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204.6.9 Digit Recognition using SVM

Link to the previous post : https://statinfer.com/204-6-8-svm-advantages-disadvantages-applications/

In this , we will put SVM into practice by solving an image classification problem.

LAB: Digit Recognition using SVM

  • Take an image of a handwritten single digit, and determine what that digit is.
  • Normalized handwritten digits, automatically scanned from envelopes by the U.S. Postal Service. The original scanned digits are binary and of different sizes and orientations; the images here have been de slanted and size normalized, resultingin 16 x 16 grayscale images (Le Cun et al., 1990).
  • The data are in two gzipped files, and each line consists of the digitid (0-9) followed by the 256 grayscale values.
  • Build an SVM model that can be used as the digit recognizer.
  • Use the test dataset to validate the true classification power of the model.
  • What is the final accuracy of the model?

Solution

#Importing test and training data
digits_train <- read.table("C:\\Amrita\\Datavedi\\Digit Recognizer\\USPS\\zip.train.txt", quote="\"", comment.char="")
digits_test <- read.table("C:\\Amrita\\Datavedi\\Digit Recognizer\\USPS\\zip.test.txt", quote="\"", comment.char="")
dim(digits_train)
## [1] 7291  257
dim(digits_test)
## [1] 2007  257
#Lets see some images. 
for(i in 1:6 )
{
data_row<-digits_train[i,-1]
pixels = matrix(as.numeric(data_row),16,16,byrow=TRUE)
image(pixels, axes = FALSE)
title(main = paste("Label is" , digits_train[i,1]), font.main = 4)
}

#Are there any missing values?

sum(is.na(digits_train))
## [1] 0
sum(is.na(digits_test))
## [1] 0
#The first variable is label
table(digits_train$V1)
## 
##    0    1    2    3    4    5    6    7    8    9 
## 1194 1005  731  658  652  556  664  645  542  644
table(digits_test$V1)
## 
##   0   1   2   3   4   5   6   7   8   9 
## 359 264 198 166 200 160 170 147 166 177
########SVM Model Building 
library(e1071)

#Lets keep an eye on runtime
pc <- proc.time()

#Verify the code with limited data 5000 rows
number.svm <- svm(V1 ~. , type="C", data = digits_train[1:5000,])

