Finding optimal for k-nn 튜닝 in R

# Optimal kNN

knn_error_rate <-function(x, y, numNeighbors, z=x) {

  y_hat <- knn(train=x, test=z, cl=y, k=numNeighbors)

  return(sum(y_hat !=y) / nrow(x))

}

ks<-c(1:10, 15, 20, 25, 30)

train_rates <- sapply(ks, FUN=knn_error_rate, x=train_q, y=train$SleepTrouble)

knn_error_rates <- data.frame(k=ks, train_rate=train_rates)

ggplot(data=knn_error_rates, aes(x=k, y=train_rate)) +

  geom_point() + geom_line() + ylab("Misclassification Rate")

 

# knn for test set (k=c(30,25,20,10,7,5,3))

SleepTrouble_knn30 <- knn(train_q, test = test_q, cl = train$SleepTrouble, k = 30)

SleepTrouble_knn25 <- knn(train_q, test = test_q, cl = train$SleepTrouble, k = 25)

SleepTrouble_knn20 <- knn(train_q, test = test_q, cl = train$SleepTrouble, k = 20)

SleepTrouble_knn10 <- knn(train_q, test = test_q, cl = train$SleepTrouble, k = 10)

SleepTrouble_knn7 <- knn(train_q, test = test_q, cl = train$SleepTrouble, k = 7)

SleepTrouble_knn5 <- knn(train_q, test = test_q, cl = train$SleepTrouble, k = 5)

SleepTrouble_knn3 <- knn(train_q, test = test_q, cl = train$SleepTrouble, k = 3)

 

 

# performance of knn for test set

confusionMatrix(table(test$SleepTrouble, SleepTrouble_knn30))

confusionMatrix(table(test$SleepTrouble, SleepTrouble_knn25))

confusionMatrix(table(test$SleepTrouble, SleepTrouble_knn20))

confusionMatrix(table(test$SleepTrouble, SleepTrouble_knn10))

confusionMatrix(table(test$SleepTrouble, SleepTrouble_knn7))

confusionMatrix(table(test$SleepTrouble, SleepTrouble_knn5))

confusionMatrix(table(test$SleepTrouble, SleepTrouble_knn3))

 

tr_knn30 <- knn(train_q, test = train_q, cl = train$SleepTrouble, k = 30)

tr_knn25 <- knn(train_q, test = train_q, cl = train$SleepTrouble, k = 25)

tr_knn20 <- knn(train_q, test = train_q, cl = train$SleepTrouble, k = 20)

tr_knn10 <- knn(train_q, test = train_q, cl = train$SleepTrouble, k = 10)

tr_knn7 <- knn(train_q, test = train_q, cl = train$SleepTrouble, k = 7)

tr_knn5 <- knn(train_q, test = train_q, cl = train$SleepTrouble, k = 5)

tr_knn3 <- knn(train_q, test = train_q, cl = train$SleepTrouble, k = 3)

 

# performance of knn for training set

confusionMatrix(table(train$SleepTrouble,tr_knn30))

confusionMatrix(table(train$SleepTrouble,tr_knn25))

confusionMatrix(table(train$SleepTrouble,tr_knn20))

confusionMatrix(table(train$SleepTrouble,tr_knn10))

confusionMatrix(table(train$SleepTrouble,tr_knn7))

confusionMatrix(table(train$SleepTrouble,tr_knn5))

confusionMatrix(table(train$SleepTrouble,tr_knn3))

300x250

 

k	Accuracy_test	Accuracy_train	Gap
3	76.13	87.19	=C2-B2 11.06
5	75.2	83.23	=C3-B3 8.03
7	74.2	81.03	=C4-B4 6.83
10	74.13	79.3	=C5-B5 5.17
20	74.4	76.53	=SIGN(LEFT)  =C6-B6 2.13
25	75.17	76.36	=C7-B7 1.19
30	74.93	76.13	=C8-B8 1.2

 

Find Optimal for kNN

Accuracy of test, train 모두 k=3에서 가장 높고, 두 군간의 gap은 k=25에서 가장 낮으나,  K-nn에서 k를 너무 키우는 것은 추천하지 않는다. 과적합의 위험이 있고, 알고리즘상유사한 데이터의 범주를 할당하는데 20개씩이나 계산해보고 할당하는 것은 계산시간으로 보나 복잡도차원으로 보더라도 그리 추천할 만 하지 않기 때문이다. 따라서 이 경우 optimal K는 k=3이다.

 

 

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