
## 19 -0.57935144
## 23  0.63671164

Model accuracy

mean(predictions$class==test.transformed$default)

## [1] 0.969985

It can be seen that, our model correctly classified 96.9% of observations, which is excellent.

Confusion Matrix

Pred <- predictions$class
Actual <- test.transformed$default

confusionMatrix(table(Pred,Actual),positive = "Yes")

## Confusion Matrix and Statistics
## 
##      Actual
## Pred    No  Yes
##   No  1926   53
##   Yes    7   13
##                                          
##                Accuracy : 0.97           
##                  95% CI : (0.9615, 0.977)
##     No Information Rate : 0.967          
##     P-Value [Acc > NIR] : 0.2488         
##                                          
##                   Kappa : 0.2914         
##                                          
##  Mcnemar's Test P-Value : 6.267e-09      
##                                          
##             Sensitivity : 0.196970       
##             Specificity : 0.996379       
##          Pos Pred Value : 0.650000       
##          Neg Pred Value : 0.973219       
##              Prevalence : 0.033017       
##          Detection Rate : 0.006503       
##    Detection Prevalence : 0.010005       
##       Balanced Accuracy : 0.596674       
##                                          
##        'Positive' Class : Yes            
##