[ 연습문제 - 군집분석 ]
cancer.csv 파일의 설명변수(id제외)만 사용하여 계층/비계층 군집분석을 진행
단, 변수 스케일링 후 군집분석을 진행하세요
[ 내 답변 ]
df <- read.csv('cancer.csv')
df$id <- NULL
head(df)
str(df)
# 변수 스케일링
f1 <- function(x) {
(x - mean(x)) / sd(x)
}
df[,-1] <- apply(df[,-1], 2, f1)
head(df)
# 계층적 군집분석
# 거리행렬 구하기
x <- df[,-1]
d1 <- dist(x)
# 학습
m1<- hclust(d1, method = 'single') # 최단거리법
m2<- hclust(d1, method = 'complete') # 최장거리법
m3<- hclust(d1, method = 'centroid') # 중심연결법
m4<- hclust(d1, method = 'average') # 평균연결법
m5<- hclust(d1, method = 'ward.D') # 와드연결법 (와드 1)
m6<- hclust(d1, method = 'ward.D2') # 와드연결법 (와드 2)
# 시각화
dev.new()
par(mfrow=c(2,3))
# 최단거리법
plot(m1, hang = -1, main = 'Single')
# 최장거리법
plot(m2, hang = -1, main = 'Complete')
# 중심연결법
plot(m3, hang = -1, main = 'Centroid')
# 평균연결법
plot(m4, hang = -1, main = 'Average')
# 와드연결법 (와드1)
plot(m5, hang = -1, main = 'Ward.D')
# 와드연결법 (와드2)
plot(m6, hang = -1, main = 'Ward.D2')
# 군집 수 구하기
result <- NbClust(data = x, min.nc=2, max.nc = 15, method = 'ward.D')
result
> result <- NbClust(data = x, min.nc=2, max.nc = 15, method = 'ward.D')
*** : The Hubert index is a graphical method of determining the number of clusters.
In the plot of Hubert index, we seek a significant knee that corresponds to a
significant increase of the value of the measure i.e the significant peak in Hubert
index second differences plot.
*** : The D index is a graphical method of determining the number of clusters.
In the plot of D index, we seek a significant knee (the significant peak in Dindex
second differences plot) that corresponds to a significant increase of the value of
the measure.
*******************************************************************
* Among all indices:
* 7 proposed 2 as the best number of clusters
* 7 proposed 3 as the best number of clusters
* 2 proposed 5 as the best number of clusters
* 1 proposed 10 as the best number of clusters
* 2 proposed 11 as the best number of clusters
* 1 proposed 14 as the best number of clusters
***** Conclusion *****
* According to the majority rule, the best number of clusters is 2
******************************************************************* 
result <- NbClust(data = x, min.nc=2, max.nc = 15, method = 'ward.D2')
result
> result <- NbClust(data = x, min.nc=2, max.nc = 15, method = 'ward.D2')
*** : The Hubert index is a graphical method of determining the number of clusters.
In the plot of Hubert index, we seek a significant knee that corresponds to a
significant increase of the value of the measure i.e the significant peak in Hubert
index second differences plot.
*** : The D index is a graphical method of determining the number of clusters.
In the plot of D index, we seek a significant knee (the significant peak in Dindex
second differences plot) that corresponds to a significant increase of the value of
the measure.
