pacman::p_load("data.table",
"tidyverse",
"dplyr", "tidyr",
"ggplot2", "GGally",
"caret",
"glmnet") # For glmnet
titanic <- fread("../Titanic.csv") # 데이터 불러오기
titanic %>%
as_tibble11 LASSO Regression
LASSO Regression의 장점
- 규제항을 통해 회귀계수를 “0”으로 추정하기 때문에 변수 선택이 가능하다.
LASSO Regression의 단점
- 예측 변수의 개수가 표본의 크기보다 큰 경우, 볼록 최적화 문제의 특성 때문에 표본의 크기보다 많은 예측 변수를 선택할 수 없다.
- 예측 변수 사이에 어떤 그룹 구조(쌍별 상관 관계가 매우 높은)가 있을 때, 그룹에서 하나의 예측 변수만 선택한다.
- 예측 변수의 개수가 표본의 크기보다 큰 상황에서 예측 변수들이 높은 상관관계를 가지고 있을 때,
Ridge Regression보다 예측 성능이 낮다.
실습 자료 : 1912년 4월 15일 타이타닉호 침몰 당시 탑승객들의 정보를 기록한 데이터셋이며, 총 11개의 변수를 포함하고 있다. 이 자료에서 Target은
Survived이다.
11.1 데이터 불러오기
# A tibble: 891 × 11
Survived Pclass Name Sex Age SibSp Parch Ticket Fare Cabin Embarked
<int> <int> <chr> <chr> <dbl> <int> <int> <chr> <dbl> <chr> <chr>
1 0 3 Braund, Mr. Owen Harris male 22 1 0 A/5 21171 7.25 "" S
2 1 1 Cumings, Mrs. John Bradley (Florence Briggs Thayer) female 38 1 0 PC 17599 71.3 "C85" C
3 1 3 Heikkinen, Miss. Laina female 26 0 0 STON/O2. 3101282 7.92 "" S
4 1 1 Futrelle, Mrs. Jacques Heath (Lily May Peel) female 35 1 0 113803 53.1 "C123" S
5 0 3 Allen, Mr. William Henry male 35 0 0 373450 8.05 "" S
6 0 3 Moran, Mr. James male NA 0 0 330877 8.46 "" Q
7 0 1 McCarthy, Mr. Timothy J male 54 0 0 17463 51.9 "E46" S
8 0 3 Palsson, Master. Gosta Leonard male 2 3 1 349909 21.1 "" S
9 1 3 Johnson, Mrs. Oscar W (Elisabeth Vilhelmina Berg) female 27 0 2 347742 11.1 "" S
10 1 2 Nasser, Mrs. Nicholas (Adele Achem) female 14 1 0 237736 30.1 "" C
# ℹ 881 more rows11.2 데이터 전처리 I
titanic %<>%
data.frame() %>% # Data Frame 형태로 변환
mutate(Survived = ifelse(Survived == 1, "yes", "no")) # Target을 문자형 변수로 변환
# 1. Convert to Factor
fac.col <- c("Pclass", "Sex",
# Target
"Survived")
titanic <- titanic %>%
mutate_at(fac.col, as.factor) # 범주형으로 변환
glimpse(titanic) # 데이터 구조 확인Rows: 891
Columns: 11
$ Survived <fct> no, yes, yes, yes, no, no, no, no, yes, yes, yes, yes, no, no, no, yes, no, yes, no, yes, no, yes, yes, yes, no, yes, no, no, yes, no, no, yes, yes, no, no, no, yes, no, no, yes, no…
$ Pclass <fct> 3, 1, 3, 1, 3, 3, 1, 3, 3, 2, 3, 1, 3, 3, 3, 2, 3, 2, 3, 3, 2, 2, 3, 1, 3, 3, 3, 1, 3, 3, 1, 1, 3, 2, 1, 1, 3, 3, 3, 3, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 1, 2, 1, 1, 2, 3, 2, 3, 3…
$ Name <chr> "Braund, Mr. Owen Harris", "Cumings, Mrs. John Bradley (Florence Briggs Thayer)", "Heikkinen, Miss. Laina", "Futrelle, Mrs. Jacques Heath (Lily May Peel)", "Allen, Mr. William Henry…
$ Sex <fct> male, female, female, female, male, male, male, male, female, female, female, female, male, male, female, female, male, male, female, female, male, male, female, male, female, femal…
$ Age <dbl> 22.0, 38.0, 26.0, 35.0, 35.0, NA, 54.0, 2.0, 27.0, 14.0, 4.0, 58.0, 20.0, 39.0, 14.0, 55.0, 2.0, NA, 31.0, NA, 35.0, 34.0, 15.0, 28.0, 8.0, 38.0, NA, 19.0, NA, NA, 40.0, NA, NA, 66.…
$ SibSp <int> 1, 1, 0, 1, 0, 0, 0, 3, 0, 1, 1, 0, 0, 1, 0, 0, 4, 0, 1, 0, 0, 0, 0, 0, 3, 1, 0, 3, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 1, 1, 1, 0, 1, 0, 0, 1, 0, 2, 1, 4, 0, 1, 1, 0, 0, 0, 0, 1, 5, 0…
$ Parch <int> 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 0, 0, 5, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 5, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0…
$ Ticket <chr> "A/5 21171", "PC 17599", "STON/O2. 3101282", "113803", "373450", "330877", "17463", "349909", "347742", "237736", "PP 9549", "113783", "A/5. 2151", "347082", "350406", "248706", "38…
$ Fare <dbl> 7.2500, 71.2833, 7.9250, 53.1000, 8.0500, 8.4583, 51.8625, 21.0750, 11.1333, 30.0708, 16.7000, 26.5500, 8.0500, 31.2750, 7.8542, 16.0000, 29.1250, 13.0000, 18.0000, 7.2250, 26.0000,…
$ Cabin <chr> "", "C85", "", "C123", "", "", "E46", "", "", "", "G6", "C103", "", "", "", "", "", "", "", "", "", "D56", "", "A6", "", "", "", "C23 C25 C27", "", "", "", "B78", "", "", "", "", ""…
$ Embarked <chr> "S", "C", "S", "S", "S", "Q", "S", "S", "S", "C", "S", "S", "S", "S", "S", "S", "Q", "S", "S", "C", "S", "S", "Q", "S", "S", "S", "C", "S", "Q", "S", "C", "C", "Q", "S", "C", "S", "…# 2. Generate New Variable
titanic <- titanic %>%
mutate(FamSize = SibSp + Parch) # "FamSize = 형제 및 배우자 수 + 부모님 및 자녀 수"로 가족 수를 의미하는 새로운 변수
glimpse(titanic) # 데이터 구조 확인Rows: 891
Columns: 12
$ Survived <fct> no, yes, yes, yes, no, no, no, no, yes, yes, yes, yes, no, no, no, yes, no, yes, no, yes, no, yes, yes, yes, no, yes, no, no, yes, no, no, yes, yes, no, no, no, yes, no, no, yes, no…
$ Pclass <fct> 3, 1, 3, 1, 3, 3, 1, 3, 3, 2, 3, 1, 3, 3, 3, 2, 3, 2, 3, 3, 2, 2, 3, 1, 3, 3, 3, 1, 3, 3, 1, 1, 3, 2, 1, 1, 3, 3, 3, 3, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 1, 2, 1, 1, 2, 3, 2, 3, 3…
$ Name <chr> "Braund, Mr. Owen Harris", "Cumings, Mrs. John Bradley (Florence Briggs Thayer)", "Heikkinen, Miss. Laina", "Futrelle, Mrs. Jacques Heath (Lily May Peel)", "Allen, Mr. William Henry…
$ Sex <fct> male, female, female, female, male, male, male, male, female, female, female, female, male, male, female, female, male, male, female, female, male, male, female, male, female, femal…
