pacman::p_load("data.table",
"tidyverse",
"dplyr", "tidyr",
"ggplot2", "GGally",
"caret",
"glmnet") # For glmnet
titanic <- fread("../Titanic.csv") # 데이터 불러오기
titanic %>%
as_tibble13 Elastic Net Regression
Elastic Net Regression의 장점
- 예측 변수의 개수가 표본의 크기보다 큰 경우,
LASSO Regression의 문제(표본의 크기보다 많은 예측 변수를 선택 X)를 극복한다. - 예측 변수 사이에 어떤 그룹 구조(쌍별 상관 관계가 매우 높은)가 있을 때,
LASSO Regression의 문제(그룹에서 하나의 예측 변수만 선택)를 극복한다.
Elastic Net Regression의 단점
Ridge Regression이나LASSO Regression에 매우 근접하지 않을 경우, 만족스럽지 않은 결과를 보여준다.- 이중 수축 문제(Double Shrinkage Problem)가 발생한다.
Ridge Regression이나LASSO Regression에 비해 분산을 크게 줄이는 데 도움이 되지 않고, 불필요한 편의(bias)가 추가로 발생한다.
- 회귀계수에 대한 추정치만 계산이 가능하며, 회귀계수에 대한 추론(신뢰 구간 등)은 불가능하다.
실습 자료 : 1912년 4월 15일 타이타닉호 침몰 당시 탑승객들의 정보를 기록한 데이터셋이며, 총 11개의 변수를 포함하고 있다. 이 자료에서 Target은
Survived이다.
13.1 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 rows13.2 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 rows13.3 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()
13.4 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$Resample1,] # Test Dataset13.5 데이터 전처리 II
# 1. Imputation
titanic.trd.Imp <- titanic.trd %>%
mutate(Age = replace_na(Age, mean(Age, na.rm = TRUE))) # 평균으로 결측값 대체
titanic.ted.Imp <- titanic.ted %>%
mutate(Age = replace_na(Age, mean(titanic.trd$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
206 0 1 0 -2.15783684 -0.455271622 0.04506631
207 0 1 1 0.15931386 -0.350469338 0.04506631
209 0 1 0 -1.07649984 -0.508037505 -0.55421976
211 0 1 1 -0.45859299 -0.521654507 -0.55421976
212 1 0 0 0.39102893 -0.250287109 -0.55421976
213 0 1 1 -0.61306970 -0.517763935 -0.55421976
214 1 0 1 0.00483715 -0.405909990 -0.55421976
216 0 0 0 0.08207551 1.544725556 0.04506631
217 0 1 0 -0.22687792 -0.504633254 -0.55421976
218 1 0 1 0.93169743 -0.133569948 0.04506631
219 0 0 0 0.15931386 0.825294596 -0.55421976
220 1 0 1 0.00483715 -0.454542140 -0.55421976
223 0 1 1 1.62684264 -0.502201647 -0.55421976
224 0 1 1 0.00000000 -0.505201278 -0.55421976
226 0 1 1 -0.61306970 -0.476912929 -0.55421976
227 1 0 1 -0.84478477 -0.454542140 -0.55421976
229 1 0 1 -0.92202313 -0.405909990 -0.55421976
230 0 1 0 0.00000000 -0.163397019 1.84292454
232 0 1 1 -0.07240121 -0.507551184 -0.55421976
233 1 0 1 2.24474949 -0.396183559 -0.55421976
235 1 0 1 -0.45859299 -0.454542140 -0.55421976
236 0 1 0 0.00000000 -0.511928077 -0.55421976
237 1 0 1 1.08617414 -0.153022808 0.04506631
238 1 0 0 -1.69440670 -0.148159593 0.64435239
240 1 0 1 0.23655222 -0.420013313 -0.55421976
242 0 1 0 0.00000000 -0.357277839 0.04506631
243 1 0 1 -0.07240121 -0.454542140 -0.55421976
244 0 1 1 -0.61306970 -0.520195543 -0.55421976
245 0 1 1 0.00483715 -0.518250257 -0.55421976
246 0 0 1 1.08617414 1.091960238 0.64435239
247 0 1 0 -0.38135463 -0.507551184 -0.55421976
248 1 0 0 -0.45859299 -0.376730699 0.64435239
249 0 0 1 0.54550565 0.363532329 0.64435239