*******************************************************************
* Among all indices:
* 9 proposed 2 as the best number of clusters
* 6 proposed 3 as the best number of clusters
* 1 proposed 5 as the best number of clusters
* 2 proposed 7 as the best number of clusters
* 1 proposed 12 as the best number of clusters
* 1 proposed 13 as the best number of clusters
***** Conclusion *****
* According to the majority rule, the best number of clusters is 2
******************************************************************* 
# 비계층적 군집분석
withss <- c() ; betss <- c()
for (i in 2:10) {
set.seed(0)
m2 <- kmeans(x, i)
withss <- c(withss, m2$tot.withinss)
betss <- c(betss, m2$betweenss)
}
par(mfrow = c(1,2))
plot(2:10, withss, xlab = 'k',
ylab = 'within_ss', type = 'o')
plot(2:10, betss, xlab = 'k',
ylab = 'between_ss', type = 'o')
set.seed(0)
m2 <- kmeans(x, 2)
> m2
K-means clustering with 2 clusters of sizes 375, 194
Cluster means:
radius_mean texture_mean perimeter_mean area_mean
1 -0.4825702 -0.2388313 -0.4999790 -0.4777212
2 0.9328033 0.4616584 0.9664542 0.9234301
smoothness_mean compactness_mean concavity_mean
1 -0.3107301 -0.5255563 -0.5785267
2 0.6006381 1.0158949 1.1182861
concave_points_mean symmetry_mean fractal_dimension_mean
1 -0.586655 -0.3088121 -0.1490098
2 1.133998 0.5969307 0.2880344
radius_se texture_se perimeter_se area_se smoothness_se
1 -0.4276089 -0.02109138 -0.4305928 -0.4013983 -0.02381032
2 0.8265636 0.04076942 0.8323315 0.7758988 0.04602510
compactness_se concavity_se concave_points_se symmetry_se
1 -0.3698751 -0.3343034 -0.3973627 -0.0748643
2 0.7149647 0.6462051 0.7680980 0.1447119
fractal_dimension_se radius_worst texture_worst perimeter_worst
1 -0.2366141 -0.5173986 -0.2512569 -0.5318435
2 0.4573726 1.0001262 0.4856771 1.0280479
area_worst smoothness_worst compactness_worst concavity_worst
1 -0.4989187 -0.3158003 -0.4918085 -0.5363714
2 0.9644047 0.6104387 0.9506607 1.0368003
concave_points_worst symmetry_worst fractal_dimension_worst
1 -0.579591 -0.3030883 -0.3364329
2 1.120343 0.5858665 0.6503213
Clustering vector:
[1] 2 2 2 2 2 2 2 2 2 2 1 2 2 1 2 2 1 2 2 1 1 1 2 2 2 2 2 2 2 2
[31] 2 2 2 2 2 2 2 1 1 1 1 1 2 2 1 2 1 2 1 1 1 1 1 2 1 1 2 2 1 1
[61] 1 1 2 1 2 2 1 1 2 1 2 1 2 1 1 2 1 2 2 1 1 2 2 2 1 2 1 2 1 2
[91] 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 2 1 1 2 1 1 1 2 1 1 1 1 2 2 1
[121] 1 2 2 1 1 1 1 2 2 2 1 2 2 1 2 1 1 1 2 1 1 2 1 1 1 1 2 1 1 1
[151] 1 1 2 1 1 1 2 1 1 1 1 2 2 1 2 1 1 2 2 1 1 1 2 1 1 1 2 2 1 1
[181] 2 2 1 1 1 1 1 1 1 1 2 1 1 2 2 1 2 2 2 2 1 2 2 2 1 1 1 1 1 1
[211] 2 1 2 2 2 2 1 1 2 2 1 1 1 2 1 1 1 1 1 2 2 1 1 2 1 1 2 2 1 2
[241] 1 1 2 1 2 1 1 2 1 1 2 1 2 2 2 1 2 2 2 2 2 1 2 1 2 2 1 1 1 1
[271] 1 1 2 1 1 1 1 1 1 1 2 1 2 2 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1
[301] 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 2 1 2 1 1 1 1 2 2
