데이터스케일링과 범주특성의 변환
데이터스케일링과 범주특성의 변환
데이터 스케일링
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스케일링이란 연속형 특성의 단위가 다를 경우 이로 인해 과대 혹은 과소한 파라미터가 추정될 수 있기 때문에 모든 자료에 대해서 동일한 기준으로 자료를 변환하는 것을 의미한다.
 - 
    
머신러닝/딥러닝 전에 특성변수의 스케일링 과정은 매우 중요하다
 
- Min-Max Scaling
 
- 가장 대표적인 머신러닝/딥러닝의 스케일링 방법
 
- 각 특성변수의 값과 최소값의 차이를 (최대-최소)로 나눔
 
- 이 경우 모든 값은 0 이상의 양(+)의 값을 가짐
 
- 이상치에 영향이 있음
 
- standardization
 
- 평균이 0, 표준편차가 1이 되는 통계적인 자료 표준화의 대표적 값
 
- 표준화를 하는 이유는?
 
머신러닝에서 사용하는 Support Vector Machine, Linear Regression, Logistic Regression 모델은 데이터가 가우시안 분포를 가지고 있다고 가정하여 구현되어 있어서 사전에 학습 데이터에 관해 표준화를 적용하는 것이 모델의 예측 성능 향상에 중요하다.
범주특성의 원핫인코딩 변환
- 
    
머신러닝에서는 one-hot-encoding을 해줘야 함
 - 
    
더미변수로 만들어 준다. (0,1 로 구성)
 
범주형 컬럼은 원핫인코딩으로 0,1으로 구성되게 변환해줌
연속형 컬럼은 Min-Max Scaling 또는 standardization으로 변환해줌
- Min-Max Scaling ,standardization 둘다 해봐서 둘 중에 더 정확한 것을 선택해야 한다
 