$ Age <dbl> 22.0, 38.0, 26.0, 35.0, 35.0, NA, 54.0, 2.0, 27.0, 14.0, 4.0, 58.0, 20.0, 39.0, 14.0, 55.0, 2.0, NA, 31.0, NA, 35.0, 34.0, 15.0, 28.0, 8.0, 38.0, NA, 19.0, NA, NA, 40.0, NA, NA, 66.…
$ SibSp <int> 1, 1, 0, 1, 0, 0, 0, 3, 0, 1, 1, 0, 0, 1, 0, 0, 4, 0, 1, 0, 0, 0, 0, 0, 3, 1, 0, 3, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 1, 1, 1, 0, 1, 0, 0, 1, 0, 2, 1, 4, 0, 1, 1, 0, 0, 0, 0, 1, 5, 0…
$ Parch <int> 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 0, 0, 5, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 5, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0…
$ Ticket <chr> "A/5 21171", "PC 17599", "STON/O2. 3101282", "113803", "373450", "330877", "17463", "349909", "347742", "237736", "PP 9549", "113783", "A/5. 2151", "347082", "350406", "248706", "38…
$ Fare <dbl> 7.2500, 71.2833, 7.9250, 53.1000, 8.0500, 8.4583, 51.8625, 21.0750, 11.1333, 30.0708, 16.7000, 26.5500, 8.0500, 31.2750, 7.8542, 16.0000, 29.1250, 13.0000, 18.0000, 7.2250, 26.0000,…
$ Cabin <chr> "", "C85", "", "C123", "", "", "E46", "", "", "", "G6", "C103", "", "", "", "", "", "", "", "", "", "D56", "", "A6", "", "", "", "C23 C25 C27", "", "", "", "B78", "", "", "", "", ""…
$ Embarked <chr> "S", "C", "S", "S", "S", "Q", "S", "S", "S", "C", "S", "S", "S", "S", "S", "S", "Q", "S", "S", "C", "S", "S", "Q", "S", "S", "S", "C", "S", "Q", "S", "C", "C", "Q", "S", "C", "S", "…
$ FamSize <int> 1, 1, 0, 1, 0, 0, 0, 4, 2, 1, 2, 0, 0, 6, 0, 0, 5, 0, 1, 0, 0, 0, 0, 0, 4, 6, 0, 5, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 1, 1, 1, 0, 3, 0, 0, 1, 0, 2, 1, 5, 0, 1, 1, 1, 0, 0, 0, 3, 7, 0…# 3. Select Variables used for Analysis
titanic1 <- titanic %>%
select(Survived, Pclass, Sex, Age, Fare, FamSize) # 분석에 사용할 변수 선택
titanic1 %>%
as_tibble# A tibble: 891 × 6
Survived Pclass Sex Age Fare FamSize
<fct> <fct> <fct> <dbl> <dbl> <int>
1 no 3 male 22 7.25 1
2 yes 1 female 38 71.3 1
3 yes 3 female 26 7.92 0
4 yes 1 female 35 53.1 1
5 no 3 male 35 8.05 0
6 no 3 male NA 8.46 0
7 no 1 male 54 51.9 0
8 no 3 male 2 21.1 4
9 yes 3 female 27 11.1 2
10 yes 2 female 14 30.1 1
# ℹ 881 more rows11.3 데이터 탐색
ggpairs(titanic1,
aes(colour = Survived)) + # Target의 범주에 따라 색깔을 다르게 표현
theme_bw()
ggpairs(titanic1,
aes(colour = Survived, alpha = 0.8)) + # Target의 범주에 따라 색깔을 다르게 표현
scale_colour_manual(values = c("#E69F00", "#56B4E9")) + # 특정 색깔 지정
scale_fill_manual(values = c("#E69F00", "#56B4E9")) + # 특정 색깔 지정
theme_bw()
11.4 데이터 분할
# Partition (Training Dataset : Test Dataset = 7:3)
y <- titanic1$Survived # Target
set.seed(200)
ind <- createDataPartition(y, p = 0.7, list =T) # Index를 이용하여 7:3으로 분할
titanic.trd <- titanic1[ind$Resample1,] # Training Dataset
titanic.ted <- titanic1[-ind$Resample1,] # Test Dataset11.5 데이터 전처리 II
# 1. Imputation
titanic.trd.Imp <- titanic.trd %>%
mutate(Age = replace_na(Age, mean(Age, na.rm = TRUE))) # 평균으로 결측값 대체
titanic.ted.Imp <- titanic.ted %>%
mutate(Age = replace_na(Age, mean(titanic.trd$Age, na.rm = TRUE))) # Training Dataset을 이용하여 결측값 대체
# 2. Standardization
preProcValues <- preProcess(titanic.trd.Imp,
method = c("center", "scale")) # Standardization 정의 -> Training Dataset에 대한 평균과 표준편차 계산
titanic.trd.Imp <- predict(preProcValues, titanic.trd.Imp) # Standardization for Training Dataset
titanic.ted.Imp <- predict(preProcValues, titanic.ted.Imp) # Standardization for Test Dataset
# 3. Convert Factor Var. into Dummy Var.
train.x <- model.matrix(Survived ~., # Survived는 Target으로 제외
titanic.trd.Imp)[,-1] # [,-1] : 절편 제거
train.x Pclass2 Pclass3 Sexmale Age Fare FamSize
1 0 1 1 -0.61306970 -0.517763935 0.04506631
3 0 1 0 -0.30411628 -0.504633254 -0.55421976
4 0 0 0 0.39102893 0.374149700 0.04506631
5 0 1 1 0.39102893 -0.502201647 -0.55421976
6 0 1 1 0.00000000 -0.494259044 -0.55421976
8 0 1 1 -2.15783684 -0.248828144 1.84292454
9 0 1 0 -0.22687792 -0.442222643 0.64435239
10 1 0 0 -1.23097656 -0.073834105 0.04506631
11 0 1 0 -2.00336012 -0.333934407 0.64435239
12 0 0 0 2.16751113 -0.142323735 -0.55421976
14 0 1 1 0.69998236 -0.050408971 3.04149669
15 0 1 0 -1.23097656 -0.506010517 -0.55421976
18 1 0 1 0.00000000 -0.405909990 -0.55421976
19 0 1 0 0.08207551 -0.308645689 0.04506631
20 0 1 0 0.00000000 -0.518250257 -0.55421976
21 1 0 1 0.39102893 -0.153022808 -0.55421976
24 0 0 1 -0.14963956 0.031779363 -0.55421976
25 0 1 0 -1.69440670 -0.248828144 1.84292454
27 0 1 1 0.00000000 -0.518250257 -0.55421976
28 0 0 1 -0.84478477 4.457305033 2.44221062
29 0 1 0 0.00000000 -0.505524195 -0.55421976
30 0 1 1 0.00000000 -0.505201278 -0.55421976
31 0 0 1 0.77722072 -0.119548327 -0.55421976
32 0 0 0 0.00000000 2.191451452 0.04506631
33 0 1 0 0.00000000 -0.508037505 -0.55421976
34 1 0 1 2.78541799 -0.454542140 -0.55421976
35 0 0 1 -0.14963956 0.939659905 0.04506631
36 0 0 1 0.93169743 0.352751554 0.04506631
38 0 1 1 -0.69030806 -0.502201647 -0.55421976
39 0 1 0 -0.92202313 -0.308645689 0.64435239
40 0 1 0 -1.23097656 -0.440113953 0.04506631
41 0 1 0 0.77722072 -0.474481321 0.04506631
42 1 0 0 -0.22687792 -0.250287109 0.04506631
43 0 1 1 0.00000000 -0.505201278 -0.55421976