[331] 2 1 1 1 1 2 1 2 1 2 1 1 1 2 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1
[361] 1 1 1 1 1 2 2 1 2 2 2 1 2 2 1 1 2 1 1 2 1 1 1 1 1 1 1 1 1 2
[391] 1 1 2 2 1 1 1 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 2 1 1
[421] 1 2 1 1 1 1 1 1 1 1 2 1 2 2 1 1 1 1 1 1 1 2 1 1 1 1 2 1 1 2
[451] 1 2 1 1 1 1 1 1 1 1 2 2 1 1 1 2 1 1 2 1 1 1 1 1 1 1 1 1 1 2
[481] 1 1 1 1 1 2 1 2 1 1 1 1 2 1 1 1 1 1 2 2 1 2 1 2 2 2 1 1 1 2
[511] 1 1 2 1 1 1 2 2 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 2 1 1 1 1
[541] 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 1
Within cluster sum of squares by cluster:
[1] 4971.437 6603.711
(between_SS / total_SS = 32.1 %)
Available components:
[1] "cluster" "centers" "totss" "withinss"
[5] "tot.withinss" "betweenss" "size" "iter"
[9] "ifault"
# 군집은 2개 (샘플사이즈는 각 375, 194)
# between_ss / total_ss = 32.1%
m2 <- kmeans(x, 3)
m2
> m2
K-means clustering with 3 clusters of sizes 110, 100, 359
Cluster means:
radius_mean texture_mean perimeter_mean area_mean
1 1.6176587 0.6260620 1.6225732 1.6616915
2 -0.1721774 0.1788294 -0.1006558 -0.2198210
3 -0.4477011 -0.2416428 -0.4691295 -0.4479219
smoothness_mean compactness_mean concavity_mean
1 0.3982143 0.9297963 1.2382477
2 0.8484791 1.0345212 0.7803190
3 -0.3583607 -0.5730633 -0.5967664
concave_points_mean symmetry_mean fractal_dimension_mean
1 1.4856628 0.4317906 -0.2866671
2 0.4989880 0.7521312 1.1829407
3 -0.5942109 -0.3418108 -0.2416732
radius_se texture_se perimeter_se area_se smoothness_se
1 1.44001760 0.09373762 1.40414509 1.4222534 -0.07260779
2 -0.08495483 0.02338187 -0.01781494 -0.1722055 0.43926501
3 -0.41756672 -0.03523489 -0.42527706 -0.3878199 -0.10011043
compactness_se concavity_se concave_points_se symmetry_se
1 0.4786511 0.4393663 0.7871419 0.05437929
2 1.0737418 0.8897247 0.7514795 0.28620432
3 -0.4457543 -0.3824590 -0.4505113 -0.09638483
fractal_dimension_se radius_worst texture_worst perimeter_worst
1 0.1189330 1.66528388 0.5424224 1.655385195
2 1.0255153 -0.08815198 0.3111937 -0.007008775
3 -0.3221007 -0.48569924 -0.2528853 -0.505268785
area_worst smoothness_worst compactness_worst concavity_worst
1 1.6834662 0.3365925 0.6697022 0.8858320
2 -0.1563397 0.9682984 1.1787346 1.0441360
3 -0.4722766 -0.3728552 -0.5335395 -0.5622705
concave_points_worst symmetry_worst fractal_dimension_worst
1 1.272063 0.3000824 0.08399194
2 0.742345 0.8092044 1.38339588
3 -0.596550 -0.3173524 -0.41108273
Clustering vector:
[1] 1 1 1 2 1 2 1 2 2 2 3 2 1 3 2 2 3 2 1 3 3 3 2 1 1 1 2 1 2 1
[31] 1 2 1 1 2 2 2 3 3 2 3 2 1 2 3 1 3 2 3 3 3 3 3 1 3 3 1 2 3 3
[61] 3 3 2 3 2 2 3 3 2 3 1 2 2 3 3 1 3 1 1 3 3 2 1 1 3 1 3 1 3 2
[91] 3 3 3 3 2 1 3 3 3 2 3 3 3 3 3 2 3 3 1 3 3 2 2 3 3 3 3 2 2 3
[121] 3 1 1 3 3 3 3 1 2 1 3 3 3 3 1 3 3 3 1 3 3 3 3 3 3 2 2 3 3 3