252 0 1 0 -0.07240121 -0.455271622 0.64435239
253 0 0 1 2.47646456 -0.142323735 -0.55421976
254 0 1 1 0.00483715 -0.345606123 0.04506631
255 0 1 0 0.85445907 -0.265606236 0.64435239
257 0 0 0 0.00000000 0.881869349 -0.55421976
258 0 0 0 0.00483715 1.023875227 -0.55421976
259 0 0 0 0.39102893 9.307471078 -0.55421976
262 0 1 1 -2.08059848 -0.048220525 3.04149669
264 0 0 1 0.77722072 -0.658797171 -0.55421976
265 0 1 0 0.00000000 -0.508037505 -0.55421976
266 1 0 1 0.46826729 -0.454542140 -0.55421976
267 0 1 1 -1.07649984 0.113238214 2.44221062
269 0 0 0 2.16751113 2.326487371 0.04506631
270 0 0 0 0.39102893 1.979658438 -0.55421976
273 1 0 0 0.85445907 -0.279466399 0.04506631
275 0 1 0 0.00000000 -0.508037505 -0.55421976
276 0 0 0 2.55370292 0.857714732 0.04506631
278 1 0 1 0.00000000 -0.658797171 -0.55421976
280 0 1 0 0.39102893 -0.264876754 0.64435239
281 0 1 1 2.70817963 -0.508037505 -0.55421976
285 0 0 1 0.00000000 -0.153022808 -0.55421976
286 0 1 1 0.23655222 -0.490286770 -0.55421976
287 0 1 1 0.00483715 -0.473995000 -0.55421976
288 0 1 1 -0.61306970 -0.505201278 -0.55421976
289 1 0 1 0.93169743 -0.405909990 -0.55421976
290 0 1 0 -0.61306970 -0.508037505 -0.55421976
291 0 0 0 -0.30411628 0.875060848 -0.55421976
292 0 0 0 -0.84478477 1.112953764 0.04506631
293 1 0 1 0.46826729 -0.408341597 -0.55421976
294 0 1 0 -0.45859299 -0.486639359 -0.55421976
296 0 0 1 0.00000000 -0.119548327 -0.55421976
297 0 1 1 -0.49721217 -0.518168555 -0.55421976
298 0 0 0 -2.15783684 2.289283776 1.24363847
299 0 0 1 0.00000000 -0.065484938 -0.55421976
300 0 0 0 1.54960428 4.156190321 0.04506631
302 0 1 1 0.00000000 -0.206518174 0.64435239
303 0 1 1 -0.84478477 -0.658797171 -0.55421976
304 1 0 0 0.00000000 -0.418554349 -0.55421976
305 0 1 1 0.00000000 -0.502201647 -0.55421976
306 0 0 1 -2.24125426 2.289283776 1.24363847
307 0 0 0 0.00000000 1.498200151 -0.55421976
309 1 0 1 0.00483715 -0.191928529 0.04506631
311 0 0 0 -0.45859299 0.958869605 -0.55421976
315 1 0 1 1.00893579 -0.148159593 0.64435239
316 0 1 0 -0.30411628 -0.506010517 -0.55421976
317 1 0 0 -0.45859299 -0.153022808 0.04506631
319 0 0 0 0.08207551 2.548331678 0.64435239
320 0 0 0 0.77722072 1.957612512 0.64435239
322 0 1 1 -0.22687792 -0.505201278 -0.55421976
323 1 0 0 0.00483715 -0.418554349 -0.55421976
324 1 0 0 -0.61306970 -0.094664228 0.64435239
325 0 1 1 0.00000000 0.694149249 5.43864100
327 0 1 1 2.39922620 -0.537459956 -0.55421976
329 0 1 0 0.08207551 -0.259527217 0.64435239
330 0 0 0 -1.07649984 0.469064095 0.04506631
331 0 1 0 0.00000000 -0.206518174 0.64435239
332 0 0 1 1.20203168 -0.104390658 -0.55421976
335 0 0 0 0.00000000 1.941077581 0.04506631
336 0 1 1 0.00000000 -0.505201278 -0.55421976
337 0 0 1 -0.07240121 0.636763311 0.04506631
339 0 1 1 1.16341250 -0.502201647 -0.55421976
340 0 0 1 1.16341250 0.031779363 -0.55421976
341 1 0 1 -2.15783684 -0.153022808 0.64435239
