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SVM Assignment.R
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SVM Assignment.R
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# Comment next line as that will just create problem
setwd("C:/Users/putripat/Downloads/SVM Dataset")
###### Loading Neccessary libraries ######
library(kernlab)
library(readr)
library(caret)
library(e1071)
###### Loading Full MNIST Data and performing sanity checks on data ######
Data <- read_csv("mnist_train.csv", col_names=FALSE)
# Reading full test MNIST dataset
testMNIST <- read_csv("mnist_test.csv", col_names=FALSE)
######## Data Preparation and EDA #########
# Checking Duplicates
which(duplicated(Data) | duplicated(Data[nrow(Data):1, ])[nrow(Data):1])
# integer(0)
# There are no duplicates in data
#Understanding Dimensions
dim(Data)
#Structure of the dataset
str(Data)
# All data is numeric & X1 is our Digit / Label Column
#printing first few rows
head(Data)
#Exploring the data
summary(Data)
#checking missing value in the dataset
sapply(Data, function(x) sum(is.na(x)))
#No columns found with NA(missing) values.
# converting target column to factor
Data$digit <- factor(Data$X1)
# checking distribution of digits
summary(Data$digit)
# 0 1 2 3 4 5 6 7 8 9
# 5923 6742 5958 6131 5842 5421 5918 6265 5851 5949
# removing the older label
Data <- Data[,-1]
# We will not remove any column as it is a digit recognition dataset
###### Sample Selection #######
# Creating a sample of 10% data for model creation
# We will use this data from here on to work this problem
set.seed(100)
Data2 = Data[sample(1:nrow(Data), 0.1*nrow(Data)),]
# checking distribution of digits in 10% sample
summary(Data2$digit)
# 0 1 2 3 4 5 6 7 8 9
# 594 649 626 612 579 555 594 657 557 577
# Both Full dataset and 10% sample have same distribution
# Checking Duplicates in Data2
which(duplicated(Data2) | duplicated(Data2[nrow(Data2):1, ])[nrow(Data2):1])
# integer(0) -> there are no duplicates
# Keepin a 10% sample of test too
test <- testMNIST[sample(1:nrow(testMNIST), 0.1*nrow(testMNIST)),]
# Scaling Data
Data2[,1:784] = (as.matrix(Data2[,1:784]/255))
test[,2:ncol(test)] = (as.matrix(test[,2:ncol(test)]/255))
####### Model Creation #######
#Constructing Individual Model
#Using Linear Kernel using vanilladot kernel
Model_linear <- ksvm(digit ~ ., data = Data2, scale = FALSE, kernel = "vanilladot")
# Evaluating the Linear SVM model on 30% test data
Eval_linear<- predict(Model_linear, test)
#confusion matrix - Linear Kernel
confusionMatrix(Eval_linear,test$X1)