45 0 1 0 -0.84478477 -0.505524195 -0.55421976
47 0 1 1 0.00000000 -0.357277839 0.04506631
48 0 1 0 0.00000000 -0.508037505 -0.55421976
49 0 1 1 0.00000000 -0.237074726 0.64435239
50 0 1 0 -0.92202313 -0.312536261 0.04506631
51 0 1 1 -1.77164505 0.113238214 2.44221062
53 0 0 0 1.47236593 0.833805222 0.04506631
55 0 0 1 2.70817963 0.546875535 0.04506631
56 0 0 1 0.00000000 0.031779363 -0.55421976
60 0 1 1 -1.46269163 0.253541968 3.64078277
61 0 1 1 -0.61306970 -0.518168555 -0.55421976
62 0 0 0 0.62274400 0.897431637 -0.55421976
64 0 1 1 -2.00336012 -0.116062374 2.44221062
65 0 0 1 0.00000000 -0.119548327 -0.55421976
70 0 1 1 -0.30411628 -0.490286770 0.64435239
72 0 1 0 -1.07649984 0.253541968 3.64078277
74 0 1 1 -0.30411628 -0.377621640 0.04506631
75 0 1 1 0.15931386 0.440207722 -0.55421976
76 0 1 1 -0.38135463 -0.509982791 -0.55421976
77 0 1 1 0.00000000 -0.505201278 -0.55421976
79 1 0 1 -2.24820571 -0.094664228 0.64435239
80 0 1 0 0.00483715 -0.416122741 -0.55421976
82 0 1 1 -0.07240121 -0.473995000 -0.55421976
83 0 1 0 0.00000000 -0.507308023 -0.55421976
84 0 0 1 -0.14963956 0.257432540 -0.55421976
85 1 0 0 -0.99926149 -0.454542140 -0.55421976
86 0 1 0 0.23655222 -0.350469338 1.24363847
88 0 1 1 0.00000000 -0.502201647 -0.55421976
89 0 0 0 -0.53583135 4.457305033 2.44221062
91 0 1 1 -0.07240121 -0.502201647 -0.55421976
92 0 1 1 -0.76754642 -0.506010517 -0.55421976
93 0 0 1 1.24065086 0.531231545 0.04506631
94 0 1 1 -0.30411628 -0.258554574 1.24363847
95 0 1 1 2.24474949 -0.517763935 -0.55421976
96 0 1 1 0.00000000 -0.502201647 -0.55421976
97 0 0 1 3.17160977 0.015326133 -0.55421976
103 0 0 1 -0.69030806 0.844665754 0.04506631
105 0 1 1 0.54550565 -0.504633254 0.64435239
107 0 1 0 -0.69030806 -0.509982791 -0.55421976
108 0 1 1 0.00000000 -0.507551184 -0.55421976
110 0 1 0 0.00000000 -0.189010600 0.04506631
111 0 0 1 1.31788921 0.352751554 -0.55421976
112 0 1 0 -1.19235738 -0.377621640 0.04506631
113 0 1 1 -0.61306970 -0.502201647 -0.55421976
114 0 1 0 -0.76754642 -0.467672820 0.04506631
115 0 1 0 -0.99926149 -0.377541884 -0.55421976
116 0 1 1 -0.69030806 -0.504633254 -0.55421976
117 0 1 1 3.13299059 -0.508037505 -0.55421976
119 0 0 1 -0.45859299 4.156190321 0.04506631
122 0 1 1 0.00000000 -0.502201647 -0.55421976
125 0 0 1 1.85855771 0.844665754 0.04506631
126 0 1 1 -1.38545327 -0.440113953 0.04506631
128 0 1 1 -0.45859299 -0.519870680 -0.55421976
129 0 1 0 0.00000000 -0.223864289 0.64435239
130 0 1 1 1.16341250 -0.523113472 -0.55421976
131 0 1 1 0.23655222 -0.505201278 -0.55421976
132 0 1 1 -0.76754642 -0.521654507 -0.55421976
134 1 0 0 -0.07240121 -0.153022808 0.04506631
136 1 0 1 -0.53583135 -0.366113328 -0.55421976
138 0 0 1 0.54550565 0.374149700 0.04506631
141 0 1 0 0.00000000 -0.362222756 0.64435239
142 0 1 0 -0.61306970 -0.508037505 -0.55421976
143 0 1 0 -0.45859299 -0.350469338 0.04506631
146 1 0 1 -0.84478477 0.056095438 0.64435239
147 0 1 1 -0.22687792 -0.507146564 -0.55421976
148 0 1 0 -1.61716834 0.009894895 1.84292454
149 1 0 1 0.50688647 -0.153022808 0.64435239
150 1 0 1 0.93169743 -0.405909990 -0.55421976
151 1 0 1 1.62684264 -0.415150098 -0.55421976
153 0 1 1 1.97441524 -0.502201647 -0.55421976
154 0 1 1 0.81583989 -0.376730699 0.64435239
156 0 0 1 1.62684264 0.535203819 0.04506631
157 0 1 0 -1.07649984 -0.508362368 -0.55421976
158 0 1 1 0.00483715 -0.502201647 -0.55421976
160 0 1 1 0.00000000 0.694149249 5.43864100
162 1 0 0 0.77722072 -0.352414624 -0.55421976
163 0 1 1 -0.30411628 -0.507551184 -0.55421976
164 0 1 1 -0.99926149 -0.490286770 -0.55421976
167 0 0 0 0.00000000 0.411110134 0.04506631
169 0 0 1 0.00000000 -0.154481773 -0.55421976
171 0 0 1 2.39922620 -0.007126358 -0.55421976
173 0 1 0 -2.23507519 -0.442222643 0.64435239
174 0 1 1 -0.69030806 -0.504633254 -0.55421976
176 0 1 1 -0.92202313 -0.506010517 0.64435239
179 1 0 1 0.00483715 -0.405909990 -0.55421976
180 0 1 1 0.46826729 -0.658797171 -0.55421976
181 0 1 0 0.00000000 0.694149249 5.43864100
182 1 0 1 0.00000000 -0.366031626 -0.55421976
184 1 0 1 -2.23507519 0.099864373 1.24363847
185 0 1 0 -2.00336012 -0.230347927 0.64435239
188 0 0 1 1.16341250 -0.142323735 -0.55421976
189 0 1 1 0.77722072 -0.357277839 0.64435239
190 0 1 1 0.46826729 -0.505201278 -0.55421976
191 1 0 0 0.15931386 -0.405909990 -0.55421976
192 1 0 1 -0.84478477 -0.405909990 -0.55421976
194 1 0 1 -2.08059848 -0.153022808 0.64435239
196 0 0 0 2.16751113 2.191451452 -0.55421976
197 0 1 1 0.00000000 -0.508037505 -0.55421976
198 0 1 1 0.93169743 -0.495311444 0.04506631
199 0 1 0 0.00000000 -0.508037505 -0.55421976
200 1 0 0 -0.45859299 -0.405909990 -0.55421976
202 0 1 1 0.00000000 0.694149249 5.43864100
203 0 1 1 0.31379058 -0.532435282 -0.55421976
204 0 1 1 1.20203168 -0.518250257 -0.55421976
205 0 1 1 -0.92202313 -0.502201647 -0.55421976
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689 0 1 1 -0.92202313 -0.507146564 -0.55421976
690 0 0 0 -1.15373820 3.452321649 0.04506631
691 0 0 1 0.08207551 0.450015854 0.04506631
692 0 1 0 -2.00336012 -0.397803983 0.04506631
693 0 1 1 0.00000000 0.440207722 -0.55421976