342 0 0 0 -0.45859299 4.457305033 2.44221062
343 1 0 1 -0.14963956 -0.405909990 -0.55421976
345 1 0 1 0.46826729 -0.405909990 -0.55421976
346 1 0 0 -0.45859299 -0.405909990 -0.55421976
348 0 1 0 0.00000000 -0.345606123 0.04506631
349 0 1 1 -2.08059848 -0.349496695 0.64435239
350 0 1 1 0.93169743 -0.490286770 -0.55421976
352 0 0 1 0.00000000 0.022052932 -0.55421976
353 0 1 1 -1.15373820 -0.518168555 0.64435239
354 0 1 1 -0.38135463 -0.312536261 0.04506631
355 0 1 1 0.00000000 -0.518250257 -0.55421976
356 0 1 1 -0.14963956 -0.473995000 -0.55421976
357 0 0 0 -0.61306970 0.411110134 0.04506631
360 0 1 0 0.00000000 -0.505524195 -0.55421976
361 0 1 1 0.77722072 -0.116062374 2.44221062
362 1 0 1 -0.07240121 -0.119548327 0.04506631
363 0 1 0 1.16341250 -0.377621640 0.04506631
365 0 1 1 0.00000000 -0.357277839 0.04506631
366 0 1 1 0.00483715 -0.517763935 -0.55421976
367 0 0 0 2.32198785 0.805030551 0.04506631
368 0 1 0 0.00000000 -0.518168555 -0.55421976
370 0 0 0 -0.45859299 0.689286034 -0.55421976
371 0 0 1 -0.38135463 0.419702463 0.04506631
372 0 1 1 -0.92202313 -0.532435282 0.04506631
373 0 1 1 -0.84478477 -0.502201647 -0.55421976
374 0 0 1 -0.61306970 1.979658438 -0.55421976
376 0 0 0 0.00000000 0.939659905 0.04506631
377 0 1 0 -0.61306970 -0.517763935 -0.55421976
379 0 1 1 -0.76754642 -0.580742570 -0.55421976
381 0 0 0 0.93169743 3.767214822 -0.55421976
382 0 1 0 -2.23507519 -0.352576083 0.64435239
383 0 1 1 0.15931386 -0.504633254 -0.55421976
384 0 0 0 0.39102893 0.352751554 0.04506631
385 0 1 1 0.00000000 -0.505201278 -0.55421976
386 1 0 1 -0.92202313 0.770988046 -0.55421976
387 0 1 1 -2.23507519 0.253541968 3.64078277
388 1 0 0 0.46826729 -0.405909990 -0.55421976
389 0 1 1 0.00000000 -0.508442125 -0.55421976
390 1 0 0 -0.99926149 -0.425362850 -0.55421976
391 0 0 1 0.46826729 1.675546040 1.24363847
392 0 1 1 -0.69030806 -0.507146564 -0.55421976
393 0 1 1 -0.14963956 -0.504633254 0.64435239
394 0 0 0 -0.53583135 1.544725556 0.04506631
395 0 1 0 -0.45859299 -0.333934407 0.64435239
396 0 1 1 -0.61306970 -0.507146564 -0.55421976
397 0 1 0 0.08207551 -0.506010517 -0.55421976
398 1 0 1 1.24065086 -0.153022808 -0.55421976
399 1 0 1 -0.53583135 -0.454542140 -0.55421976
401 0 1 1 0.69998236 -0.504633254 -0.55421976
402 0 1 1 -0.30411628 -0.502201647 -0.55421976
404 0 1 1 -0.14963956 -0.350469338 0.04506631
405 0 1 0 -0.76754642 -0.490286770 -0.55421976
406 1 0 1 0.31379058 -0.250287109 0.04506631
407 0 1 1 1.62684264 -0.508037505 -0.55421976
408 1 0 1 -2.08059848 -0.294056044 0.64435239
410 0 1 0 0.00000000 -0.163397019 1.84292454
411 0 1 1 0.00000000 -0.505201278 -0.55421976
414 1 0 1 0.00000000 -0.658797171 -0.55421976
417 1 0 0 0.31379058 -0.026579218 0.64435239
421 0 1 1 0.00000000 -0.505201278 -0.55421976
422 0 1 1 -0.69030806 -0.508362368 -0.55421976
423 0 1 1 -0.07240121 -0.505605898 -0.55421976
425 0 1 1 -0.92202313 -0.265606236 0.64435239