실습
1. 데이터 불러오기 & 범주/연속/레이블 분류
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data<-read.csv("data/vote.csv", header=T)
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head(data)
| gender | region | edu | income | age | score_gov | score_progress | score_intention | vote | parties | 
|---|---|---|---|---|---|---|---|---|---|
| 1 | 4 | 3 | 3 | 3 | 2 | 2 | 4.0 | 1 | 2 | 
| 1 | 5 | 2 | 3 | 3 | 2 | 4 | 3.0 | 0 | 3 | 
| 1 | 3 | 1 | 2 | 4 | 1 | 3 | 2.8 | 1 | 4 | 
| 2 | 1 | 2 | 1 | 3 | 5 | 4 | 2.6 | 1 | 1 | 
| 1 | 1 | 1 | 2 | 4 | 4 | 3 | 2.4 | 1 | 1 | 
| 1 | 1 | 1 | 2 | 4 | 1 | 4 | 3.8 | 1 | 2 | 
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data
| gender | region | edu | income | age | score_gov | score_progress | score_intention | vote | parties | 
|---|---|---|---|---|---|---|---|---|---|
| 1 | 4 | 3 | 3 | 3 | 2 | 2 | 4.0 | 1 | 2 | 
| 1 | 5 | 2 | 3 | 3 | 2 | 4 | 3.0 | 0 | 3 | 
| 1 | 3 | 1 | 2 | 4 | 1 | 3 | 2.8 | 1 | 4 | 
| 2 | 1 | 2 | 1 | 3 | 5 | 4 | 2.6 | 1 | 1 | 
| 1 | 1 | 1 | 2 | 4 | 4 | 3 | 2.4 | 1 | 1 | 
| 1 | 1 | 1 | 2 | 4 | 1 | 4 | 3.8 | 1 | 2 | 
| 1 | 1 | 1 | 2 | 4 | 4 | 4 | 2.0 | 1 | 1 | 
| 1 | 5 | 2 | 4 | 4 | 3 | 4 | 3.6 | 1 | 3 | 
| 1 | 2 | 1 | 2 | 4 | 2 | 2 | 2.0 | 0 | 2 | 
| 1 | 1 | 1 | 2 | 3 | 4 | 2 | 3.0 | 1 | 1 | 
| 1 | 1 | 1 | 2 | 3 | 2 | 4 | 2.2 | 0 | 2 | 
| 2 | 4 | 1 | 1 | 3 | 3 | 2 | 2.6 | 1 | 1 | 
| 1 | 5 | 1 | 2 | 4 | 3 | 2 | 3.0 | 1 | 1 | 
| 1 | 2 | 2 | 4 | 4 | 3 | 3 | 2.4 | 1 | 3 | 
| 1 | 4 | 3 | 4 | 3 | 3 | 4 | 3.6 | 1 | 3 | 
| 1 | 1 | 2 | 3 | 3 | 3 | 3 | 3.2 | 1 | 4 | 
| 1 | 5 | 2 | 4 | 3 | 4 | 3 | 4.0 | 1 | 4 | 
| 2 | 1 | 2 | 2 | 3 | 5 | 4 | 2.6 | 1 | 1 | 
| 2 | 3 | 1 | 2 | 2 | 3 | 2 | 3.0 | 0 | 4 | 
| 2 | 5 | 3 | 4 | 3 | 3 | 3 | 3.0 | 1 | 1 | 
| 1 | 1 | 1 | 1 | 2 | 3 | 3 | 2.0 | 0 | 2 | 
| 2 | 1 | 3 | 2 | 2 | 3 | 4 | 2.2 | 1 | 4 | 
| 2 | 4 | 2 | 2 | 2 | 3 | 3 | 1.4 | 1 | 4 | 
| 1 | 1 | 1 | 3 | 3 | 3 | 4 | 1.6 | 1 | 4 | 
| 1 | 4 | 2 | 3 | 3 | 3 | 2 | 3.6 | 1 | 2 | 
| 1 | 1 | 2 | 2 | 2 | 3 | 2 | 3.2 | 1 | 4 | 
| 2 | 1 | 2 | 3 | 2 | 3 | 4 | 2.8 | 1 | 1 | 
| 2 | 1 | 2 | 4 | 3 | 4 | 4 | 3.0 | 1 | 1 | 
| 1 | 1 | 1 | 3 | 3 | 1 | 2 | 3.0 | 1 | 2 | 
| 2 | 1 | 2 | 4 | 4 | 3 | 3 | 2.2 | 1 | 3 | 
| ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | 
| 1 | 1 | 2 | 1 | 2 | 3 | 5 | 2.2 | 1 | 1 | 
| 1 | 2 | 2 | 1 | 2 | 4 | 3 | 3.4 | 1 | 4 | 
| 2 | 1 | 1 | 1 | 1 | 4 | 2 | 3.4 | 1 | 4 | 
| 1 | 4 | 1 | 1 | 2 | 1 | 4 | 2.8 | 1 | 4 | 
| 2 | 1 | 1 | 1 | 1 | 3 | 4 | 2.8 | 1 | 2 | 
| 2 | 1 | 1 | 1 | 2 | 2 | 4 | 3.0 | 0 | 4 | 
| 1 | 5 | 2 | 2 | 3 | 4 | 3 | 3.4 | 0 | 1 | 
| 1 | 1 | 2 | 1 | 1 | 3 | 3 | 2.8 | 1 | 4 | 
| 1 | 1 | 1 | 1 | 2 | 3 | 3 | 3.0 | 1 | 4 | 
| 1 | 5 | 1 | 1 | 1 | 2 | 2 | 2.6 | 0 | 2 | 
| 2 | 1 | 2 | 1 | 3 | 4 | 4 | 4.4 | 1 | 4 | 
| 2 | 2 | 1 | 1 | 1 | 3 | 4 | 2.8 | 0 | 4 | 