[151] 3 2 2 3 3 3 1 3 3 3 3 1 1 3 1 3 3 3 1 3 3 3 2 3 3 3 2 2 3 3
[181] 1 1 3 3 3 3 3 3 3 3 2 3 3 2 2 3 2 1 1 2 3 1 1 2 3 3 3 3 2 3
[211] 1 3 1 2 2 2 2 3 1 1 3 3 3 2 3 3 3 3 3 2 2 3 3 1 3 3 1 1 3 1
[241] 3 3 2 3 1 3 3 2 3 3 1 3 1 3 1 3 1 2 1 2 1 3 1 3 1 1 3 3 3 2
[271] 3 3 1 3 3 3 3 3 3 3 1 3 1 2 3 3 3 3 2 3 2 3 3 3 3 3 3 3 3 3
[301] 1 3 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 2 3 3 1 3 1 3 3 3 3 2 2
[331] 2 3 3 3 3 1 3 1 3 1 3 3 3 1 3 3 3 3 3 3 3 2 1 2 3 3 2 3 3 3
[361] 3 3 3 3 3 1 1 3 1 1 2 3 1 1 3 3 2 3 3 2 3 3 3 2 3 3 3 3 2 1
[391] 3 3 2 1 3 3 3 3 3 3 2 3 3 3 3 3 3 3 1 3 3 3 3 3 3 3 3 1 3 3
[421] 3 2 3 3 3 3 3 3 3 3 2 3 1 1 3 2 3 3 3 3 2 1 3 3 3 3 1 3 3 1
[451] 3 1 3 3 3 3 3 3 3 3 1 1 3 3 3 2 3 3 1 2 3 3 3 3 3 3 3 3 3 2
[481] 3 3 3 3 3 2 3 1 3 3 3 3 1 3 3 3 2 3 1 1 3 2 3 1 2 2 3 2 3 2
[511] 3 3 2 3 3 3 1 1 3 3 2 1 3 3 3 3 3 3 3 3 3 3 3 1 3 1 3 2 3 2
[541] 3 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 1 1 1 3 1 3
Within cluster sum of squares by cluster:
[1] 2894.489 2791.854 4357.771
(between_SS / total_SS = 41.1 %)
Available components:
[1] "cluster" "centers" "totss" "withinss"
[5] "tot.withinss" "betweenss" "size" "iter"
[9] "ifault" # 군집은 3개 (샘플사이즈는 각 110, 100, 359)
# between_ss / total_ss = 41.1%
[ 문제풀이 ]
# STEP1: 데이터 로딩)
cancer <- read.csv('cancer.csv')
cancer$diagnosis <- factor(cancer$diagnosis)
# STEP2: 불필요 변수 제거)
cancer$id <- NULL
# STEP3: 스케일링
cancer[,-1] <- scale(cancer[,-1])
# STEP4: 계층적 군집분석 수행)
X <- cancer[,-1]
d1 <- dist(X)
# 학습
m1 <- hclust(d1, method = 'single') # 최단거리법
m2 <- hclust(d1, method = 'complete') # 최장거리법
m3 <- hclust(d1, method = 'centroid') # 중심연결법
m4 <- hclust(d1, method = 'average') # 평균연결법
m5 <- hclust(d1, method = 'ward.D') # 와드1
m6 <- hclust(d1, method = 'ward.D2') # 와드2
# 시각화
dev.new()
par(mfrow=c(2,3))
plot(m1, hang = -1, main = 'Single')
rect.hclust(m1, k = 2)
plot(m2, hang = -1, main = 'Complete')
rect.hclust(m2, k = 2)
plot(m3, hang = -1, main = 'Centroid')
rect.hclust(m3, k = 2)
plot(m4, hang = -1, main = 'Average')
rect.hclust(m4, k = 2)
plot(m5, hang = -1, main = 'Ward.D')
rect.hclust(m5, k = 2)
plot(m6, hang = -1, main = 'Ward.D2')
rect.hclust(m6, k = 2)
# 평가
library(NbClust)
result <- NbClust(data = X, # 데이터
min.nc = 2, # 최소군집수
max.nc = 10, # 최대군집수
method = 'ward.D') # 군집간 거리
result
# *******************************************************************
# * Among all indices:
# * 8 proposed 2 as the best number of clusters
# * 7 proposed 3 as the best number of clusters
# * 2 proposed 5 as the best number of clusters
# * 1 proposed 7 as the best number of clusters
# * 2 proposed 10 as the best number of clusters
#
# ***** Conclusion *****
#
# * According to the majority rule, the best number of clusters is 2
# STEP4: 비계층적 군집분석 수행)
set.seed(0)
m1 <- kmeans(X, 2)
m1
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