694 0 1 1 -0.38135463 -0.518250257 -0.55421976
695 0 0 1 2.32198785 -0.142323735 -0.55421976
699 0 0 1 1.47236593 1.498200151 0.64435239
701 0 0 0 -0.92202313 3.767214822 0.04506631
702 0 0 1 0.39102893 -0.147430111 -0.55421976
703 0 1 0 -0.92202313 -0.377621640 0.04506631
704 0 1 1 -0.38135463 -0.508198964 -0.55421976
705 0 1 1 -0.30411628 -0.506010517 0.04506631
708 0 0 1 0.93169743 -0.147430111 -0.55421976
709 0 0 0 -0.61306970 2.289283776 -0.55421976
710 0 1 1 0.00000000 -0.362222756 0.64435239
712 0 0 1 0.00000000 -0.142323735 -0.55421976
713 0 0 1 1.39512757 0.352751554 0.04506631
714 0 1 1 -0.07240121 -0.474319863 -0.55421976
716 0 1 1 -0.84478477 -0.509982791 -0.55421976
717 0 0 0 0.62274400 3.767214822 -0.55421976
718 1 0 0 -0.22687792 -0.454542140 -0.55421976
719 0 1 1 0.00000000 -0.357277839 -0.55421976
720 0 1 1 0.23655222 -0.507551184 -0.55421976
721 1 0 0 -1.84888341 -0.016852788 0.04506631
723 1 0 1 0.31379058 -0.405909990 -0.55421976
725 0 0 1 -0.22687792 0.374149700 0.04506631
726 0 1 1 -0.76754642 -0.490286770 -0.55421976
728 0 1 0 0.00000000 -0.508280666 -0.55421976
729 1 0 1 -0.38135463 -0.153022808 0.04506631
730 0 1 0 -0.38135463 -0.504633254 0.04506631
732 0 1 1 -1.46269163 -0.293326562 -0.55421976
735 1 0 1 -0.53583135 -0.405909990 -0.55421976
736 0 1 1 -0.11102039 -0.345606123 -0.55421976
737 0 1 0 1.39512757 0.009894895 1.84292454
738 0 0 1 0.39102893 9.307471078 -0.55421976
739 0 1 1 0.00000000 -0.505201278 -0.55421976
740 0 1 1 0.00000000 -0.505201278 -0.55421976
742 0 0 1 0.46826729 0.875060848 0.04506631
743 0 0 0 -0.69030806 4.445146996 1.84292454
744 0 1 1 -0.45859299 -0.345606123 0.04506631
745 0 1 1 0.08207551 -0.504633254 -0.55421976
749 0 0 1 -0.84478477 0.374149700 0.04506631
750 0 1 1 0.08207551 -0.508037505 -0.55421976
752 0 1 1 -1.84888341 -0.416122741 0.04506631
753 0 1 1 0.23655222 -0.473995000 -0.55421976
754 0 1 1 -0.53583135 -0.505201278 -0.55421976
755 1 0 0 1.39512757 0.605638735 1.24363847
757 0 1 1 -0.14963956 -0.507146564 -0.55421976
759 0 1 1 0.31379058 -0.502201647 -0.55421976
760 0 0 0 0.23655222 1.023875227 -0.55421976
762 0 1 1 0.85445907 -0.520195543 -0.55421976
763 0 1 1 -0.76754642 -0.518168555 -0.55421976
764 0 0 0 0.46826729 1.675546040 1.24363847
766 0 0 0 1.62684264 0.857714732 0.04506631
767 0 0 1 0.00000000 0.111536089 -0.55421976
768 0 1 0 0.04345633 -0.508037505 -0.55421976
769 0 1 1 0.00000000 -0.189010600 0.04506631
770 0 1 1 0.15931386 -0.496122628 -0.55421976
771 0 1 1 -0.45859299 -0.473995000 -0.55421976
773 1 0 0 2.09027278 -0.454542140 -0.55421976
774 0 1 1 0.00000000 -0.518250257 -0.55421976
777 0 1 1 0.00000000 -0.508037505 -0.55421976
778 0 1 0 -1.92612177 -0.416122741 -0.55421976
780 0 0 0 1.00893579 3.452321649 0.04506631
781 0 1 0 -1.30821491 -0.518168555 -0.55421976
782 0 0 0 -0.99926149 0.450015854 0.04506631
783 0 0 1 -0.07240121 -0.075211368 -0.55421976
784 0 1 1 0.00000000 -0.202627602 1.24363847
786 0 1 1 -0.38135463 -0.517763935 -0.55421976
789 0 1 1 -2.23507519 -0.258554574 1.24363847
790 0 0 1 1.24065086 0.881869349 -0.55421976
791 0 1 1 0.00000000 -0.508037505 -0.55421976
792 1 0 1 -1.07649984 -0.153022808 -0.55421976
793 0 1 0 0.00000000 0.694149249 5.43864100
794 0 0 1 0.00000000 -0.061676068 -0.55421976
795 0 1 1 -0.38135463 -0.505201278 -0.55421976
796 1 0 1 0.69998236 -0.405909990 -0.55421976
797 0 0 0 1.47236593 -0.154400071 -0.55421976
799 0 1 1 0.00483715 -0.518168555 -0.55421976
800 0 1 0 0.00483715 -0.189010600 0.64435239
801 1 0 1 0.31379058 -0.405909990 -0.55421976
803 0 0 1 -1.46269163 1.675546040 1.24363847
804 0 1 1 -2.27987344 -0.493122997 0.04506631
806 0 1 1 0.08207551 -0.507551184 -0.55421976
808 0 1 0 -0.92202313 -0.507551184 -0.55421976
811 0 1 1 -0.30411628 -0.505362737 -0.55421976
812 0 1 1 0.69998236 -0.189010600 -0.55421976
813 1 0 1 0.39102893 -0.454542140 -0.55421976
815 0 1 1 0.04345633 -0.502201647 -0.55421976
816 0 0 1 0.00000000 -0.658797171 -0.55421976
817 0 1 0 -0.53583135 -0.504633254 -0.55421976
819 0 1 1 1.00893579 -0.533326223 -0.55421976
822 0 1 1 -0.22687792 -0.490286770 -0.55421976
823 0 0 1 0.62274400 -0.658797171 -0.55421976
824 0 1 0 -0.22687792 -0.416122741 0.04506631
825 0 1 1 -2.15783684 0.113238214 2.44221062
826 0 1 1 0.00000000 -0.523599793 -0.55421976
827 0 1 1 0.00000000 0.440207722 -0.55421976
828 1 0 1 -2.23507519 0.061040355 0.64435239
831 0 1 0 -1.15373820 -0.377621640 0.04506631
832 1 0 1 -2.24820571 -0.294056044 0.64435239
833 0 1 1 0.00000000 -0.518168555 -0.55421976
835 0 1 1 -0.92202313 -0.497338432 -0.55421976
836 0 0 0 0.69998236 0.958869605 0.64435239
838 0 1 1 0.00000000 -0.502201647 -0.55421976
840 0 0 1 0.00000000 -0.081047226 -0.55421976
843 0 0 0 0.00483715 -0.055758508 -0.55421976
845 0 1 1 -0.99926149 -0.490286770 -0.55421976
846 0 1 1 0.93169743 -0.511928077 -0.55421976
847 0 1 1 0.00000000 0.694149249 5.43864100
849 1 0 1 -0.14963956 -0.016852788 0.04506631
850 0 0 0 0.00000000 1.074534365 0.04506631
851 0 1 1 -2.00336012 -0.050408971 3.04149669
852 0 1 1 3.40332484 -0.507551184 -0.55421976
