问题

作为R中的新手,我不太确定如何选择最佳数量的集群来进行k均值分析.在绘制以下数据的子集之后,多少个集群将是适当的?如何执行集群树状图分析?

n = 1000
kk = 10    
x1 = runif(kk)
y1 = runif(kk)
z1 = runif(kk)    
x4 = sample(x1,length(x1))
y4 = sample(y1,length(y1)) 
randObs <- function()
{
  ix = sample( 1:length(x4), 1 )
  iy = sample( 1:length(y4), 1 )
  rx = rnorm( 1, x4[ix], runif(1)/8 )
  ry = rnorm( 1, y4[ix], runif(1)/8 )
  return( c(rx,ry) )
}  
x = c()
y = c()
for ( k in 1:n )
{
  rPair  =  randObs()
  x  =  c( x, rPair[1] )
  y  =  c( y, rPair[2] )
}
z <- rnorm(n)
d <- data.frame( x, y, z )


解决方法

如果你的问题是,如何确定多少个集群适合我的数据的kmeans分析?,这里有一些选项.关于确定群集数量的维基百科文章对这些方法中的一些有很好的回顾.

首先,一些可重现的数据(Q中的数据对我不清楚):

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)

输入图片说明here

一个.在平方误差平方和(SSE)谱图中查找弯曲或弯头.请参见 http://www.statmethods.net/advstats/cluster.html &amp; http://www.mattpeeples.net/kmeans.html 了解详情.在结果图中肘的位置表明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,这个方法会指示4个群集: 在这里输入图片说明

两个.您可以使用fpc软件包中的 pamk 函数在medoids周围进行分区以估计簇数.

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))

输入图片描述here enter image description here

# 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

. Calinsky标准:另一种诊断多少个簇适合数据的方法.在这种情况下,我们尝试1到10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!

输入图片描述here

.根据用于参数化高斯混合模型的分级聚类初始化的期望最大化的贝叶斯信息准则确定聚类的最优模型和数量

# 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)

输入图片描述here enter image description here enter image description here

.关联性传播(AP)群集,请参见 http://dx.doi.org/10.1126/science.11​​36800 < / p>

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)

在这里输入图片说明 在这里输入图片说明

.用于估计群集数的间隙统计.另请参见一些代码,以获得良好的图形输出.尝试2-10个群集:

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

以下是Edwin Chen执行差距统计的结果: 在这里输入图片说明

.您还可能发现使用聚类图来浏览数据以显示聚类分配很有用,请参阅 http://www.r-statistics.com/2010/06/clustergram-visualization-and-diagnostics-for-cluster-analysis-r-code/ 了解详情.

. NbClust软件包提供了30个索引,用于确定数据集中的集群数.

library(NbClust)
nb <- NbClust(d, diss="NULL", distance = "euclidean", 
        min.nc=2, max.nc=15, method = "kmeans", 
        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!

在这里输入图片描述

如果您的问题是如何产生一个树形图以显示我的群集分析结果,那么您应该从这些开始: http://www.statmethods.net/advstats/cluster.html http://www.r-tutor.com/gpu-computing/clustering/hierarchical-聚类分析 http://gastonsanchez.wordpress.com/2012/10 / 03/7-ways-to-plot-dendrograms-in-r / 在这里看到更多奇异的方法: http://cran.r-project.org/web/views/Cluster.html

以下是几个例子:

d_dist <- dist(as.matrix(d))   # find distance matrix 
plot(hclust(d_dist))           # apply hirarchical clustering and plot

在这里输入图片说明

# 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

输入图片描述here

对于高维数据,还有 pvclust 库,它通过多尺度引导重采样计算层次聚类的p值.这里是文档的例子(不工作在这样的低维数据,如我的例子):

library(pvclust)
library(MASS)
data(Boston)
boston.pv <- pvclust(Boston)
plot(boston.pv)

输入图片描述here

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