| 1 | 5 | 1 | 1 | 2 | 3 | 4 | 3.4 | 1 | 4 | 
| 1 | 2 | 2 | 1 | 2 | 2 | 1 | 2.2 | 1 | 2 | 
| 1 | 5 | 1 | 1 | 1 | 3 | 3 | 3.0 | 0 | 4 | 
| 2 | 1 | 2 | 2 | 3 | 2 | 4 | 3.0 | 1 | 4 | 
| 2 | 1 | 1 | 1 | 3 | 2 | 3 | 3.0 | 1 | 4 | 
| 1 | 1 | 2 | 1 | 2 | 4 | 4 | 5.0 | 1 | 1 | 
| 1 | 1 | 1 | 1 | 2 | 3 | 2 | 2.2 | 1 | 4 | 
| 2 | 1 | 2 | 1 | 2 | 4 | 3 | 3.0 | 1 | 1 | 
| 2 | 1 | 2 | 1 | 2 | 4 | 4 | 3.6 | 0 | 1 | 
| 1 | 1 | 2 | 1 | 2 | 3 | 3 | 3.4 | 1 | 1 | 
| 2 | 1 | 2 | 2 | 2 | 3 | 3 | 3.6 | 1 | 4 | 
| 2 | 1 | 1 | 1 | 1 | 5 | 4 | 3.2 | 0 | 1 | 
| 2 | 1 | 1 | 3 | 4 | 3 | 2 | 1.0 | 1 | 2 | 
| 1 | 4 | 1 | 4 | 4 | 3 | 3 | 1.8 | 1 | 2 | 
| 1 | 1 | 2 | 1 | 2 | 3 | 4 | 2.6 | 1 | 4 | 
| 1 | 2 | 2 | 1 | 2 | 3 | 3 | 2.6 | 1 | 2 | 
| 1 | 1 | 2 | 3 | 4 | 3 | 2 | 4.0 | 1 | 4 | 
| 2 | 1 | 2 | 2 | 2 | 3 | 3 | 3.8 | 1 | 2 | 
범주형 자료 따로 분리해주기
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data_cat <-subset(data, select=c(gender, region))
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data_cat
| gender | region | 
|---|---|
| 1 | 4 | 
| 1 | 5 | 
| 1 | 3 | 
| 2 | 1 | 
| 1 | 1 | 
| 1 | 1 | 
| 1 | 1 | 
| 1 | 5 | 
| 1 | 2 | 
| 1 | 1 | 
| 1 | 1 | 
| 2 | 4 | 
| 1 | 5 | 
| 1 | 2 | 
| 1 | 4 | 
| 1 | 1 | 
| 1 | 5 | 
| 2 | 1 | 
| 2 | 3 | 
| 2 | 5 | 
| 1 | 1 | 
| 2 | 1 | 
| 2 | 4 | 
| 1 | 1 | 
| 1 | 4 | 
| 1 | 1 | 
| 2 | 1 | 
| 2 | 1 | 
| 1 | 1 | 
| 2 | 1 | 
| ... | ... | 
| 1 | 1 | 
| 1 | 2 | 
| 2 | 1 | 
| 1 | 4 | 
| 2 | 1 | 
| 2 | 1 | 
| 1 | 5 | 
| 1 | 1 | 
| 1 | 1 | 
| 1 | 5 | 
| 2 | 1 | 
| 2 | 2 | 
| 1 | 5 | 
| 1 | 2 | 
| 1 | 5 | 
| 2 | 1 | 
| 2 | 1 | 
| 1 | 1 | 
| 1 | 1 | 
| 2 | 1 | 
| 2 | 1 | 
| 1 | 1 | 
| 2 | 1 | 
| 2 | 1 | 
| 2 | 1 | 
| 1 | 4 | 
| 1 | 1 | 
| 1 | 2 | 
| 1 | 1 | 
| 2 | 1 | 
연속형 자료 따로 분리해주기
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data_num <-subset(data, select = c(edu, income, age, score_gov, score_progress, score_intention))
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data_num
| edu | income | age | score_gov | score_progress | score_intention | 
|---|---|---|---|---|---|
| 3 | 3 | 3 | 2 | 2 | 4.0 | 
| 2 | 3 | 3 | 2 | 4 | 3.0 | 
| 1 | 2 | 4 | 1 | 3 | 2.8 | 
| 2 | 1 | 3 | 5 | 4 | 2.6 | 
| 1 | 2 | 4 | 4 | 3 | 2.4 | 
| 1 | 2 | 4 | 1 | 4 | 3.8 | 
| 1 | 2 | 4 | 4 | 4 | 2.0 | 
| 2 | 4 | 4 | 3 | 4 | 3.6 | 
| 1 | 2 | 4 | 2 | 2 | 2.0 | 
| 1 | 2 | 3 | 4 | 2 | 3.0 | 
| 1 | 2 | 3 | 2 | 4 | 2.2 | 
| 1 | 1 | 3 | 3 | 2 | 2.6 | 
| 1 | 2 | 4 | 3 | 2 | 3.0 | 
| 2 | 4 | 4 | 3 | 3 | 2.4 | 
| 3 | 4 | 3 | 3 | 4 | 3.6 | 
| 2 | 3 | 3 | 3 | 3 | 3.2 | 
| 2 | 4 | 3 | 4 | 3 | 4.0 | 
| 2 | 2 | 3 | 5 | 4 | 2.6 | 
| 1 | 2 | 2 | 3 | 2 | 3.0 | 
| 3 | 4 | 3 | 3 | 3 | 3.0 | 
| 1 | 1 | 2 | 3 | 3 | 2.0 | 
| 3 | 2 | 2 | 3 | 4 | 2.2 | 
| 2 | 2 | 2 | 3 | 3 | 1.4 | 
| 1 | 3 | 3 | 3 | 4 | 1.6 | 
| 2 | 3 | 3 | 3 | 2 | 3.6 | 
| 2 | 2 | 2 | 3 | 2 | 3.2 | 