853 0 1 0 -1.61716834 -0.362222756 0.64435239
855 1 0 0 1.08617414 -0.153022808 0.04506631
856 0 1 0 -0.92202313 -0.476912929 0.04506631
857 0 0 0 1.16341250 2.548331678 0.64435239
858 0 0 1 1.62684264 -0.142323735 -0.55421976
859 0 1 0 -0.45859299 -0.284168155 1.24363847
860 0 1 1 0.00000000 -0.518168555 -0.55421976
861 0 1 1 0.85445907 -0.384350385 0.64435239
862 1 0 1 -0.69030806 -0.435089280 0.04506631
864 0 1 0 0.00000000 0.694149249 5.43864100
865 1 0 1 -0.45859299 -0.405909990 -0.55421976
867 1 0 0 -0.22687792 -0.389213600 0.04506631
868 0 0 1 0.08207551 0.323490562 -0.55421976
871 0 1 1 -0.30411628 -0.505201278 -0.55421976
872 0 0 0 1.31788921 0.363532329 0.64435239
874 0 1 1 1.31788921 -0.483721430 -0.55421976
877 0 1 1 -0.76754642 -0.467268201 -0.55421976
878 0 1 1 -0.84478477 -0.505201278 -0.55421976
879 0 1 1 0.00000000 -0.505201278 -0.55421976
880 0 0 0 2.01303442 0.958869605 0.04506631
881 1 0 0 -0.38135463 -0.153022808 0.04506631
882 0 1 1 0.23655222 -0.505201278 -0.55421976
883 0 1 0 -0.61306970 -0.454217277 -0.55421976
885 0 1 1 -0.38135463 -0.521654507 -0.55421976
886 0 1 0 0.69998236 -0.092232621 2.44221062
887 1 0 1 -0.22687792 -0.405909990 -0.55421976
888 0 0 0 -0.84478477 -0.075211368 -0.55421976
889 0 1 0 0.00000000 -0.202627602 1.24363847test.x <- model.matrix(Survived ~., # Survived는 Target으로 제외
titanic.ted.Imp)[,-1] # [,-1] : 절편 제거
test.x Pclass2 Pclass3 Sexmale Age Fare FamSize
2 0 0 0 0.62274400 0.727866891 0.04506631
7 0 0 1 1.85855771 0.350076786 -0.55421976
13 0 1 1 -0.76754642 -0.502201647 -0.55421976
16 1 0 0 1.93579607 -0.347551409 -0.55421976
17 0 1 1 -2.15783684 -0.092232621 2.44221062
22 1 0 1 0.31379058 -0.405909990 -0.55421976
23 0 1 0 -1.15373820 -0.502606266 -0.55421976
26 0 1 0 0.62274400 -0.048220525 3.04149669
37 0 1 1 0.00000000 -0.518168555 -0.55421976
44 1 0 0 -2.08059848 0.150037190 1.24363847
46 0 1 1 0.00000000 -0.502201647 -0.55421976
52 0 1 1 -0.69030806 -0.507064862 -0.55421976
54 1 0 0 -0.07240121 -0.153022808 0.04506631
57 1 0 0 -0.69030806 -0.454542140 -0.55421976
58 0 1 1 -0.11102039 -0.518168555 -0.55421976
59 1 0 0 -1.92612177 -0.118980303 1.24363847
63 0 0 1 1.16341250 0.965030325 0.04506631
66 0 1 1 0.00000000 -0.362222756 0.64435239
67 1 0 0 -0.07240121 -0.454542140 -0.55421976
68 0 1 1 -0.84478477 -0.500094902 -0.55421976
69 0 1 0 -0.99926149 -0.504633254 3.04149669
71 1 0 1 0.15931386 -0.454542140 -0.55421976
73 1 0 1 -0.69030806 0.770988046 -0.55421976
78 0 1 1 0.00000000 -0.502201647 -0.55421976
81 0 1 1 -0.61306970 -0.483721430 -0.55421976
87 0 1 1 -1.07649984 0.009894895 1.84292454
90 0 1 1 -0.45859299 -0.502201647 -0.55421976
98 0 0 1 -0.53583135 0.573702975 0.04506631
99 1 0 0 0.31379058 -0.211381389 0.04506631
100 1 0 1 0.31379058 -0.153022808 0.04506631
101 0 1 0 -0.14963956 -0.505201278 -0.55421976
102 0 1 1 0.00000000 -0.505201278 -0.55421976
104 0 1 1 0.23655222 -0.490448229 -0.55421976
106 0 1 1 -0.14963956 -0.505201278 -0.55421976
109 0 1 1 0.62274400 -0.505201278 -0.55421976
118 1 0 1 -0.07240121 -0.250287109 0.04506631
120 0 1 0 -2.15783684 -0.050408971 3.04149669
121 1 0 1 -0.69030806 0.770988046 0.64435239
123 1 0 1 0.19793304 -0.073834105 0.04506631
124 1 0 0 0.19793304 -0.405909990 -0.55421976
127 0 1 1 0.00000000 -0.508037505 -0.55421976
133 0 1 0 1.31788921 -0.376730699 0.04506631
135 1 0 1 -0.38135463 -0.405909990 -0.55421976
137 0 0 0 -0.84478477 -0.147511813 0.64435239
139 0 1 1 -1.07649984 -0.479505995 -0.55421976
140 0 0 1 -0.45859299 0.881869349 -0.55421976
144 0 1 1 -0.84478477 -0.527490365 -0.55421976
145 1 0 1 -0.92202313 -0.435089280 -0.55421976
152 0 0 0 -0.61306970 0.636763311 0.04506631
155 0 1 1 0.00000000 -0.516548131 -0.55421976
159 0 1 1 0.00000000 -0.490286770 -0.55421976
161 0 1 1 1.08617414 -0.345606123 0.04506631
165 0 1 1 -2.23507519 0.113238214 2.44221062
166 0 1 1 -1.61716834 -0.259527217 0.64435239
168 0 1 0 1.16341250 -0.116062374 2.44221062
170 0 1 1 -0.14963956 0.440207722 -0.55421976
172 0 1 1 -2.00336012 -0.092232621 2.44221062
175 0 0 1 2.01303442 -0.061676068 -0.55421976
177 0 1 1 0.00000000 -0.163397019 1.84292454
178 0 0 0 1.54960428 -0.100256925 -0.55421976
183 0 1 1 -1.61716834 -0.048220525 3.04149669
186 0 0 1 0.00000000 0.313845834 -0.55421976
187 0 1 0 0.00000000 -0.357277839 0.04506631
193 0 1 0 -0.84478477 -0.506010517 0.04506631
195 0 0 0 1.08617414 -0.119548327 -0.55421976
201 0 1 1 -0.14963956 -0.473995000 -0.55421976
208 0 1 1 -0.30411628 -0.293326562 -0.55421976
210 0 0 1 0.77722072 -0.055758508 -0.55421976
215 0 1 1 0.00000000 -0.508037505 0.04506631
221 0 1 1 -1.07649984 -0.502201647 -0.55421976
222 1 0 1 -0.22687792 -0.405909990 -0.55421976
225 0 0 1 0.62274400 1.091960238 0.04506631
228 0 1 1 -0.72892724 -0.517763935 -0.55421976
231 0 0 0 0.39102893 0.965030325 0.04506631
234 0 1 0 -1.92612177 -0.048220525 3.04149669
239 1 0 1 -0.84478477 -0.454542140 -0.55421976
241 0 1 0 0.00000000 -0.377621640 0.04506631
250 1 0 1 1.85855771 -0.153022808 0.04506631
251 0 1 1 0.00000000 -0.517763935 -0.55421976