proc.time() - pc
##    user  system elapsed 
##   38.25    0.14   39.37
summary(number.svm)
## 
## Call:
## svm(formula = V1 ~ ., data = digits_train[1:5000, ], type = "C")
## 
## 
## Parameters:
##    SVM-Type:  C-classification 
##  SVM-Kernel:  radial 
##        cost:  1 
##       gamma:  0.00390625 
## 
## Number of Support Vectors:  2028
## 
##  ( 181 232 245 189 195 45 220 206 305 210 )
## 
## 
## Number of Classes:  10 
## 
## Levels: 
##  0 1 2 3 4 5 6 7 8 9
#Confusion Matrix
library(caret)
label_predicted<-predict(number.svm, type = "class")
confusionMatrix(label_predicted,digits_train[1:5000, 1])
## Confusion Matrix and Statistics
## 
##           Reference
## Prediction   0   1   2   3   4   5   6   7   8   9
##          0 847   0   0   0   0   0   1   0   0   0
##          1   0 674   1   0   1   0   1   0   0   0
##          2   0   0 484   0   0   1   0   0   0   0
##          3   0   0   1 392   0   0   0   0   1   1
##          4   0   0   2   0 429   0   0   1   0   0
##          5   0   0   0   1   0 350   1   0   2   0
##          6   0   0   0   0   1   1 475   0   0   0
##          7   0   0   0   0   0   0   0 459   1   2
##          8   0   0   0   2   0   0   0   0 383   0
##          9   0   0   0   0   3   0   0   1   0 481
## 
## Overall Statistics
##                                           
##                Accuracy : 0.9948          
##                  95% CI : (0.9924, 0.9966)
##     No Information Rate : 0.1694          
##     P-Value [Acc > NIR] : < 2.2e-16       
##                                           
##                   Kappa : 0.9942          
##  Mcnemar's Test P-Value : NA              
## 
## Statistics by Class:
## 
##                      Class: 0 Class: 1 Class: 2 Class: 3 Class: 4 Class: 5
## Sensitivity            1.0000   1.0000   0.9918   0.9924   0.9885   0.9943
## Specificity            0.9998   0.9993   0.9998   0.9993   0.9993   0.9991
## Pos Pred Value         0.9988   0.9956   0.9979   0.9924   0.9931   0.9887
## Neg Pred Value         1.0000   1.0000   0.9991   0.9993   0.9989   0.9996
## Prevalence             0.1694   0.1348   0.0976   0.0790   0.0868   0.0704
## Detection Rate         0.1694   0.1348   0.0968   0.0784   0.0858   0.0700
## Detection Prevalence   0.1696   0.1354   0.0970   0.0790   0.0864   0.0708
## Balanced Accuracy      0.9999   0.9997   0.9958   0.9959   0.9939   0.9967
##                      Class: 6 Class: 7 Class: 8 Class: 9
## Sensitivity            0.9937   0.9957   0.9897   0.9938
## Specificity            0.9996   0.9993   0.9996   0.9991
## Pos Pred Value         0.9958   0.9935   0.9948   0.9918
## Neg Pred Value         0.9993   0.9996   0.9991   0.9993
## Prevalence             0.0956   0.0922   0.0774   0.0968
## Detection Rate         0.0950   0.0918   0.0766   0.0962
## Detection Prevalence   0.0954   0.0924   0.0770   0.0970
## Balanced Accuracy      0.9966   0.9975   0.9946   0.9965
table(label_predicted,digits_train[1:5000, 1])
##                
## label_predicted   0   1   2   3   4   5   6   7   8   9
##               0 847   0   0   0   0   0   1   0   0   0
##               1   0 674   1   0   1   0   1   0   0   0
##               2   0   0 484   0   0   1   0   0   0   0
##               3   0   0   1 392   0   0   0   0   1   1
##               4   0   0   2   0 429   0   0   1   0   0
##               5   0   0   0   1   0 350   1   0   2   0
##               6   0   0   0   0   1   1 475   0   0   0
##               7   0   0   0   0   0   0   0 459   1   2
##               8   0   0   0   2   0   0   0   0 383   0
##               9   0   0   0   0   3   0   0   1   0 481
###Out of time validation with test data
test_label_predicted<-predict(number.svm, newdata =digits_test[,-1] , type = "class")
confusionMatrix(test_label_predicted,digits_test[,1])
## Confusion Matrix and Statistics
## 
##           Reference
## Prediction   0   1   2   3   4   5   6   7   8   9
##          0 351   0   3   0   0   3   5   0   3   0
##          1   0 253   0   0   1   0   0   0   0   0
##          2   6   2 182   6   5   4   4   3   4   0
##          3   0   0   4 144   0   3   0   0   4   0
##          4   1   5   4   0 185   1   2   5   0   4
##          5   0   0   0  11   2 145   1   0   5   1
##          6   0   3   1   0   3   0 158   0   1   0
##          7   0   0   1   1   1   0   0 137   0   1
##          8   1   0   3   3   0   1   0   0 146   2
##          9   0   1   0   1   3   3   0   2   3 169
## 
## Overall Statistics
##                                           
##                Accuracy : 0.9317          
##                  95% CI : (0.9198, 0.9424)
##     No Information Rate : 0.1789          
##     P-Value [Acc > NIR] : < 2.2e-16       
##                                           
##                   Kappa : 0.9233          
##  Mcnemar's Test P-Value : NA              
## 
## Statistics by Class:
## 
##                      Class: 0 Class: 1 Class: 2 Class: 3 Class: 4 Class: 5
## Sensitivity            0.9777   0.9583  0.91919  0.86747  0.92500  0.90625
## Specificity            0.9915   0.9994  0.98121  0.99402  0.98783  0.98917
## Pos Pred Value         0.9616   0.9961  0.84259  0.92903  0.89372  0.87879
## Neg Pred Value         0.9951   0.9937  0.99107  0.98812  0.99167  0.99186
## Prevalence             0.1789   0.1315  0.09865  0.08271  0.09965  0.07972
## Detection Rate         0.1749   0.1261  0.09068  0.07175  0.09218  0.07225
## Detection Prevalence   0.1819   0.1266  0.10762  0.07723  0.10314  0.08221
## Balanced Accuracy      0.9846   0.9789  0.95020  0.93075  0.95641  0.94771
##                      Class: 6 Class: 7 Class: 8 Class: 9
## Sensitivity           0.92941  0.93197  0.87952  0.95480
## Specificity           0.99565  0.99785  0.99457  0.99290
## Pos Pred Value        0.95181  0.97163  0.93590  0.92857
## Neg Pred Value        0.99348  0.99464  0.98920  0.99562
## Prevalence            0.08470  0.07324  0.08271  0.08819
## Detection Rate        0.07872  0.06826  0.07275  0.08421
## Detection Prevalence  0.08271  0.07025  0.07773  0.09068
## Balanced Accuracy     0.96253  0.96491  0.93704  0.97385
#####Model on Full Data 