426 0 1 1 0.00000000 -0.517763935 -0.55421976
428 1 0 0 -0.84478477 -0.153022808 -0.55421976
429 0 1 1 0.00000000 -0.508037505 -0.55421976
431 0 0 1 -0.14963956 -0.142323735 -0.55421976
432 0 1 0 0.00000000 -0.345606123 0.04506631
433 1 0 0 0.93169743 -0.153022808 0.04506631
434 0 1 1 -0.99926149 -0.520195543 -0.55421976
435 0 0 1 1.54960428 0.428617708 0.04506631
437 0 1 0 -0.69030806 0.009894895 1.84292454
438 1 0 0 -0.45859299 -0.294056044 2.44221062
439 0 0 1 2.63094127 4.457305033 2.44221062
443 0 1 1 -0.38135463 -0.507551184 0.04506631
444 1 0 0 -0.14963956 -0.405909990 -0.55421976
446 0 0 1 -2.00336012 0.933580887 0.64435239
449 0 1 0 -1.92612177 -0.284168155 1.24363847
451 1 0 1 0.46826729 -0.118980303 1.24363847
453 0 0 1 0.00483715 -0.118980303 -0.55421976
454 0 0 1 1.47236593 1.074534365 0.04506631
456 0 1 1 -0.07240121 -0.505201278 -0.55421976
459 1 0 0 1.54960428 -0.454542140 -0.55421976
460 0 1 1 0.00000000 -0.508037505 -0.55421976
461 0 0 1 1.39512757 -0.142323735 -0.55421976
463 0 0 1 1.31788921 0.090137943 -0.55421976
464 1 0 1 1.39512757 -0.405909990 -0.55421976
465 0 1 1 0.00000000 -0.502201647 -0.55421976
466 0 1 1 0.62274400 -0.521654507 -0.55421976
468 0 0 1 2.01303442 -0.142323735 -0.55421976
470 0 1 0 -2.25438478 -0.284168155 1.24363847
471 0 1 1 0.00000000 -0.517763935 -0.55421976
472 0 1 1 0.62274400 -0.490286770 -0.55421976
474 1 0 0 -0.53583135 -0.390509160 -0.55421976
475 0 1 0 -0.61306970 -0.467429660 -0.55421976
479 0 1 1 -0.61306970 -0.512496101 -0.55421976
480 0 1 0 -2.15783684 -0.419770152 0.04506631
481 0 1 1 -1.61716834 0.253541968 3.64078277
484 0 1 0 2.55370292 -0.472292875 -0.55421976
485 0 0 1 -0.38135463 1.112953764 0.04506631
486 0 1 0 0.00000000 -0.163397019 1.84292454
487 0 0 0 0.39102893 1.091960238 0.04506631
489 0 1 1 0.00483715 -0.502201647 -0.55421976
491 0 1 1 0.00000000 -0.270387749 0.04506631
493 0 0 1 1.93579607 -0.065484938 -0.55421976
494 0 0 1 3.17160977 0.304201106 -0.55421976
497 0 0 0 1.85855771 0.863713994 0.04506631
498 0 1 1 0.00000000 -0.365058983 -0.55421976
499 0 0 0 -0.38135463 2.289283776 1.24363847
500 0 1 1 -0.45859299 -0.507146564 -0.55421976
501 0 1 1 -0.99926149 -0.490286770 -0.55421976
502 0 1 0 -0.69030806 -0.508037505 -0.55421976
503 0 1 0 0.00000000 -0.510387411 -0.55421976
504 0 1 0 0.54550565 -0.472292875 -0.55421976
505 0 0 0 -1.07649984 1.023875227 -0.55421976
506 0 0 1 -0.92202313 1.459619293 0.04506631
507 1 0 0 0.23655222 -0.153022808 0.64435239
508 0 0 1 0.00000000 -0.142323735 -0.55421976
509 0 1 1 -0.14963956 -0.220621497 -0.55421976
511 0 1 1 -0.07240121 -0.508037505 -0.55421976
512 0 1 1 0.00000000 -0.502201647 -0.55421976
513 0 0 1 0.46826729 -0.147430111 -0.55421976
514 0 0 0 1.85855771 0.496702719 0.04506631
516 0 0 1 1.31788921 0.003004692 -0.55421976
517 1 0 0 0.31379058 -0.454542140 -0.55421976