| 2 | 3 | 2 | 3 | 4 | 2.8 | 
| 2 | 4 | 3 | 4 | 4 | 3.0 | 
| 1 | 3 | 3 | 1 | 2 | 3.0 | 
| 2 | 4 | 4 | 3 | 3 | 2.2 | 
| ... | ... | ... | ... | ... | ... | 
| 2 | 1 | 2 | 3 | 5 | 2.2 | 
| 2 | 1 | 2 | 4 | 3 | 3.4 | 
| 1 | 1 | 1 | 4 | 2 | 3.4 | 
| 1 | 1 | 2 | 1 | 4 | 2.8 | 
| 1 | 1 | 1 | 3 | 4 | 2.8 | 
| 1 | 1 | 2 | 2 | 4 | 3.0 | 
| 2 | 2 | 3 | 4 | 3 | 3.4 | 
| 2 | 1 | 1 | 3 | 3 | 2.8 | 
| 1 | 1 | 2 | 3 | 3 | 3.0 | 
| 1 | 1 | 1 | 2 | 2 | 2.6 | 
| 2 | 1 | 3 | 4 | 4 | 4.4 | 
| 1 | 1 | 1 | 3 | 4 | 2.8 | 
| 1 | 1 | 2 | 3 | 4 | 3.4 | 
| 2 | 1 | 2 | 2 | 1 | 2.2 | 
| 1 | 1 | 1 | 3 | 3 | 3.0 | 
| 2 | 2 | 3 | 2 | 4 | 3.0 | 
| 1 | 1 | 3 | 2 | 3 | 3.0 | 
| 2 | 1 | 2 | 4 | 4 | 5.0 | 
| 1 | 1 | 2 | 3 | 2 | 2.2 | 
| 2 | 1 | 2 | 4 | 3 | 3.0 | 
| 2 | 1 | 2 | 4 | 4 | 3.6 | 
| 2 | 1 | 2 | 3 | 3 | 3.4 | 
| 2 | 2 | 2 | 3 | 3 | 3.6 | 
| 1 | 1 | 1 | 5 | 4 | 3.2 | 
| 1 | 3 | 4 | 3 | 2 | 1.0 | 
| 1 | 4 | 4 | 3 | 3 | 1.8 | 
| 2 | 1 | 2 | 3 | 4 | 2.6 | 
| 2 | 1 | 2 | 3 | 3 | 2.6 | 
| 2 | 3 | 4 | 3 | 2 | 4.0 | 
| 2 | 2 | 2 | 3 | 3 | 3.8 | 
레이블 데이터 분리해주기
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data_class<-subset(data, select=c(vote, parties))
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data_class
| vote | parties | 
|---|---|
| 1 | 2 | 
| 0 | 3 | 
| 1 | 4 | 
| 1 | 1 | 
| 1 | 1 | 
| 1 | 2 | 
| 1 | 1 | 
| 1 | 3 | 
| 0 | 2 | 
| 1 | 1 | 
| 0 | 2 | 
| 1 | 1 | 
| 1 | 1 | 
| 1 | 3 | 
| 1 | 3 | 
| 1 | 4 | 
| 1 | 4 | 
| 1 | 1 | 
| 0 | 4 | 
| 1 | 1 | 
| 0 | 2 | 
| 1 | 4 | 
| 1 | 4 | 
| 1 | 4 | 
| 1 | 2 | 
| 1 | 4 | 
| 1 | 1 | 
| 1 | 1 | 
| 1 | 2 | 
| 1 | 3 | 
| ... | ... | 
| 1 | 1 | 
| 1 | 4 | 
| 1 | 4 | 
| 1 | 4 | 
| 1 | 2 | 
| 0 | 4 | 
| 0 | 1 | 
| 1 | 4 | 
| 1 | 4 | 
| 0 | 2 | 
| 1 | 4 | 
| 0 | 4 | 
| 1 | 4 | 
| 1 | 2 | 
| 0 | 4 | 
| 1 | 4 | 
| 1 | 4 | 
| 1 | 1 | 
| 1 | 4 | 
| 1 | 1 | 
| 0 | 1 | 
| 1 | 1 | 
| 1 | 4 | 
| 0 | 1 | 
| 1 | 2 | 
| 1 | 2 | 
| 1 | 4 | 
| 1 | 2 | 
| 1 | 4 | 
| 1 | 2 | 
2. 범주형 특성의 웟핫인코딩(one-hot-encoding)
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data_cat$gender<-factor(data_cat$gender, labels=c("male", "female"))
str(data_cat)
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'data.frame':	211 obs. of  2 variables:
 $ gender: Factor w/ 2 levels "male","female": 1 1 1 2 1 1 1 1 1 1 ...
 $ region: int  4 5 3 1 1 1 1 5 2 1 ...
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data_cat$region<-factor(data_cat$region, labels=c('Sudo', 'Chungcheung', 'Honam', 'Youngnam', 'Others'))
str(data_cat)
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'data.frame':	211 obs. of  2 variables:
 $ gender: Factor w/ 2 levels "male","female": 1 1 1 2 1 1 1 1 1 1 ...
 $ region: Factor w/ 5 levels "Sudo","Chungcheung",..: 4 5 3 1 1 1 1 5 2 1 ...
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data_cat
| gender | region | 
|---|---|