# Confusion Matrix and Statistics
# Reference
# Prediction 0 1 2 3 4 5 6 7 8 9
# 0 100 0 1 1 0 1 4 0 2 0
# 1 0 112 2 1 0 0 0 2 1 1
# 2 0 0 99 2 0 0 1 1 1 0
# 3 0 0 0 96 0 4 0 2 4 1
# 4 0 0 1 0 77 1 0 1 0 8
# 5 1 1 0 3 0 82 2 0 2 0
# 6 1 1 4 0 1 1 97 0 1 0
# 7 0 0 2 1 0 0 0 93 1 3
# 8 0 0 1 3 0 0 0 0 86 3
# 9 0 0 0 1 1 1 0 2 0 78
#
# Overall Statistics
#
# Accuracy : 0.92
# 95% CI : (0.9014, 0.9361)
# No Information Rate : 0.114
# P-Value [Acc > NIR] : < 2.2e-16
#
# Kappa : 0.911
# Mcnemar's Test P-Value : NA
#
# Statistics by Class:
#
# Class: 0 Class: 1 Class: 2 Class: 3 Class: 4 Class: 5 Class: 6 Class: 7 Class: 8 Class: 9
# Sensitivity 0.9804 0.9825 0.9000 0.8889 0.9747 0.9111 0.9327 0.9208 0.8776 0.8298
# Specificity 0.9900 0.9921 0.9944 0.9877 0.9881 0.9901 0.9900 0.9922 0.9922 0.9945
# Pos Pred Value 0.9174 0.9412 0.9519 0.8972 0.8750 0.9011 0.9151 0.9300 0.9247 0.9398
# Neg Pred Value 0.9978 0.9977 0.9877 0.9866 0.9978 0.9912 0.9922 0.9911 0.9868 0.9826
# Prevalence 0.1020 0.1140 0.1100 0.1080 0.0790 0.0900 0.1040 0.1010 0.0980 0.0940
# Detection Rate 0.1000 0.1120 0.0990 0.0960 0.0770 0.0820 0.0970 0.0930 0.0860 0.0780
# Detection Prevalence 0.1090 0.1190 0.1040 0.1070 0.0880 0.0910 0.1060 0.1000 0.0930 0.0830
# Balanced Accuracy 0.9852 0.9873 0.9472 0.9383 0.9814 0.9506 0.9613 0.9565 0.9349 0.9121
# Accuracy of Linear Model - 92%
# Tuning the model
############ Hyperparameter tuning and Cross Validation #####################
# We will use the train function from caret package to perform Cross Validation.
#traincontrol function Controls the computational nuances of the train function.
# i.e. method = CV means Cross Validation.
# Number = 2 implies Number of folds in CV.
trainControl <- trainControl(method="cv", number=5)
# Metric <- "Accuracy" implies our Evaluation metric is Accuracy.
metric <- "Accuracy"
#Expand.grid functions takes set of hyperparameters, that we shall pass to our model.
set.seed(10)
#train function takes Target ~ Prediction, Data, Method = Algorithm
# Metric = Type of metric, tuneGrid = Grid of Parameters,
# trcontrol = Our traincontrol method.
## Trying linear model
grid <- expand.grid(C = c(0, 0.05, 0.1, 0.5, 1, 1.5, 2, 5))
# Trying SVM Linear model here with C from 1 to 5
# Performing 5-fold cross validation
fit.svm <- train(digit ~ ., data=Data2, method="svmLinear", metric=metric,
tuneGrid=grid, trControl=trainControl)
# Checking the accuracy and other coeffs of the model
print(fit.svm)
# Accuracy is coming out to be 92.13% on 5-Fold Cross Validation
# And the accuracy is best at C = 0.05
# Support Vector Machines with Linear Kernel
#
# 6000 samples
# 784 predictor
# 10 classes: '0', '1', '2', '3', '4', '5', '6', '7', '8', '9'
#
# No pre-processing
# Resampling: Cross-Validated (5 fold)
# Summary of sample sizes: 4800, 4801, 4800, 4798, 4801
# Resampling results across tuning parameters:
#
# C Accuracy Kappa
# 0.00 NaN NaN
# 0.05 0.9213392 0.9125818
# 0.10 0.9196740 0.9107299
# 0.50 0.9108373 0.9009087
# 1.00 0.9070042 0.8966487
# 1.50 0.9061721 0.8957237
# 2.00 0.9061721 0.8957237
# 5.00 0.9061721 0.8957237
#
# Accuracy was used to select the optimal model using the largest value.
# The final value used for the model was C = 0.05.
# Plotting model results
plot(fit.svm)
# Evaluating the model on test
evaluate_linear_test<- predict(fit.svm, test)
# Checking the Confusion Matrix to see the accuracy of our SVM model
confusionMatrix(evaluate_linear_test, test$X1)