518 0 1 1 0.00000000 -0.189010600 -0.55421976
519 1 0 0 0.46826729 -0.153022808 0.04506631
521 0 0 0 0.00483715 1.160045248 -0.55421976
522 0 1 1 -0.61306970 -0.505201278 -0.55421976
524 0 0 0 1.08617414 0.469064095 0.04506631
526 0 1 1 0.81583989 -0.508037505 -0.55421976
528 0 0 1 0.00000000 3.655442578 -0.55421976
530 1 0 1 -0.53583135 -0.435089280 1.24363847
532 0 1 1 0.00000000 -0.518168555 -0.55421976
533 0 1 1 -0.99926149 -0.518168555 0.64435239
535 0 1 0 0.00483715 -0.490286770 -0.55421976
536 1 0 0 -1.77164505 -0.148159593 0.64435239
537 0 0 1 1.16341250 -0.142323735 -0.55421976
538 0 0 0 0.00483715 1.411473465 -0.55421976
541 0 0 0 0.46826729 0.722355896 0.64435239
542 0 1 0 -1.61716834 -0.050408971 3.04149669
543 0 1 0 -1.46269163 -0.050408971 3.04149669
544 1 0 1 0.15931386 -0.153022808 0.04506631
545 0 0 1 1.54960428 1.411473465 0.04506631
546 0 0 1 2.63094127 -0.153022808 -0.55421976
547 1 0 0 -0.84478477 -0.153022808 0.04506631
548 1 0 1 0.00000000 -0.389131898 -0.55421976
549 0 1 1 0.23655222 -0.259527217 0.64435239
552 1 0 1 -0.22687792 -0.153022808 -0.55421976
553 0 1 1 0.00000000 -0.506496838 -0.55421976
555 0 1 0 -0.61306970 -0.507551184 -0.55421976
556 0 0 1 2.47646456 -0.142323735 -0.55421976
557 0 0 0 1.39512757 0.111536089 0.04506631
558 0 0 1 0.00000000 3.767214822 -0.55421976
559 0 0 0 0.69998236 0.890623136 0.64435239
560 0 1 0 0.46826729 -0.320317405 0.04506631
561 0 1 1 0.00000000 -0.508037505 -0.55421976
563 1 0 1 -0.14963956 -0.396183559 -0.55421976
564 0 1 1 0.00000000 -0.502201647 -0.55421976
565 0 1 0 0.00000000 -0.502201647 -0.55421976
567 0 1 1 -0.84478477 -0.505201278 -0.55421976
568 0 1 0 -0.07240121 -0.248828144 1.84292454
569 0 1 1 0.00000000 -0.518168555 -0.55421976
570 0 1 1 0.15931386 -0.506010517 -0.55421976
573 0 0 1 0.46826729 -0.145484825 -0.55421976
575 0 1 1 -1.07649984 -0.502201647 -0.55421976
576 0 1 1 -0.84478477 -0.376730699 -0.55421976
577 1 0 0 0.31379058 -0.405909990 -0.55421976
578 0 0 0 0.69998236 0.428617708 0.04506631
579 0 1 0 0.00000000 -0.377541884 0.04506631
580 0 1 1 0.15931386 -0.504633254 -0.55421976
581 1 0 0 -0.38135463 -0.075211368 0.64435239
584 0 0 1 0.46826729 0.121748840 -0.55421976
585 0 1 1 0.00000000 -0.489314127 -0.55421976
587 1 0 1 1.31788921 -0.367004269 -0.55421976
588 0 0 1 2.32198785 0.881869349 0.64435239
590 0 1 1 0.00000000 -0.502201647 -0.55421976
591 0 1 1 0.39102893 -0.520195543 -0.55421976
592 0 0 0 1.70408100 0.863713994 0.04506631
593 0 1 1 1.31788921 -0.517763935 -0.55421976
594 0 1 0 0.00000000 -0.508037505 0.64435239
595 1 0 1 0.54550565 -0.153022808 0.04506631
596 0 1 1 0.46826729 -0.189010600 0.64435239
597 1 0 0 0.00000000 -0.016852788 -0.55421976
598 0 1 1 1.47236593 -0.658797171 -0.55421976
600 0 0 1 1.47236593 0.448638592 0.04506631
601 1 0 0 -0.45859299 -0.133569948 1.24363847
603 0 0 1 0.00000000 0.166004097 -0.55421976