| male | Youngnam | 
| male | Others | 
| male | Honam | 
| female | Sudo | 
| male | Sudo | 
| male | Sudo | 
| male | Sudo | 
| male | Others | 
| male | Chungcheung | 
| male | Sudo | 
| male | Sudo | 
| female | Youngnam | 
| male | Others | 
| male | Chungcheung | 
| male | Youngnam | 
| male | Sudo | 
| male | Others | 
| female | Sudo | 
| female | Honam | 
| female | Others | 
| male | Sudo | 
| female | Sudo | 
| female | Youngnam | 
| male | Sudo | 
| male | Youngnam | 
| male | Sudo | 
| female | Sudo | 
| female | Sudo | 
| male | Sudo | 
| female | Sudo | 
| ... | ... | 
| male | Sudo | 
| male | Chungcheung | 
| female | Sudo | 
| male | Youngnam | 
| female | Sudo | 
| female | Sudo | 
| male | Others | 
| male | Sudo | 
| male | Sudo | 
| male | Others | 
| female | Sudo | 
| female | Chungcheung | 
| male | Others | 
| male | Chungcheung | 
| male | Others | 
| female | Sudo | 
| female | Sudo | 
| male | Sudo | 
| male | Sudo | 
| female | Sudo | 
| female | Sudo | 
| male | Sudo | 
| female | Sudo | 
| female | Sudo | 
| female | Sudo | 
| male | Youngnam | 
| male | Sudo | 
| male | Chungcheung | 
| male | Sudo | 
| female | Sudo | 
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install.packages("caret")
library(caret)
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  There is a binary version available but the source version is later:
      binary source needs_compilation
caret 6.0-86 6.0-90              TRUE
  Binaries will be installed
package 'caret' successfully unpacked and MD5 sums checked
The downloaded binary packages are in
	C:\Users\MyCom\AppData\Local\Temp\RtmpEDGEx8\downloaded_packages
Warning message:
"package 'caret' was built under R version 3.6.3"Loading required package: lattice
Loading required package: ggplot2
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one_hot <- dummyVars(" ~ .", data = data_cat)
one_hot
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Dummy Variable Object
Formula: ~.
<environment: 0x00000000691091c0>
2 variables, 2 factors
Variables and levels will be separated by '.'
A less than full rank encoding is used
데이터 프레임으로 바꿔주기
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data_cat2 <- data.frame(predict(one_hot, newdata = data_cat))
head(data_cat2)
| gender.male | gender.female | region.Sudo | region.Chungcheung | region.Honam | region.Youngnam | region.Others | 
|---|---|---|---|---|---|---|
| 1 | 0 | 0 | 0 | 0 | 1 | 0 | 
| 1 | 0 | 0 | 0 | 0 | 0 | 1 | 
| 1 | 0 | 0 | 0 | 1 | 0 | 0 | 
| 0 | 1 | 1 | 0 | 0 | 0 | 0 | 
| 1 | 0 | 1 | 0 | 0 | 0 | 0 | 
| 1 | 0 | 1 | 0 | 0 | 0 | 0 | 
3. 연속형 특성의 Scaling
3-1. 표준화(평균 0, 표준편차 1) scaling
연속형 컬럼은 Min-Max Scaling 또는 standardization으로 변환해줌
- Min-Max Scaling ,standardization 둘다 해봐서 둘 중에 더 정확한 것을 선택해야 한다
 