pc <- proc.time()
number.svm <- svm(V1 ~. , type="C", data = digits_train)
proc.time() - pc
##    user  system elapsed 
##   76.94    0.26   87.24
summary(number.svm)
## 
## Call:
## svm(formula = V1 ~ ., data = digits_train, type = "C")
## 
## 
## Parameters:
##    SVM-Type:  C-classification 
##  SVM-Kernel:  radial 
##        cost:  1 
##       gamma:  0.00390625 
## 
## Number of Support Vectors:  2606
## 
##  ( 213 326 319 235 285 63 256 262 401 246 )
## 
## 
## Number of Classes:  10 
## 
## Levels: 
##  0 1 2 3 4 5 6 7 8 9
#Confusion Matrix
library(caret)
label_predicted<-predict(number.svm, type = "class")
confusionMatrix(label_predicted,digits_train[,1])
## Confusion Matrix and Statistics
## 
##           Reference
## Prediction    0    1    2    3    4    5    6    7    8    9
##          0 1194    0    0    0    0    0    2    0    0    0
##          1    0 1005    1    1    2    0    1    0    1    0
##          2    0    0  724    0    0    1    0    0    0    0
##          3    0    0    2  651    0    0    0    0    0    1
##          4    0    0    4    0  648    1    0    2    1    1
##          5    0    0    0    3    0  553    0    0    2    0
##          6    0    0    0    0    0    1  661    0    0    0
##          7    0    0    0    0    0    0    0  641    2    3
##          8    0    0    0    3    0    0    0    0  536    0
##          9    0    0    0    0    2    0    0    2    0  639
## 
## Overall Statistics
##                                           
##                Accuracy : 0.9947          
##                  95% CI : (0.9927, 0.9962)
##     No Information Rate : 0.1638          
##     P-Value [Acc > NIR] : < 2.2e-16       
##                                           
##                   Kappa : 0.994           
##  Mcnemar's Test P-Value : NA              
## 
## Statistics by Class:
## 
##                      Class: 0 Class: 1 Class: 2 Class: 3 Class: 4 Class: 5
## Sensitivity            1.0000   1.0000  0.99042  0.98936  0.99387  0.99460
## Specificity            0.9997   0.9990  0.99985  0.99955  0.99864  0.99926
## Pos Pred Value         0.9983   0.9941  0.99862  0.99541  0.98630  0.99104
## Neg Pred Value         1.0000   1.0000  0.99893  0.99895  0.99940  0.99955
## Prevalence             0.1638   0.1378  0.10026  0.09025  0.08943  0.07626
## Detection Rate         0.1638   0.1378  0.09930  0.08929  0.08888  0.07585
## Detection Prevalence   0.1640   0.1387  0.09944  0.08970  0.09011  0.07653
## Balanced Accuracy      0.9998   0.9995  0.99514  0.99445  0.99625  0.99693
##                      Class: 6 Class: 7 Class: 8 Class: 9
## Sensitivity           0.99548  0.99380  0.98893  0.99224
## Specificity           0.99985  0.99925  0.99956  0.99940
## Pos Pred Value        0.99849  0.99226  0.99443  0.99378
## Neg Pred Value        0.99955  0.99940  0.99911  0.99925
## Prevalence            0.09107  0.08847  0.07434  0.08833
## Detection Rate        0.09066  0.08792  0.07352  0.08764
## Detection Prevalence  0.09080  0.08860  0.07393  0.08819
## Balanced Accuracy     0.99767  0.99652  0.99424  0.99582
###Out of time validation with test data
test_label_predicted<-predict(number.svm, newdata =digits_test[,-1] , type = "class")
confusionMatrix(test_label_predicted,digits_test[,1])
## Confusion Matrix and Statistics
## 
##           Reference
## Prediction   0   1   2   3   4   5   6   7   8   9
##          0 351   0   2   0   0   3   4   0   4   0
##          1   0 253   0   0   1   0   0   0   0   0
##          2   6   1 183   5   3   2   4   2   2   0
##          3   0   0   4 146   0   3   0   0   3   0
##          4   1   5   3   0 186   1   2   5   0   4
##          5   0   1   0  11   1 147   1   0   2   1
##          6   0   3   1   0   2   0 158   0   1   0
##          7   0   1   1   1   3   0   0 138   0   0
##          8   1   0   4   3   1   1   1   0 151   2
##          9   0   0   0   0   3   3   0   2   3 170
## 
## Overall Statistics
##                                           
##                Accuracy : 0.9382          
##                  95% CI : (0.9268, 0.9484)
##     No Information Rate : 0.1789          
##     P-Value [Acc > NIR] : < 2.2e-16       
##                                           
##                   Kappa : 0.9306          
##  Mcnemar's Test P-Value : NA              
## 
## Statistics by Class:
## 
##                      Class: 0 Class: 1 Class: 2 Class: 3 Class: 4 Class: 5
## Sensitivity            0.9777   0.9583  0.92424  0.87952  0.93000  0.91875
## Specificity            0.9921   0.9994  0.98618  0.99457  0.98838  0.99080
## Pos Pred Value         0.9643   0.9961  0.87981  0.93590  0.89855  0.89634
## Neg Pred Value         0.9951   0.9937  0.99166  0.98920  0.99222  0.99295
## Prevalence             0.1789   0.1315  0.09865  0.08271  0.09965  0.07972
## Detection Rate         0.1749   0.1261  0.09118  0.07275  0.09268  0.07324
## Detection Prevalence   0.1814   0.1266  0.10364  0.07773  0.10314  0.08171
## Balanced Accuracy      0.9849   0.9789  0.95521  0.93704  0.95919  0.95477
##                      Class: 6 Class: 7 Class: 8 Class: 9
## Sensitivity           0.92941  0.93878  0.90964  0.96045
## Specificity           0.99619  0.99677  0.99294  0.99399
## Pos Pred Value        0.95758  0.95833  0.92073  0.93923
## Neg Pred Value        0.99349  0.99517  0.99186  0.99617
## Prevalence            0.08470  0.07324  0.08271  0.08819
## Detection Rate        0.07872  0.06876  0.07524  0.08470
## Detection Prevalence  0.08221  0.07175  0.08171  0.09018
## Balanced Accuracy     0.96280  0.96777  0.95129  0.97722
#Lets see some predictions. 
digits_test$predicted<-test_label_predicted