605 0 0 1 0.39102893 -0.142323735 -0.55421976
606 0 1 1 0.46826729 -0.356305196 0.04506631
608 0 0 1 -0.22687792 -0.065484938 -0.55421976
609 1 0 0 -0.61306970 0.150037190 1.24363847
610 0 0 0 0.77722072 2.326487371 -0.55421976
611 0 1 0 0.69998236 -0.050408971 3.04149669
612 0 1 1 0.00000000 -0.521654507 -0.55421976
613 0 1 0 0.00000000 -0.357277839 0.04506631
614 0 1 1 0.00000000 -0.508037505 -0.55421976
615 0 1 1 0.39102893 -0.502201647 -0.55421976
616 1 0 0 -0.45859299 0.605638735 1.24363847
617 0 1 1 0.31379058 -0.378675985 0.64435239
618 0 1 0 -0.30411628 -0.345606123 0.04506631
619 1 0 0 -2.00336012 0.099864373 1.24363847
621 0 1 1 -0.22687792 -0.377621640 0.04506631
622 0 0 1 0.93169743 0.363532329 0.04506631
623 0 1 1 -0.76754642 -0.352576083 0.64435239
624 0 1 1 -0.69030806 -0.506010517 -0.55421976
625 0 1 1 -0.69030806 -0.345606123 -0.55421976
626 0 0 1 2.39922620 -0.030065170 -0.55421976
627 1 0 1 2.09027278 -0.418554349 -0.55421976
631 0 0 1 3.86675498 -0.075211368 -0.55421976
633 0 0 1 0.15931386 -0.065484938 -0.55421976
634 0 0 1 0.00000000 -0.658797171 -0.55421976
635 0 1 0 -1.61716834 -0.116062374 2.44221062
637 0 1 1 0.15931386 -0.504633254 -0.55421976
638 1 0 1 0.08207551 -0.148159593 0.64435239
639 0 1 0 0.85445907 0.113238214 2.44221062
640 0 1 1 0.00000000 -0.345606123 0.04506631
641 0 1 1 -0.76754642 -0.506010517 -0.55421976
642 0 0 0 -0.45859299 0.689286034 -0.55421976
644 0 1 1 0.00000000 0.440207722 -0.55421976
645 0 1 0 -2.25438478 -0.284168155 1.24363847
646 0 0 1 1.39512757 0.833805222 0.04506631
647 0 1 1 -0.84478477 -0.505201278 -0.55421976
648 0 0 1 2.01303442 0.031779363 -0.55421976
649 0 1 1 0.00000000 -0.511928077 -0.55421976
650 0 1 0 -0.53583135 -0.511928077 -0.55421976
651 0 1 1 0.00000000 -0.505201278 -0.55421976
654 0 1 0 0.00000000 -0.506496838 -0.55421976
655 0 1 0 -0.92202313 -0.527490365 -0.55421976
656 1 0 1 -0.45859299 0.770988046 0.64435239
658 0 1 0 0.15931386 -0.357277839 0.64435239
659 1 0 1 -0.53583135 -0.405909990 -0.55421976
661 0 0 1 1.54960428 1.941077581 0.64435239
662 0 1 1 0.77722072 -0.518250257 -0.55421976
663 0 0 1 1.31788921 -0.161047113 -0.55421976
667 1 0 1 -0.38135463 -0.405909990 -0.55421976
668 0 1 1 0.00000000 -0.507551184 -0.55421976
670 0 0 0 0.00000000 0.352751554 0.04506631
671 1 0 0 0.77722072 0.099864373 0.64435239
674 1 0 1 0.08207551 -0.405909990 -0.55421976
677 0 1 1 -0.41997381 -0.502201647 -0.55421976
678 0 1 0 -0.92202313 -0.467347958 -0.55421976
679 0 1 0 1.00893579 0.253541968 3.64078277
681 0 1 0 0.00000000 -0.500499522 -0.55421976
682 0 0 1 -0.22687792 0.833805222 -0.55421976
683 0 1 1 -0.76754642 -0.479344536 -0.55421976
687 0 1 1 -1.23097656 0.113238214 2.44221062
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 -0.5542197613.6 모형 훈련
Package "glmnet"에서 제공하는 함수 glmnet()을 이용하여 Elastic Net 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.
