如果您的问题是how can I determine how many clusters are appropriate for a kmeans analysis of my data?，那么这里有一些选项。关于确定集群数量的维基百科文章对其中一些方法进行了很好的回顾。
首先，一些可重复的数据（Q 中的数据......我不清楚）：
n = 100
g = 6
set.seed(g)
d <- data.frame(x = unlist(lapply(1:g, function(i) rnorm(n/g, runif(1)*i^2))),
y = unlist(lapply(1:g, function(i) rnorm(n/g, runif(1)*i^2))))
plot(d)
一。在平方误差和 (SSE) 碎石图中寻找弯曲或弯头。有关更多信息，请参见http://www.statmethods.net/advstats/cluster.html和http://www.mattpeeples.net/kmeans.html。结果图中肘部的位置表明了 kmeans 的合适数量的聚类：
mydata <- d
wss <- (nrow(mydata)-1)*sum(apply(mydata,2,var))
for (i in 2:15) wss[i] <- sum(kmeans(mydata,
centers=i)$withinss)
plot(1:15, wss, type="b", xlab="Number of Clusters",
ylab="Within groups sum of squares")
我们可能会得出结论，这种方法将指示 4 个集群：
二。pamk您可以使用fpc 包中的函数围绕中心点进行分区以估计集群的数量。
library(fpc)
pamk.best <- pamk(d)
cat("number of clusters estimated by optimum average silhouette width:", pamk.best$nc, "\n")
plot(pam(d, pamk.best$nc))
# we could also do:
library(fpc)
asw <- numeric(20)
for (k in 2:20)
asw[[k]] <- pam(d, k) $ silinfo $ avg.width
k.best <- which.max(asw)
cat("silhouette-optimal number of clusters:", k.best, "\n")
# still 4
三。Calinsky 标准：另一种诊断有多少集群适合数据的方法。在这种情况下，我们尝试 1 到 10 个组。
require(vegan)
fit <- cascadeKM(scale(d, center = TRUE, scale = TRUE), 1, 10, iter = 1000)
plot(fit, sortg = TRUE, grpmts.plot = TRUE)
calinski.best <- as.numeric(which.max(fit$results[2,]))
cat("Calinski criterion optimal number of clusters:", calinski.best, "\n")
# 5 clusters!
四。根据期望最大化的贝叶斯信息准则确定最优模型和簇数，通过参数化高斯混合模型的层次聚类初始化
# See http://www.jstatsoft.org/v18/i06/paper
# http://www.stat.washington.edu/research/reports/2006/tr504.pdf
#
library(mclust)
# Run the function to see how many clusters
# it finds to be optimal, set it to search for
# at least 1 model and up 20.
d_clust <- Mclust(as.matrix(d), G=1:20)
m.best <- dim(d_clust$z)[2]
cat("model-based optimal number of clusters:", m.best, "\n")
# 4 clusters
plot(d_clust)
五。亲和传播 (AP) 聚类，参见http://dx.doi.org/10.1126/science.1136800
library(apcluster)
d.apclus <- apcluster(negDistMat(r=2), d)
cat("affinity propogation optimal number of clusters:", length(d.apclus@clusters), "\n")
# 4
heatmap(d.apclus)
plot(d.apclus, d)
六。用于估计聚类数量的差距统计。另请参阅一些代码以获得漂亮的图形输出。在这里尝试 2-10 个集群：
library(cluster)
clusGap(d, kmeans, 10, B = 100, verbose = interactive())
Clustering k = 1,2,..., K.max (= 10): .. done
Bootstrapping, b = 1,2,..., B (= 100) [one "." per sample]:
.................................................. 50
.................................................. 100
Clustering Gap statistic ["clusGap"].
B=100 simulated reference sets, k = 1..10
--> Number of clusters (method 'firstSEmax', SE.factor=1): 4
logW E.logW gap SE.sim
[1,] 5.991701 5.970454 -0.0212471 0.04388506
[2,] 5.152666 5.367256 0.2145907 0.04057451
[3,] 4.557779 5.069601 0.5118225 0.03215540
[4,] 3.928959 4.880453 0.9514943 0.04630399
[5,] 3.789319 4.766903 0.9775842 0.04826191
[6,] 3.747539 4.670100 0.9225607 0.03898850
[7,] 3.582373 4.590136 1.0077628 0.04892236
[8,] 3.528791 4.509247 0.9804556 0.04701930
[9,] 3.442481 4.433200 0.9907197 0.04935647
[10,] 3.445291 4.369232 0.9239414 0.05055486
这是 Edwin Chen 实施差距统计的输出：
七。您可能还会发现使用 clustergrams 探索数据以可视化集群分配很有用，请参阅http://www.r-statistics.com/2010/06/clustergram-visualization-and-diagnostics-for-cluster-analysis-r-代码/了解更多详情。
八。NbClust包提供 30 个索引来确定数据集中的集群数量。
library(NbClust)
nb <- NbClust(d, diss=NULL, distance = "euclidean",
method = "kmeans", min.nc=2, max.nc=15,
index = "alllong", alphaBeale = 0.1)
hist(nb$Best.nc[1,], breaks = max(na.omit(nb$Best.nc[1,])))
# Looks like 3 is the most frequently determined number of clusters
# and curiously, four clusters is not in the output at all!
如果你的问题是how can I produce a dendrogram to visualize the results of my cluster analysis，那么你应该从这些开始：http:
//www.statmethods.net/advstats/cluster.html
http://www.r-tutor.com/gpu-computing/clustering/hierarchical-cluster-analysis
http://gastonsanchez.wordpress.com/2012/10/03/7-ways-to-plot-dendrograms-in-r/更多奇特的方法见这里： http: //cran.r-project.org/ web/views/Cluster.html
这里有一些例子：
d_dist <- dist(as.matrix(d)) # find distance matrix
plot(hclust(d_dist)) # apply hirarchical clustering and plot
# a Bayesian clustering method, good for high-dimension data, more details:
# http://vahid.probstat.ca/paper/2012-bclust.pdf
install.packages("bclust")
library(bclust)
x <- as.matrix(d)
d.bclus <- bclust(x, transformed.par = c(0, -50, log(16), 0, 0, 0))
viplot(imp(d.bclus)$var); plot(d.bclus); ditplot(d.bclus)
dptplot(d.bclus, scale = 20, horizbar.plot = TRUE,varimp = imp(d.bclus)$var, horizbar.distance = 0, dendrogram.lwd = 2)
# I just include the dendrogram here
对于高维数据，还有一个pvclust库，它通过多尺度引导重采样计算层次聚类的 p 值。这是文档中的示例（不会像我的示例那样处理低维数据）：
library(pvclust)
library(MASS)
data(Boston)
boston.pv <- pvclust(Boston)
plot(boston.pv)
这些有帮助吗？