256 0 1 0 -0.07240121 -0.362222756 0.64435239
260 1 0 0 1.54960428 -0.153022808 0.04506631
261 0 1 1 0.00000000 -0.508037505 -0.55421976
263 0 0 1 1.70408100 0.890623136 0.64435239
268 0 1 1 -0.38135463 -0.507551184 0.04506631
271 0 0 1 0.00000000 -0.055758508 -0.55421976
272 0 1 1 -0.38135463 -0.658797171 -0.55421976
274 0 0 1 0.54550565 -0.081047226 0.04506631
277 0 1 0 1.16341250 -0.508037505 -0.55421976
279 0 1 1 -1.77164505 -0.092232621 2.44221062
282 0 1 1 -0.14963956 -0.506010517 -0.55421976
283 0 1 1 -1.07649984 -0.473995000 -0.55421976
284 0 1 1 -0.84478477 -0.502201647 -0.55421976
295 0 1 1 -0.45859299 -0.505201278 -0.55421976
301 0 1 0 0.00000000 -0.508037505 -0.55421976
308 0 0 0 -0.99926149 1.459619293 0.04506631
310 0 0 0 0.00483715 0.448638592 -0.55421976
312 0 0 0 -0.92202313 4.445146996 1.84292454
313 1 0 0 -0.30411628 -0.153022808 0.64435239
314 0 1 1 -0.14963956 -0.505201278 -0.55421976
318 1 0 1 1.85855771 -0.386457129 -0.55421976
321 0 1 1 -0.61306970 -0.517763935 -0.55421976
326 0 0 0 0.46826729 1.979658438 -0.55421976
328 1 0 0 0.46826729 -0.405909990 -0.55421976
333 0 0 1 0.62274400 2.326487371 0.04506631
334 0 1 1 -1.07649984 -0.308645689 0.64435239
338 0 0 0 0.85445907 1.957612512 -0.55421976
344 1 0 1 -0.38135463 -0.405909990 -0.55421976
347 1 0 0 0.77722072 -0.405909990 -0.55421976
351 0 1 1 -0.53583135 -0.479344536 -0.55421976
358 1 0 0 0.62274400 -0.405909990 -0.55421976
359 0 1 0 0.00000000 -0.505524195 -0.55421976
364 0 1 1 0.39102893 -0.521654507 -0.55421976
369 0 1 0 0.00000000 -0.508037505 -0.55421976
375 0 1 0 -2.08059848 -0.248828144 1.84292454
378 0 0 1 -0.22687792 3.455482739 0.64435239
380 0 1 1 -0.84478477 -0.507551184 -0.55421976
400 1 0 0 -0.14963956 -0.412718491 -0.55421976
403 0 1 0 -0.69030806 -0.467672820 0.04506631
409 0 1 1 -0.69030806 -0.507551184 -0.55421976
412 0 1 1 0.00000000 -0.525383620 -0.55421976
413 0 0 0 0.23655222 1.091960238 0.04506631
415 0 1 1 1.08617414 -0.504633254 -0.55421976
416 0 1 0 0.00000000 -0.502201647 -0.55421976
418 1 0 0 -0.92202313 -0.405909990 0.64435239
419 1 0 1 0.00483715 -0.405909990 -0.55421976
420 0 1 0 -1.53992998 -0.189010600 0.64435239
424 0 1 0 -0.14963956 -0.378675985 0.64435239
427 1 0 0 -0.14963956 -0.153022808 0.04506631
430 0 1 1 0.15931386 -0.502201647 -0.55421976
436 0 0 0 -1.23097656 1.675546040 1.24363847
440 1 0 1 0.08207551 -0.454542140 -0.55421976
441 1 0 0 1.16341250 -0.148159593 0.64435239
442 0 1 1 -0.76754642 -0.473995000 -0.55421976
445 0 1 1 0.00000000 -0.500985843 -0.55421976
447 1 0 0 -1.30821491 -0.279466399 0.04506631
448 0 0 1 0.31379058 -0.142323735 -0.55421976
450 0 0 1 1.70408100 -0.065484938 -0.55421976
452 0 1 1 0.00000000 -0.270387749 0.04506631
455 0 1 1 0.00000000 -0.502201647 -0.55421976
457 0 0 1 2.70817963 -0.142323735 -0.55421976
458 0 0 0 0.00000000 0.350076786 0.04506631
462 0 1 1 0.31379058 -0.502201647 -0.55421976
467 1 0 1 0.00000000 -0.658797171 -0.55421976
469 0 1 1 0.00000000 -0.508523827 -0.55421976
473 1 0 0 0.23655222 -0.118980303 1.24363847
476 0 0 1 0.00000000 0.352751554 -0.55421976
477 1 0 1 0.31379058 -0.250287109 0.04506631
478 0 1 1 -0.07240121 -0.521736209 0.04506631
482 1 0 1 0.00000000 -0.658797171 -0.55421976
483 0 1 1 1.54960428 -0.502201647 -0.55421976
488 0 0 1 2.16751113 -0.081047226 -0.55421976
490 0 1 1 -1.61716834 -0.349496695 0.64435239
492 0 1 1 -0.69030806 -0.517763935 -0.55421976
495 0 1 1 -0.69030806 -0.502201647 -0.55421976
496 0 1 1 0.00000000 -0.377541884 -0.55421976
510 0 1 1 -0.30411628 0.440207722 -0.55421976
515 0 1 1 -0.45859299 -0.512982422 -0.55421976
520 0 1 1 0.15931386 -0.505201278 -0.55421976
523 0 1 1 0.00000000 -0.518250257 -0.55421976
525 0 1 1 0.00000000 -0.518168555 -0.55421976
527 1 0 0 1.54960428 -0.454542140 -0.55421976
529 0 1 1 0.69998236 -0.504633254 -0.55421976
531 1 0 0 -2.15783684 -0.153022808 0.64435239
534 0 1 0 0.00000000 -0.223864289 0.64435239
539 0 1 1 0.00000000 -0.376730699 -0.55421976
540 0 0 0 -0.61306970 0.304119404 0.64435239
550 1 0 1 -1.69440670 0.056095438 0.64435239
551 0 0 1 -0.99926149 1.498200151 0.64435239
554 0 1 1 -0.61306970 -0.518250257 -0.55421976
562 0 1 1 0.77722072 -0.505201278 -0.55421976
566 0 1 1 -0.45859299 -0.189010600 0.64435239
571 1 0 1 2.47646456 -0.454542140 -0.55421976
572 0 0 0 1.78131935 0.342620505 0.64435239
574 0 1 0 0.00000000 -0.508037505 -0.55421976
582 0 0 0 0.69998236 1.498200151 0.64435239
583 1 0 1 1.85855771 -0.153022808 -0.55421976
586 0 0 0 -0.92202313 0.890623136 0.64435239
589 0 1 1 -0.61306970 -0.502201647 -0.55421976
599 0 1 1 0.00000000 -0.518250257 -0.55421976
602 0 1 1 0.00000000 -0.505201278 -0.55421976
604 0 1 1 1.08617414 -0.502201647 -0.55421976
607 0 1 1 0.00483715 -0.505201278 -0.55421976
620 1 0 1 -0.30411628 -0.454542140 -0.55421976
628 0 0 0 -0.69030806 0.857714732 -0.55421976
629 0 1 1 -0.30411628 -0.505201278 -0.55421976
630 0 1 1 0.00000000 -0.508362368 -0.55421976
632 0 1 1 1.62684264 -0.521572805 -0.55421976
636 1 0 0 -0.14963956 -0.405909990 -0.55421976
643 0 1 0 -2.15783684 -0.116062374 2.44221062