13.6.1 람다 값 직접 지정
elast.fit <- glmnet(x = train.x, # 예측 변수를 포함하는 행렬
y = titanic.trd.Imp$Survived,# Target
family = "binomial", # Binary Classification
alpha = 0.5, # 0 : Ridge / 1 : Lasso / 0 < alpha < 1 : Elastic Net
lambda = 0.1)
round(coef(elast.fit), 3) # 회귀계수 추정치7 x 1 sparse Matrix of class "dgCMatrix"
s0
(Intercept) 0.781
Pclass2 .
Pclass3 -0.715
Sexmale -1.439
Age .
Fare 0.065
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. \[
\begin{align*}
\log{\frac{p}{1-p}} = &\;0.781 -0.715 X_{\text{Pclass3}} -1.439 X_{\text{Sexmale}} + 0.065 Z_{\text{Fare}}
\end{align*}
\] 여기서, \(Z_{\text{예측 변수}}\)는 표준화한 예측 변수, \(X_{\text{예측 변수}}\)는 더미 변수를 의미한다.
13.6.2 교차 검증을 통한 최적의 람다 값
# 100개의 람다 값에 따른 결과
elast.fit <- glmnet(x = train.x, # 예측 변수를 포함하는 행렬
y = titanic.trd.Imp$Survived,# Target
family = "binomial", # Binary Classification
alpha = 0.5) # 0 : Ridge / 1 : Lasso / 0 < alpha < 1 : Elastic Net
plot(elast.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.
elast.fit$lambda # 100개의 람다 값 [1] 0.5015509422 0.4569945389 0.4163964036 0.3794048947 0.3456996095 0.3149886090 0.2870058891 0.2615090770 0.2382773313 0.2171094299 0.1978220265 0.1802480629 0.1642353218 0.1496451085 0.1363510495
[16] 0.1242379980 0.1132010367 0.1031445686 0.0939814894 0.0856324329 0.0780250836 0.0710935502 0.0647777951 0.0590231144 0.0537796636 0.0490020265 0.0446488215 0.0406823432 0.0370682360 0.0337751961
[31] 0.0307747007 0.0280407611 0.0255496972 0.0232799325 0.0212118075 0.0193274090 0.0176104152 0.0160459545 0.0146204761 0.0133216333 0.0121381761 0.0110598540 0.0100773271 0.0091820851 0.0083663740
[46] 0.0076231284 0.0069459106 0.0063288551 0.0057666170 0.0052543267 0.0047875468 0.0043622343 0.0039747054 0.0036216036 0.0032998703 0.0030067189 0.0027396103 0.0024962309 0.0022744726 0.0020724147
[61] 0.0018883071 0.0017205551 0.0015677057 0.0014284351 0.0013015368 0.0011859119 0.0010805587 0.0009845649 0.0008970989Caution! \(\lambda\)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.