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library(caret)
StandardScale <- preProcess(data_num, method=c("center", "scale"))
print(StandardScale)
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Created from 211 samples and 6 variables
Pre-processing:
  - centered (6)
  - ignored (0)
  - scaled (6)
- 데이터 프레임으로 만들어주기
 
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data_standard <- predict(StandardScale, data_num)
head(data_standard)
| edu | income | age | score_gov | score_progress | score_intention | 
|---|---|---|---|---|---|
| 1.8095327 | 0.7421712 | 0.3966776 | -1.1190329 | -1.13873228 | 1.5020451 | 
| 0.2119955 | 0.7421712 | 0.3966776 | -1.1190329 | 0.94154920 | 0.1228827 | 
| -1.3855418 | -0.1955421 | 1.5432389 | -2.1778487 | -0.09859154 | -0.1529498 | 
| 0.2119955 | -1.1332554 | 0.3966776 | 2.0574147 | 0.94154920 | -0.4287823 | 
| -1.3855418 | -0.1955421 | 1.5432389 | 0.9985988 | -0.09859154 | -0.7046147 | 
| -1.3855418 | -0.1955421 | 1.5432389 | -2.1778487 | 0.94154920 | 1.2262127 | 
3-2. min-max scaling
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MinMaxScale <- preProcess(data_num, method=c("range"))
print(MinMaxScale)
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Created from 211 samples and 6 variables
Pre-processing:
  - ignored (0)
  - re-scaling to [0, 1] (6)
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data_minmax <- predict(MinMaxScale, data_num)
head(data_minmax)
| edu | income | age | score_gov | score_progress | score_intention | 
|---|---|---|---|---|---|
| 1.0 | 0.6666667 | 0.6666667 | 0.25 | 0.25 | 0.75 | 
| 0.5 | 0.6666667 | 0.6666667 | 0.25 | 0.75 | 0.50 | 
| 0.0 | 0.3333333 | 1.0000000 | 0.00 | 0.50 | 0.45 | 
| 0.5 | 0.0000000 | 0.6666667 | 1.00 | 0.75 | 0.40 | 
| 0.0 | 0.3333333 | 1.0000000 | 0.75 | 0.50 | 0.35 | 
| 0.0 | 0.3333333 | 1.0000000 | 0.00 | 0.75 | 0.70 | 
4. 데이터 통합 및 저장
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# cbind로 종 데이터를 추가해준다. cbind 외에도 여러가지 방법으로 같은 작업이 가능하다
Fvote = cbind(data_cat2, data_standard, data_class)
Fvote
| gender.male | gender.female | region.Sudo | region.Chungcheung | region.Honam | region.Youngnam | region.Others | edu | income | age | score_gov | score_progress | score_intention | vote | parties | 
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1.8095327 | 0.7421712 | 0.3966776 | -1.11903285 | -1.13873228 | 1.5020451 | 1 | 2 | 
| 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0.2119955 | 0.7421712 | 0.3966776 | -1.11903285 | 0.94154920 | 0.1228827 | 0 | 3 | 
| 1 | 0 | 0 | 0 | 1 | 0 | 0 | -1.3855418 | -0.1955421 | 1.5432389 | -2.17784869 | -0.09859154 | -0.1529498 | 1 | 4 | 
| 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0.2119955 | -1.1332554 | 0.3966776 | 2.05741467 | 0.94154920 | -0.4287823 | 1 | 1 | 
| 1 | 0 | 1 | 0 | 0 | 0 | 0 | -1.3855418 | -0.1955421 | 1.5432389 | 0.99859883 | -0.09859154 | -0.7046147 | 1 | 1 | 
| 1 | 0 | 1 | 0 | 0 | 0 | 0 | -1.3855418 | -0.1955421 | 1.5432389 | -2.17784869 | 0.94154920 | 1.2262127 | 1 | 2 | 
| 1 | 0 | 1 | 0 | 0 | 0 | 0 | -1.3855418 | -0.1955421 | 1.5432389 | 0.99859883 | 0.94154920 | -1.2562797 | 1 | 1 | 
| 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0.2119955 | 1.6798845 | 1.5432389 | -0.06021701 | 0.94154920 | 0.9503802 | 1 | 3 | 
| 1 | 0 | 0 | 1 | 0 | 0 | 0 | -1.3855418 | -0.1955421 | 1.5432389 | -1.11903285 | -1.13873228 | -1.2562797 | 0 | 2 | 