652 1 0 0 -0.92202313 -0.211381389 0.04506631
653 0 1 1 -0.69030806 -0.494745366 -0.55421976
657 0 1 1 0.00000000 -0.505201278 -0.55421976
660 0 0 1 2.16751113 1.544725556 0.64435239
664 0 1 1 0.46826729 -0.512982422 -0.55421976
665 0 1 1 -0.76754642 -0.504633254 0.04506631
666 1 0 1 0.15931386 0.770988046 0.64435239
669 0 1 1 1.00893579 -0.502201647 -0.55421976
672 0 0 1 0.08207551 0.352751554 0.04506631
673 1 0 1 3.09437141 -0.454542140 -0.55421976
675 1 0 1 0.00000000 -0.658797171 -0.55421976
676 0 1 1 -0.92202313 -0.507551184 -0.55421976
680 0 0 1 0.46826729 9.307471078 0.04506631
684 0 1 1 -1.23097656 0.253541968 3.64078277
685 1 0 1 2.32198785 0.099864373 0.64435239
686 1 0 1 -0.38135463 0.150037190 1.24363847
688 0 1 1 -0.84478477 -0.460946021 -0.55421976
696 1 0 1 1.70408100 -0.396183559 -0.55421976
697 0 1 1 1.08617414 -0.502201647 -0.55421976
698 0 1 0 0.00000000 -0.508362368 -0.55421976
700 0 1 1 0.93169743 -0.509982791 -0.55421976
706 1 0 1 0.69998236 -0.153022808 -0.55421976
707 1 0 0 1.16341250 -0.396183559 -0.55421976
711 0 0 0 -0.45859299 0.304201106 -0.55421976
715 1 0 1 1.70408100 -0.405909990 -0.55421976
722 0 1 1 -0.99926149 -0.521572805 0.04506631
724 1 0 1 1.54960428 -0.405909990 -0.55421976
727 1 0 0 0.00483715 -0.250287109 1.24363847
731 0 0 0 -0.07240121 3.452321649 -0.55421976
733 1 0 1 0.00000000 -0.658797171 -0.55421976
734 1 0 1 -0.53583135 -0.405909990 -0.55421976
741 0 0 1 0.00000000 -0.075211368 -0.55421976
746 0 0 1 3.09437141 0.722355896 0.64435239
747 0 1 1 -1.07649984 -0.264876754 0.64435239
748 1 0 0 0.00483715 -0.405909990 -0.55421976
751 1 0 0 -2.00336012 -0.211381389 0.64435239
756 1 0 1 -2.26056385 -0.376730699 0.64435239
758 1 0 1 -0.92202313 -0.435089280 -0.55421976
761 0 1 1 0.00000000 -0.376730699 -0.55421976
765 0 1 1 -1.07649984 -0.507551184 -0.55421976
772 0 1 1 1.39512757 -0.506010517 -0.55421976
775 1 0 0 1.85855771 -0.211381389 1.84292454
776 0 1 1 -0.92202313 -0.508037505 -0.55421976
779 0 1 1 0.00000000 -0.508280666 -0.55421976
785 0 1 1 -0.38135463 -0.521654507 -0.55421976
787 0 1 0 -0.92202313 -0.512982422 -0.55421976
788 0 1 1 -1.69440670 -0.092232621 2.44221062
798 0 1 0 0.08207551 -0.489882151 -0.55421976
802 1 0 0 0.08207551 -0.148159593 0.64435239
805 0 1 1 -0.22687792 -0.523113472 -0.55421976
807 0 0 1 0.69998236 -0.658797171 -0.55421976
809 1 0 1 0.69998236 -0.405909990 -0.55421976
810 0 0 0 0.23655222 0.374149700 0.04506631
814 0 1 0 -1.84888341 -0.050408971 3.04149669
818 1 0 1 0.08207551 0.061040355 0.64435239
820 0 1 1 -1.53992998 -0.116062374 2.44221062
821 0 0 0 1.70408100 1.160045248 0.64435239
829 0 1 1 0.00000000 -0.508037505 -0.55421976
830 0 0 0 2.47646456 0.897431637 -0.55421976
834 0 1 1 -0.53583135 -0.506010517 -0.55421976
837 0 1 1 -0.69030806 -0.490286770 -0.55421976
839 0 1 1 0.15931386 0.440207722 -0.55421976
841 0 1 1 -0.76754642 -0.504633254 -0.55421976
842 1 0 1 -1.07649984 -0.454542140 -0.55421976
844 0 1 1 0.35240975 -0.533569384 -0.55421976
848 0 1 1 0.39102893 -0.505201278 -0.55421976
854 0 0 0 -1.07649984 0.107645517 0.04506631
863 0 0 0 1.39512757 -0.154400071 -0.55421976
866 1 0 0 0.93169743 -0.405909990 -0.55421976
869 0 1 1 0.00000000 -0.473995000 -0.55421976
870 0 1 1 -2.00336012 -0.442222643 0.64435239
873 0 0 1 0.23655222 -0.561532870 -0.55421976
875 1 0 0 -0.14963956 -0.191928529 0.04506631
876 0 1 0 -1.15373820 -0.518250257 -0.55421976
884 1 0 1 -0.14963956 -0.454542140 -0.55421976
890 0 0 1 -0.30411628 -0.075211368 -0.55421976
891 0 1 1 0.15931386 -0.508037505 -0.5542197611.6 모형 훈련
Package "glmnet"에서 제공하는 함수 glmnet()을 이용하여 LASSO Regression을 수행할 수 있다. 함수 glmnet()는 Target이 2개의 클래스를 가질 때 “두 번째 클래스”에 속할 확률을 모델링하며, “두 번째 클래스”란 “Factor” 변환하였을 때 두 번째 수준(Level)을 의미한다. 예를 들어, “a”와 “b” 2개의 클래스를 가진 Target을 “Factor” 변환하였을 때 수준이 “a” “b”라면, 첫 번째 클래스는 “a”, 두 번째 클래스는 “b”가 된다. 함수 glmnet()에 대한 자세한 옵션은 여기를 참고한다.
glmnet(x, y, family, alpha, lambda, ...)x: 예측 변수를 포함하는 행렬y: Target을 포함하는 변수family: Target의 분포"gaussian": 수치형인 Target"binomial": 2개의 클래스를 가지는 Target"multinomial": 3개 이상 클래스를 가지는 Target"poisson": Count Data인 Target
alpha: Elasticnet Mixing Parameter0: Ridge Regression1: Lasso Regression0 < alpha < 1: Elastic Net Regression
lambda: Regularization Parameter- 직접 값을 지정하면 해당 값에 대한 결과만 보여준다.
- 값을 지정하지 않으면 100개의
lambda값에 대한 결과를 보여준다.
11.6.1 람다 값 직접 지정
lasso.fit <- glmnet(x = train.x, # 예측 변수를 포함하는 행렬
y = titanic.trd.Imp$Survived,# Target
family = "binomial", # Binary Classification
alpha = 1, # 0 : Ridge / 1 : Lasso / 0 < alpha < 1 : Elastic Net
lambda = 0.1)
round(coef(lasso.fit), 3) # 회귀계수 추정치7 x 1 sparse Matrix of class "dgCMatrix"
s0
(Intercept) 0.571
Pclass2 .
Pclass3 -0.459
Sexmale -1.308
Age .
Fare .
FamSize . Result! 데이터 “titanic.trd.Imp”의 Target “Survived”은 “no”와 “yes” 2개의 클래스를 가지며, “Factor” 변환하면 알파벳순으로 수준을 부여하기 때문에 “yes”가 두 번째 클래스가 된다. 즉, “yes”에 속할 확률(= 탑승객이 생존할 확률)을 \(p\)라고 할 때, 추정된 회귀계수를 이용하여 다음과 같은 모형식을 얻을 수 있다. \[
\begin{align*}
\log{\frac{p}{1-p}} = &\;0.571 -0.459 X_{\text{Pclass3}} -1.308 X_{\text{Sexmale}}
\end{align*}
\] 여기서, \(X_{\text{예측 변수}}\)는 더미 변수를 의미한다.