# 교차검증을 통한 최적의 람다 값
set.seed(200) # Seed 고정 -> 동일한 결과를 출력하기 위해
cv.elast.fit <- cv.glmnet(x = train.x, # 예측 변수를 포함하는 행렬
y = titanic.trd.Imp$Survived,# Target
family = "binomial", # Binary Classification
alpha = 0.5, # 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.elast.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.elast.fit$lambda.min # 최적의 람다 값[1] 0.0008970989max(cv.elast.fit$cvm) # 최적의 람다 값에 대한 AUC[1] 0.8502147round(coef(cv.elast.fit, s = cv.elast.fit$lambda.min), 3) # 최적의 람다 값에 대한 회귀계수 추정치7 x 1 sparse Matrix of class "dgCMatrix"
s1
(Intercept) 2.521
Pclass2 -1.007
Pclass3 -2.320
Sexmale -2.690
Age -0.515
Fare 0.127
FamSize -0.388Result! 최적의 \(\lambda\) 값에 대해 추정된 회귀계수를 이용하여 다음과 같은 모형식을 얻을 수 있다. \[
\begin{align*}
\log{\frac{p}{1-p}} = &\;2.521 - 1.007 X_{\text{Pclass2}} - 2.320 X_{\text{Pclass3}} -2.690 X_{\text{Sexmale}} \\
&-0.515 Z_{\text{Age}} +0.127 Z_{\text{Fare}} - 0.388 Z_{\text{FamSize}}
\end{align*}
\]
13.7 모형 평가
Caution! 모형 평가를 위해 Test Dataset에 대한 예측 class/확률 이 필요하며, 함수 predict()를 이용하여 생성한다.
# 예측 class 생성
test.elast.class <- predict(cv.elast.fit,
newx = test.x, # Test Dataset including Only 예측 변수
s = "lambda.min", # 최적의 람다 값 기반
type = "class") # 예측 class 생성
test.elast.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 rows13.7.1 ConfusionMatrix
CM <- caret::confusionMatrix(as.factor(test.elast.class), titanic.ted.Imp$Survived,
positive = "yes") # confusionMatrix(예측 class, 실제 class, positive = "관심 class")
CMConfusion Matrix and Statistics
Reference
Prediction no yes
no 148 32
yes 16 70
Accuracy : 0.8195
95% CI : (0.768, 0.8638)
No Information Rate : 0.6165
P-Value [Acc > NIR] : 5.675e-13
Kappa : 0.6067
Mcnemar's Test P-Value : 0.03038
Sensitivity : 0.6863
Specificity : 0.9024
Pos Pred Value : 0.8140
Neg Pred Value : 0.8222
Prevalence : 0.3835
Detection Rate : 0.2632
Detection Prevalence : 0.3233
Balanced Accuracy : 0.7944
'Positive' Class : yes
13.7.2 ROC 곡선
# 예측 확률 생성
test.elast.prob <- predict(cv.elast.fit,
newx = test.x, # Test Dataset including Only 예측 변수
s = "lambda.min", # 최적의 람다 값 기반
type = "response") # 예측 확률 생성
test.elast.prob %>% # "Survived = yes"에 대한 예측 확률
as_tibble# A tibble: 266 × 1
lambda.min
<dbl>
1 0.907
2 0.296
3 0.125
4 0.665
5 0.0882
6 0.236
7 0.720
8 0.213
9 0.0878
10 0.893
# ℹ 256 more rowsac <- titanic.ted.Imp$Survived # Test Dataset의 실제 class
pp <- as.numeric(test.elast.prob) # 예측 확률을 수치형으로 변환13.7.2.1 Package “pROC”
pacman::p_load("pROC")
elast.roc <- roc(ac, pp, plot = T, col = "gray") # roc(실제 class, 예측 확률)
auc <- round(auc(elast.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(elast.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(elast.roc) +
annotate(geom = "text", x = 0.9, y = 1.0,
label = paste("AUC = ", auc),
size = 5,
color="red") +
theme_bw()
13.7.2.2 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) 
13.7.2.3 Package “ROCR”
pacman::p_load("ROCR")
elast.pred <- prediction(pp, ac) # prediction(예측 확률, 실제 class)
elast.perf <- performance(elast.pred, "tpr", "fpr") # performance(, "민감도", "1-특이도")
plot(elast.perf, col = "gray") # ROC Curve
perf.auc <- performance(elast.pred, "auc") # AUC
auc <- attributes(perf.auc)$y.values
legend("bottomright", legend = auc, bty = "n")
13.7.3 향상 차트
13.7.3.1 Package “ROCR”
elast.perf <- performance(elast.pred, "lift", "rpp") # Lift Chart
plot(elast.perf, main = "lift curve",
colorize = T, # Coloring according to cutoff
lwd = 2) 