| 1 | 0 | 1 | 0 | 0 | 0 | 0 | -1.3855418 | -0.1955421 | 0.3966776 | 0.99859883 | -1.13873228 | 0.1228827 | 1 | 1 | 
| 1 | 0 | 1 | 0 | 0 | 0 | 0 | -1.3855418 | -0.1955421 | 0.3966776 | -1.11903285 | 0.94154920 | -0.9804472 | 0 | 2 | 
| 0 | 1 | 0 | 0 | 0 | 1 | 0 | -1.3855418 | -1.1332554 | 0.3966776 | -0.06021701 | -1.13873228 | -0.4287823 | 1 | 1 | 
| 1 | 0 | 0 | 0 | 0 | 0 | 1 | -1.3855418 | -0.1955421 | 1.5432389 | -0.06021701 | -1.13873228 | 0.1228827 | 1 | 1 | 
| 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0.2119955 | 1.6798845 | 1.5432389 | -0.06021701 | -0.09859154 | -0.7046147 | 1 | 3 | 
| 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1.8095327 | 1.6798845 | 0.3966776 | -0.06021701 | 0.94154920 | 0.9503802 | 1 | 3 | 
| 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0.2119955 | 0.7421712 | 0.3966776 | -0.06021701 | -0.09859154 | 0.3987152 | 1 | 4 | 
| 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0.2119955 | 1.6798845 | 0.3966776 | 0.99859883 | -0.09859154 | 1.5020451 | 1 | 4 | 
| 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0.2119955 | -0.1955421 | 0.3966776 | 2.05741467 | 0.94154920 | -0.4287823 | 1 | 1 | 
| 0 | 1 | 0 | 0 | 1 | 0 | 0 | -1.3855418 | -0.1955421 | -0.7498837 | -0.06021701 | -1.13873228 | 0.1228827 | 0 | 4 | 
| 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1.8095327 | 1.6798845 | 0.3966776 | -0.06021701 | -0.09859154 | 0.1228827 | 1 | 1 | 
| 1 | 0 | 1 | 0 | 0 | 0 | 0 | -1.3855418 | -1.1332554 | -0.7498837 | -0.06021701 | -0.09859154 | -1.2562797 | 0 | 2 | 
| 0 | 1 | 1 | 0 | 0 | 0 | 0 | 1.8095327 | -0.1955421 | -0.7498837 | -0.06021701 | 0.94154920 | -0.9804472 | 1 | 4 | 
| 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0.2119955 | -0.1955421 | -0.7498837 | -0.06021701 | -0.09859154 | -2.0837772 | 1 | 4 | 
| 1 | 0 | 1 | 0 | 0 | 0 | 0 | -1.3855418 | 0.7421712 | 0.3966776 | -0.06021701 | 0.94154920 | -1.8079447 | 1 | 4 | 
| 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0.2119955 | 0.7421712 | 0.3966776 | -0.06021701 | -1.13873228 | 0.9503802 | 1 | 2 | 
| 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0.2119955 | -0.1955421 | -0.7498837 | -0.06021701 | -1.13873228 | 0.3987152 | 1 | 4 | 
| 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0.2119955 | 0.7421712 | -0.7498837 | -0.06021701 | 0.94154920 | -0.1529498 | 1 | 1 | 
| 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0.2119955 | 1.6798845 | 0.3966776 | 0.99859883 | 0.94154920 | 0.1228827 | 1 | 1 | 
| 1 | 0 | 1 | 0 | 0 | 0 | 0 | -1.3855418 | 0.7421712 | 0.3966776 | -2.17784869 | -1.13873228 | 0.1228827 | 1 | 2 | 
| 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0.2119955 | 1.6798845 | 1.5432389 | -0.06021701 | -0.09859154 | -0.9804472 | 1 | 3 | 
| ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | 
| 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0.2119955 | -1.1332554 | -0.7498837 | -0.06021701 | 1.98168994 | -0.9804472 | 1 | 1 | 
| 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0.2119955 | -1.1332554 | -0.7498837 | 0.99859883 | -0.09859154 | 0.6745477 | 1 | 4 | 
| 0 | 1 | 1 | 0 | 0 | 0 | 0 | -1.3855418 | -1.1332554 | -1.8964449 | 0.99859883 | -1.13873228 | 0.6745477 | 1 | 4 | 
| 1 | 0 | 0 | 0 | 0 | 1 | 0 | -1.3855418 | -1.1332554 | -0.7498837 | -2.17784869 | 0.94154920 | -0.1529498 | 1 | 4 | 
| 0 | 1 | 1 | 0 | 0 | 0 | 0 | -1.3855418 | -1.1332554 | -1.8964449 | -0.06021701 | 0.94154920 | -0.1529498 | 1 | 2 | 
