使用cluster程序包内Fanny（）函数进行c-均值模糊聚类。
在传统的聚类结果中，每个对象只能分配给唯一的一个组，然而，c-均值聚类结果不同，一个对象可以赋予不同的组，对象与组之间的归属度可以通过成员值（membership value.）衡量。
rm(list = ls())
setwd("D:\\Users\\Administrator\\Desktop\\RStudio\\数量生态学\\DATA")
spe <- read.csv("DoubsSpe.csv", row.names=1)
env <- read.csv("DoubsEnv.csv", row.names=1)
spa <- read.csv("DoubsSpa.csv", row.names=1)
# 删除无物种数据的样方8
spe <- spe[-8,]
env <- env[-8,]
spa <- spa[-8,]
# 物种多度数据：先计算样方之间的弦距离矩阵，然后进行单连接聚合聚类
# **************************************************************
spe.norm <- decostand(spe, "normalize")
spe.ch <- vegdist(spe.norm, "euc")
spe.ch.single <- hclust(spe.ch, method="single")
# 鱼类数据的c-均值模糊聚类
# ************************
k <- 4 # 选择聚类分组的数量
spe.fuz <- fanny(spe.ch, k=k, memb.exp=1.5)
summary(spe.fuz)
Fuzzy Clustering object of class 'fanny' :
m.ship.expon. 1.5
objective 6.065589
tolerance 1e-15
iterations 115
converged 1
maxit 500
n 29
Membership coefficients (in %, rounded):
[,1] [,2] [,3] [,4]
1 42 28 13 18
2 86 9 2 3
3 86 10 2 2
4 66 25 4 5
5 17 43 20 20
6 47 41 5 7
7 83 13 2 3
9 18 36 17 29
10 36 48 7 9
11 73 18 4 6
12 84 11 2 3
13 70 20 4 6
14 60 29 5 6
15 29 57 6 8
16 14 70 8 8
17 11 70 10 9
18 10 58 18 13
19 10 40 30 20
20 3 10 73 13
21 1 3 90 5
22 1 4 90 5
23 3 6 6 84
24 3 4 7 86
25 5 9 14 72
26 2 5 80 12
27 1 3 90 5
28 2 4 89 6
29 2 5 88 5
30 3 7 81 9
Fuzzyness coefficients:
dunn_coeff normalized
0.5757451 0.4343269
Closest hard clustering:
1 2 3 4 5 6 7 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
1 1 1 1 2 1 1 2 2 1 1 1 1 2 2 2 2 2 3 3 3 4 4 4 3 3 3 3 3
Silhouette plot information:
cluster neighbor sil_width
2 1 2 0.52060562
3 1 2 0.49263816
12 1 2 0.48842628
7 1 2 0.44908829
13 1 2 0.42622825
11 1 2 0.42572426
4 1 2 0.34706151
14 1 2 0.32623078
1 1 2 0.27343990
6 1 2 0.16117188
17 2 3 0.22202399
16 2 1 0.18163541
9 2 4 0.08426515
18 2 3 0.03401264
5 2 3 0.02286117
15 2 1 -0.11888413
10 2 1 -0.13208427
19 2 3 -0.14864026
21 3 4 0.64316265
22 3 4 0.64086333
29 3 4 0.64026483
27 3 4 0.63512401
28 3 4 0.63102753
30 3 4 0.59003815
26 3 4 0.50955370
20 3 4 0.50797154
23 4 3 0.42148143
24 4 3 0.38039206
25 4 3 0.21960419
Average silhouette width per cluster:
[1] 0.39106149 0.01814871 0.59975072 0.34049256
Average silhouette width of total data set:
[1] 0.3405272
Available components:
[1] "membership" "coeff" "memb.exp" "clustering" "k.crisp" "objective" "convergence" "diss"
[9] "call" "silinfo"
spefuz.g <- spe.fuz$clustering
# 样方成员值
spe.fuz$membership
[,1] [,2] [,3] [,4]
1 0.41983293 0.27938150 0.12507006 0.17571551
2 0.86333399 0.09160712 0.01872811 0.02633079
3 0.86009710 0.09794009 0.01766820 0.02429460
4 0.66104474 0.24709547 0.04069775 0.05116203
5 0.17081624 0.42786571 0.20384018 0.19747787
6 0.46991417 0.40943844 0.05307161 0.06757579
7 0.82698989 0.12550961 0.01958153 0.02791898
9 0.17845384 0.36031665 0.16941554 0.29181397
10 0.36242730 0.47881889 0.06556495 0.09318886
11 0.72787234 0.17931783 0.03775983 0.05505000
12 0.83703665 0.11498506 0.01966949 0.02830879
13 0.70047249 0.20084165 0.04108743 0.05759844
14 0.59873829 0.28911587 0.04766088 0.06448496
15 0.29396867 0.57042116 0.05897579 0.07663437
16 0.14473808 0.69577978 0.07675396 0.08272817
17 0.11117893 0.69749883 0.09890084 0.09242140
18 0.10161983 0.57950673 0.18443183 0.13444161
19 0.10315906 0.40097836 0.29706350 0.19879907
20 0.03321635 0.09978590 0.73408504 0.13291271
21 0.01305429 0.03432591 0.90451831 0.04810149
22 0.01397900 0.03563244 0.90016255 0.05022601
23 0.03467200 0.05789778 0.06303980 0.84439042
24 0.02570392 0.04371767 0.07027107 0.86030734
25 0.04932806 0.09308773 0.14017276 0.71741146
26 0.02218219 0.04921691 0.80439767 0.12420324
27 0.01448996 0.03317050 0.89817571 0.05416383
28 0.01646103 0.03672029 0.88854853 0.05827015
29 0.01920502 0.04781543 0.87803550 0.05494406
30 0.03235038 0.07222784 0.80641410 0.08900768
# 每个样方最接近的聚类簇
spe.fuz$clustering
1 2 3 4 5 6 7 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
1 1 1 1 2 1 1 2 2 1 1 1 1 2 2 2 2 2 3 3 3 4 4 4 3 3 3 3 3
# 轮廓图
plot(silhouette(spe.fuz), main="鱼类数据的c-均值模糊聚类",
+ cex.names=0.8, col=spe.fuz$silinfo$widths+1,border="white")
# 模糊聚类簇的主坐标排序(PCoA)
dc.pcoa <- cmdscale(spe.ch)
dc.scores <- scores(dc.pcoa, choices=c(1,2))
plot(scores(dc.pcoa), asp=1, type="n",
main="模糊聚类簇的排序(PCoA)")
abline(h=0, lty="dotted")
abline(v=0, lty="dotted")
for (i in 1:k) {
gg <- dc.scores[spefuz.g==i,]
hpts <- chull(gg)
hpts <- c(hpts, hpts[1])
lines(gg[hpts,], col=i+1)
}
stars(spe.fuz$membership, location=scores(dc.pcoa), draw.segments=TRUE,
add=TRUE, scale=FALSE, len=0.1, col.segments=2:(k+1))
legend(locator(1), paste("组", 1:k, sep=" "),
pch=15, pt.cex=2, col=2:(k+1), bty="n")
# 在图上任意点击某一处放置图例
模糊聚类(FCM)介绍及R语言实现
模糊c均值聚类和k-means聚类的数学原理
FCM(Fuzzy C-Means)模糊C聚类
对模糊聚类的小结
模糊聚类分析
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