# Over All Accuracy of of Linear Model - 92.9%
# This is slightly better than the training data where the accuracy was 92.13%
# Confusion Matrix and Statistics
#
# Reference
# Prediction 0 1 2 3 4 5 6 7 8 9
# 0 102 0 1 1 0 1 1 0 1 0
# 1 0 112 0 0 1 0 0 2 1 1
# 2 0 0 101 4 0 0 0 1 0 0
# 3 0 0 0 98 0 4 0 3 6 2
# 4 0 0 1 0 76 1 1 1 0 5
# 5 0 1 0 2 0 81 4 0 3 0
# 6 0 1 4 0 1 1 98 0 1 0
# 7 0 0 2 1 0 0 0 92 1 2
# 8 0 0 1 1 0 1 0 0 85 0
# 9 0 0 0 1 1 1 0 2 0 84
#
# Overall Statistics
#
# Accuracy : 0.929
# 95% CI : (0.9113, 0.9441)
# No Information Rate : 0.114
# P-Value [Acc > NIR] : < 2.2e-16
#
# Kappa : 0.921
# Mcnemar's Test P-Value : NA
#
# Statistics by Class:
#
# Class: 0 Class: 1 Class: 2 Class: 3 Class: 4 Class: 5 Class: 6 Class: 7 Class: 8 Class: 9
# Sensitivity 1.0000 0.9825 0.9182 0.9074 0.9620 0.9000 0.9423 0.9109 0.8673 0.8936
# Specificity 0.9944 0.9944 0.9944 0.9832 0.9902 0.9890 0.9911 0.9933 0.9967 0.9945
# Pos Pred Value 0.9533 0.9573 0.9528 0.8673 0.8941 0.8901 0.9245 0.9388 0.9659 0.9438
# Neg Pred Value 1.0000 0.9977 0.9899 0.9887 0.9967 0.9901 0.9933 0.9900 0.9857 0.9890
# Prevalence 0.1020 0.1140 0.1100 0.1080 0.0790 0.0900 0.1040 0.1010 0.0980 0.0940
# Detection Rate 0.1020 0.1120 0.1010 0.0980 0.0760 0.0810 0.0980 0.0920 0.0850 0.0840
# Detection Prevalence 0.1070 0.1170 0.1060 0.1130 0.0850 0.0910 0.1060 0.0980 0.0880 0.0890
# Balanced Accuracy 0.9972 0.9884 0.9563 0.9453 0.9761 0.9445 0.9667 0.9521 0.9320 0.9440
# We will stick with the linear model as this is a performing really very well on the test data
# Better than it did while in training phase of the model
# the accuracy is increasing as we move from training data to test data
#########################################################################
#Using RBF Kernel
Model_RBF <- ksvm(digit ~ ., data = Data2, scale = FALSE, kernel = "rbfdot")
# Evaluating the RBF SVM model on test data
Eval_RBF<- predict(Model_RBF, test)
#confusion matrix - RBF Kernel
confusionMatrix(Eval_RBF, test$X1)
# Confusion Matrix and Statistics
#
# Reference
# Prediction 0 1 2 3 4 5 6 7 8 9
# 0 101 0 0 0 0 1 0 0 1 0
# 1 0 113 0 0 0 0 0 2 1 1
# 2 0 0 101 0 0 0 0 2 0 0
# 3 0 0 1 105 0 1 0 2 2 1
# 4 0 0 1 0 76 0 0 0 0 4
# 5 0 0 0 1 0 86 1 0 0 0
# 6 1 1 3 0 1 2 103 0 1 0
# 7 0 0 3 2 1 0 0 93 1 2
# 8 0 0 1 0 0 0 0 0 92 1
# 9 0 0 0 0 1 0 0 2 0 85
#
# Overall Statistics
#
# Accuracy : 0.955
# 95% CI : (0.9402, 0.967)
# No Information Rate : 0.114
# P-Value [Acc > NIR] : < 2.2e-16
#
# Kappa : 0.9499
# Mcnemar's Test P-Value : NA
#
# Statistics by Class:
#
# Class: 0 Class: 1 Class: 2 Class: 3 Class: 4 Class: 5 Class: 6 Class: 7 Class: 8 Class: 9
# Sensitivity 0.9902 0.9912 0.9182 0.9722 0.9620 0.9556 0.9904 0.9208 0.9388 0.9043
# Specificity 0.9978 0.9955 0.9978 0.9922 0.9946 0.9978 0.9900 0.9900 0.9978 0.9967
# Pos Pred Value 0.9806 0.9658 0.9806 0.9375 0.9383 0.9773 0.9196 0.9118 0.9787 0.9659
# Neg Pred Value 0.9989 0.9989 0.9900 0.9966 0.9967 0.9956 0.9989 0.9911 0.9934 0.9901
# Prevalence 0.1020 0.1140 0.1100 0.1080 0.0790 0.0900 0.1040 0.1010 0.0980 0.0940
# Detection Rate 0.1010 0.1130 0.1010 0.1050 0.0760 0.0860 0.1030 0.0930 0.0920 0.0850
# Detection Prevalence 0.1030 0.1170 0.1030 0.1120 0.0810 0.0880 0.1120 0.1020 0.0940 0.0880
# Balanced Accuracy 0.9940 0.9934 0.9580 0.9822 0.9783 0.9767 0.9902 0.9554 0.9683 0.9505
# Accuracy of Overall Model - 95.5%
# Tuning Radial SVM model
set.seed(35)
# Creating new grid for CV
grid <- expand.grid(.sigma=c(10^(-1:2)), .C=c(.05,0.1,2))
#
#
#
##train function takes Target ~ Prediction, Data, Method = Algorithm
##Metric = Type of metric, tuneGrid = Grid of Parameters,
## trcontrol = Our traincontrol method.
#
fit.svm_radial <- train(digit ~ ., data=Data2, method="svmRadial", metric=metric,
tuneGrid=grid, trControl=trainControl)
print(fit.svm_radial)
# Though RBF is performing better but it is -
# 1. A complex model
# 2. And an accuracy of 95% in training means high bias and is prone to overfitting
# which means there is a good chance it might be a bad choice for data that it has not seen yet.
# We will go with a Simpler model, Linear SVM Model