11.6.2 교차 검증을 통한 최적의 람다 값
# 100개의 람다 값에 따른 결과
lasso.fit <- glmnet(x = train.x, # 예측 변수를 포함하는 행렬
y = titanic.trd.Imp$Survived,# Target
family = "binomial", # Binary Classification
alpha = 1) # 0 : Ridge / 1 : Lasso / 0 < alpha < 1 : Elastic Net
plot(lasso.fit, xvar = "lambda") # 람다 값에 따른 회귀계수 추정치 확인
Result! 100개의 \(\lambda\) 값에 대한 회귀계수 추정치의 변화를 보여준다. 해당 그림을 통해 \(\lambda\) 값이 클수록 회귀계수 추정치는 작아진다는 것을 알 수 있다.
lasso.fit$lambda # 100개의 람다 값 [1] 0.2507754711 0.2284972694 0.2081982018 0.1897024473 0.1728498048 0.1574943045 0.1435029446 0.1307545385 0.1191386657 0.1085547150 0.0989110133 0.0901240315 0.0821176609 0.0748225542 0.0681755247
[16] 0.0621189990 0.0566005184 0.0515722843 0.0469907447 0.0428162165 0.0390125418 0.0355467751 0.0323888976 0.0295115572 0.0268898318 0.0245010132 0.0223244107 0.0203411716 0.0185341180 0.0168875980
[31] 0.0153873504 0.0140203806 0.0127748486 0.0116399663 0.0106059037 0.0096637045 0.0088052076 0.0080229772 0.0073102381 0.0066608167 0.0060690881 0.0055299270 0.0050386635 0.0045910425 0.0041831870
[46] 0.0038115642 0.0034729553 0.0031644275 0.0028833085 0.0026271633 0.0023937734 0.0021811172 0.0019873527 0.0018108018 0.0016499351 0.0015033595 0.0013698051 0.0012481154 0.0011372363 0.0010362074
[61] 0.0009441536 0.0008602776 0.0007838529Caution! \(\lambda\)는 모형이 Training Dataset에 과적합 되는 것을 방지하기 위해 사용하는 모수이며, 교차 검증(Cross Validation)을 통해 최적의 값을 찾을 수 있다. 이러한 방법은 package "glmnet"에서 제공하는 함수 cv.glmnet()을 통해 수행할 수 있으며, 함수에 대한 자세한 옵션은 여기를 참고한다.
set.seed(200) # Seed 고정 -> 동일한 결과를 출력하기 위해
cv.lasso.fit <- cv.glmnet(x = train.x, # 예측 변수를 포함하는 행렬
y = titanic.trd.Imp$Survived,# Target
family = "binomial", # Binary Classification
alpha = 1, # 0 : Ridge / 1 : Lasso / 0 < alpha < 1 : Elastic Net
nfolds = 5, # 5-Fold Cross Validation
type.measure = "auc") # AUC에 기반하여 최적의 람다 값 찾기
plot(cv.lasso.fit) # Plot
Result! 100개의 \(\lambda\) 값에 대한 AUC의 변화를 보여준다.
Caution! 만약 \(\lambda\) 값에 대해 직접 후보 값을 지정하고 싶으면 함수 cv.glmnet()의 옵션 lambda = 후보 값을 이용하면 된다.
cv.lasso.fit$lambda.min # 최적의 람다 값[1] 0.0007838529max(cv.lasso.fit$cvm) # 최적의 람다 값에 대한 AUC[1] 0.850222round(coef(cv.lasso.fit, s = cv.lasso.fit$lambda.min), 3) # 최적의 람다 값에 대한 회귀계수 추정치7 x 1 sparse Matrix of class "dgCMatrix"
s1
(Intercept) 2.529
Pclass2 -1.011
Pclass3 -2.330
Sexmale -2.694
Age -0.515
Fare 0.122
FamSize -0.385Result! 최적의 \(\lambda\) 값에 대해 추정된 회귀계수를 이용하여 다음과 같은 모형식을 얻을 수 있다. \[
\begin{align*}
\log{\frac{p}{1-p}} = &\;2.529 - 1.011 X_{\text{Pclass2}} - 2.330 X_{\text{Pclass3}} -2.694 X_{\text{Sexmale}} \\
&-0.515 Z_{\text{Age}} +0.122 Z_{\text{Fare}} - 0.385 Z_{\text{FamSize}}
\end{align*}
\]
여기서, \(Z_{\text{예측 변수}}\)는 표준화한 예측 변수, \(X_{\text{예측 변수}}\)는 더미 변수를 의미한다.
11.7 모형 평가
Caution! 모형 평가를 위해 Test Dataset에 대한 예측 class/확률 이 필요하며, 함수 predict()를 이용하여 생성한다.
# 예측 class 생성
test.lasso.class <- predict(cv.lasso.fit,
newx = test.x, # Test Dataset including Only 예측 변수
s = "lambda.min", # 최적의 람다 값 기반
type = "class") # 예측 class 생성
test.lasso.class %>%
as_tibble# A tibble: 266 × 1
lambda.min
<chr>
1 yes
2 no
3 no
4 yes
5 no
6 no
7 yes
8 no
9 no
10 yes
# ℹ 256 more rows11.7.1 ConfusionMatrix
CM <- caret::confusionMatrix(as.factor(test.lasso.class), titanic.ted.Imp$Survived,
positive = "yes") # confusionMatrix(예측 class, 실제 class, positive = "관심 class")
CMConfusion Matrix and Statistics
Reference
Prediction no yes
no 148 32
yes 16 70
Accuracy : 0.8195
95% CI : (0.768, 0.8638)
No Information Rate : 0.6165
P-Value [Acc > NIR] : 5.675e-13
Kappa : 0.6067
Mcnemar's Test P-Value : 0.03038
Sensitivity : 0.6863
Specificity : 0.9024
Pos Pred Value : 0.8140
Neg Pred Value : 0.8222
Prevalence : 0.3835
Detection Rate : 0.2632
Detection Prevalence : 0.3233
Balanced Accuracy : 0.7944
'Positive' Class : yes
11.7.2 ROC 곡선
# 예측 확률 생성
test.lasso.prob <- predict(cv.lasso.fit,
newx = test.x, # Test Dataset including Only 예측 변수
s = "lambda.min", # 최적의 람다 값 기반
type = "response") # 예측 확률 생성
test.lasso.prob %>% # "Survived = yes"에 대한 예측 확률
as_tibble# A tibble: 266 × 1
lambda.min
<dbl>
1 0.907
2 0.296
3 0.125
4 0.666
5 0.0882
6 0.236
7 0.720
8 0.214
9 0.0875
10 0.894
# ℹ 256 more rowsac <- titanic.ted.Imp$Survived # Test Dataset의 실제 class
pp <- as.numeric(test.lasso.prob) # 예측 확률을 수치형으로 변환11.7.2.1 Package “pROC”
pacman::p_load("pROC")
lasso.roc <- roc(ac, pp, plot = T, col = "gray") # roc(실제 class, 예측 확률)
auc <- round(auc(lasso.roc), 3)
legend("bottomright", legend = auc, bty = "n")
Caution! Package "pROC"를 통해 출력한 ROC 곡선은 다양한 함수를 이용해서 그래프를 수정할 수 있다.
# 함수 plot.roc() 이용
plot.roc(lasso.roc,
col="gray", # Line Color
print.auc = TRUE, # AUC 출력 여부
print.auc.col = "red", # AUC 글씨 색깔
print.thres = TRUE, # Cutoff Value 출력 여부
print.thres.pch = 19, # Cutoff Value를 표시하는 도형 모양
print.thres.col = "red", # Cutoff Value를 표시하는 도형의 색깔
auc.polygon = TRUE, # 곡선 아래 면적에 대한 여부
auc.polygon.col = "gray90") # 곡선 아래 면적의 색깔
# 함수 ggroc() 이용
ggroc(lasso.roc) +
annotate(geom = "text", x = 0.9, y = 1.0,
label = paste("AUC = ", auc),
size = 5,
color="red") +
theme_bw()
11.7.2.2 Package “Epi”
pacman::p_load("Epi")
# install_version("etm", version = "1.1", repos = "http://cran.us.r-project.org")
ROC(pp, ac, plot = "ROC") # ROC(예측 확률, 실제 class) 
11.7.2.3 Package “ROCR”
pacman::p_load("ROCR")
lasso.pred <- prediction(pp, ac) # prediction(예측 확률, 실제 class)
lasso.perf <- performance(lasso.pred, "tpr", "fpr") # performance(, "민감도", "1-특이도")
plot(lasso.perf, col = "gray") # ROC Curve
perf.auc <- performance(lasso.pred, "auc") # AUC
auc <- attributes(perf.auc)$y.values
legend("bottomright", legend = auc, bty = "n")
11.7.3 향상 차트
11.7.3.1 Package “ROCR”
lasso.perf <- performance(lasso.pred, "lift", "rpp") # Lift Chart
plot(lasso.perf, main = "lift curve",
colorize = T, # Coloring according to cutoff
lwd = 2) 