| 0 | 1 | 1 | 0 | 0 | 0 | 0 | -1.3855418 | -1.1332554 | -0.7498837 | -1.11903285 | 0.94154920 | 0.1228827 | 0 | 4 | 
| 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0.2119955 | -0.1955421 | 0.3966776 | 0.99859883 | -0.09859154 | 0.6745477 | 0 | 1 | 
| 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0.2119955 | -1.1332554 | -1.8964449 | -0.06021701 | -0.09859154 | -0.1529498 | 1 | 4 | 
| 1 | 0 | 1 | 0 | 0 | 0 | 0 | -1.3855418 | -1.1332554 | -0.7498837 | -0.06021701 | -0.09859154 | 0.1228827 | 1 | 4 | 
| 1 | 0 | 0 | 0 | 0 | 0 | 1 | -1.3855418 | -1.1332554 | -1.8964449 | -1.11903285 | -1.13873228 | -0.4287823 | 0 | 2 | 
| 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0.2119955 | -1.1332554 | 0.3966776 | 0.99859883 | 0.94154920 | 2.0537101 | 1 | 4 | 
| 0 | 1 | 0 | 1 | 0 | 0 | 0 | -1.3855418 | -1.1332554 | -1.8964449 | -0.06021701 | 0.94154920 | -0.1529498 | 0 | 4 | 
| 1 | 0 | 0 | 0 | 0 | 0 | 1 | -1.3855418 | -1.1332554 | -0.7498837 | -0.06021701 | 0.94154920 | 0.6745477 | 1 | 4 | 
| 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0.2119955 | -1.1332554 | -0.7498837 | -1.11903285 | -2.17887302 | -0.9804472 | 1 | 2 | 
| 1 | 0 | 0 | 0 | 0 | 0 | 1 | -1.3855418 | -1.1332554 | -1.8964449 | -0.06021701 | -0.09859154 | 0.1228827 | 0 | 4 | 
| 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0.2119955 | -0.1955421 | 0.3966776 | -1.11903285 | 0.94154920 | 0.1228827 | 1 | 4 | 
| 0 | 1 | 1 | 0 | 0 | 0 | 0 | -1.3855418 | -1.1332554 | 0.3966776 | -1.11903285 | -0.09859154 | 0.1228827 | 1 | 4 | 
| 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0.2119955 | -1.1332554 | -0.7498837 | 0.99859883 | 0.94154920 | 2.8812076 | 1 | 1 | 
| 1 | 0 | 1 | 0 | 0 | 0 | 0 | -1.3855418 | -1.1332554 | -0.7498837 | -0.06021701 | -1.13873228 | -0.9804472 | 1 | 4 | 
| 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0.2119955 | -1.1332554 | -0.7498837 | 0.99859883 | -0.09859154 | 0.1228827 | 1 | 1 | 
| 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0.2119955 | -1.1332554 | -0.7498837 | 0.99859883 | 0.94154920 | 0.9503802 | 0 | 1 | 
| 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0.2119955 | -1.1332554 | -0.7498837 | -0.06021701 | -0.09859154 | 0.6745477 | 1 | 1 | 
| 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0.2119955 | -0.1955421 | -0.7498837 | -0.06021701 | -0.09859154 | 0.9503802 | 1 | 4 | 
| 0 | 1 | 1 | 0 | 0 | 0 | 0 | -1.3855418 | -1.1332554 | -1.8964449 | 2.05741467 | 0.94154920 | 0.3987152 | 0 | 1 | 
| 0 | 1 | 1 | 0 | 0 | 0 | 0 | -1.3855418 | 0.7421712 | 1.5432389 | -0.06021701 | -1.13873228 | -2.6354421 | 1 | 2 | 
| 1 | 0 | 0 | 0 | 0 | 1 | 0 | -1.3855418 | 1.6798845 | 1.5432389 | -0.06021701 | -0.09859154 | -1.5321122 | 1 | 2 | 
| 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0.2119955 | -1.1332554 | -0.7498837 | -0.06021701 | 0.94154920 | -0.4287823 | 1 | 4 | 
| 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0.2119955 | -1.1332554 | -0.7498837 | -0.06021701 | -0.09859154 | -0.4287823 | 1 | 2 | 
| 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0.2119955 | 0.7421712 | 1.5432389 | -0.06021701 | -1.13873228 | 1.5020451 | 1 | 4 | 
| 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0.2119955 | -0.1955421 | -0.7498837 | -0.06021701 | -0.09859154 | 1.2262127 | 1 | 2 | 
1
write.csv(Fvote, file="Fvote2.csv", row.names=TRUE)
        
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