for(i in 1:10 )
{
data_row<-digits_test[i,c(-1,-ncol(digits_test))]
pixels = matrix(as.numeric(data_row),16,16,byrow=TRUE)
image(pixels, axes = FALSE)
title(main = paste("Label is" , digits_test[i,1] ,"  Prediction is" , digits_test[i,ncol(digits_test)]))
}

#Lets see some errors in predictions images. 
# Wrong predictions
digits_test$predicted<-test_label_predicted
wrong_predictions<-digits_test[!(digits_test$predicted==digits_test$V1),]
nrow(wrong_predictions)
## [1] 124
for(i in 1:10 )
{
data_row<-wrong_predictions[i,c(-1,-ncol(wrong_predictions))]
pixels = matrix(as.numeric(data_row),16,16,byrow=TRUE)
image(pixels, axes = FALSE)
title(main = paste("Label is" , wrong_predictions[i,1] ,"  Prediction is" , wrong_predictions[i,ncol(wrong_predictions)]))
}

Conclusion

  • Many software tools are available for SVM implementation
  • SVMs are really good for text classification
  • SVMs are good at finding the best linear separator. The kernel trick makes SVMs non-linear learning algorithms
  • Choosing an appropriate kernel is the key for good SVM and choosing the right kernel function is not easy
  • We need to be patient while building SVMs on large datasets. They take a lot of time for training.

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