问题描述
作为R的新手，我不太确定如何选择最佳数目的聚类来进行k均值分析.在绘制了以下数据的子集之后，多少个簇才是合适的?如何执行聚类Dendro分析?
Being a newbie in R, I'm not very sure how to choose the best number of clusters to do a k-means analysis. After plotting a subset of below data, how many clusters will be appropriate? How can I perform cluster dendro analysis?
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 )
推荐答案
如果您的问题是how can I determine how many clusters are appropriate for a kmeans analysis of my data?，那么这里有一些选择. 维基百科文章中有关确定簇数的文章对其中一些方法进行了很好的回顾.
If your question is how can I determine how many clusters are appropriate for a kmeans analysis of my data?, then here are some options. The wikipedia article on determining numbers of clusters has a good review of some of these methods.
首先，一些可重现的数据(Q中的数据对我来说尚不清楚):
First, some reproducible data (the data in the Q are... unclear to me):
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)
一个.在平方误差和(SSE)碎石图的总和中查找弯曲或弯头.参见 http://www.statmethods.net/advstats/cluster.html & http://www.mattpeeples.net/kmeans.html 了解更多.弯头在结果图中的位置表明适合kmeans的簇数:
One. Look for a bend or elbow in the sum of squared error (SSE) scree plot. See http://www.statmethods.net/advstats/cluster.html & http://www.mattpeeples.net/kmeans.html for more. The location of the elbow in the resulting plot suggests a suitable number of clusters for the kmeans:
mydata <- d
wss <- (nrow(mydata)-1)*sum(apply(mydata,2,var))
for (i in 2:15) wss[i] <- sum(kmeans(mydata,
centers=i)$withinss)
plot(1:15, wss, type="b", xlab="Number of Clusters",
ylab="Within groups sum of squares")
我们可以得出结论，此方法将指示4个聚类:
We might conclude that 4 clusters would be indicated by this method:
两个.您可以使用fpc软件包中的pamk函数对类固醇进行分区以估计簇数.
Two. You can do partitioning around medoids to estimate the number of clusters using the pamk function in the fpc package.
library(fpc)
pamk.best <- pamk(d)
cat("number of clusters estimated by optimum average silhouette width:", pamk.best$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
三个. Calinsky准则:诊断有多少簇适合数据的另一种方法.在这种情况下，我们尝试1至10组.
Three. Calinsky criterion: Another approach to diagnosing how many clusters suit the data. In this case we try 1 to 10 groups.
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$results[2,]))
cat("Calinski criterion optimal number of clusters:", calinski.best, "\n")
# 5 clusters!
四个.根据贝叶斯信息准则确定期望模型的最佳模型和数量，并通过分层聚类对参数化的高斯混合模型进行初始化
Four. Determine the optimal model and number of clusters according to the Bayesian Information Criterion for expectation-maximization, initialized by hierarchical clustering for parameterized Gaussian mixture models
# See http://www.jstatsoft.org/v18/i06/paper
# http://www.stat.washington.edu/research/reports/2006/tr504.pdf
#
library(mclust)
# Run the function to see how many clusters
# it finds to be optimal, set it to search for
# at least 1 model and up 20.
d_clust <- Mclust(as.matrix(d), G=1:20)
m.best <- dim(d_clust$z)[2]
cat("model-based optimal number of clusters:", m.best, "\n")
# 4 clusters
plot(d_clust)
五个.相似性传播(AP)群集，请参见 http://dx.doi.org/10.1126/science.1136800
Five. Affinity propagation (AP) clustering, see 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)
六个.估计簇数的差距统计.另请参见一些代码，以提供精美的图形输出.在这里尝试2-10个群集:
Six. Gap Statistic for Estimating the Number of Clusters. See also some code for a nice graphical output. Trying 2-10 clusters here:
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实施差距统计的输出:
Here's the output from Edwin Chen's implementation of the gap statistic:
七个.您可能还会发现使用聚类图浏览数据以可视化聚类分配很有用，请参阅 http://www.r-statistics.com/2010/06/clustergram-visualization-and-diagnostics-for-cluster-analysis-r-code/有关更多详细信息.
Seven. You may also find it useful to explore your data with clustergrams to visualize cluster assignment, see http://www.r-statistics.com/2010/06/clustergram-visualization-and-diagnostics-for-cluster-analysis-r-code/ for more details.
八. NbClust软件包提供了30个索引来确定其中的簇数数据集.
Eight. The NbClust package provides 30 indices to determine the number of clusters in a dataset.
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!
如果您的问题是how can I produce a dendrogram to visualize the results of my cluster analysis，则应从以下内容开始: 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/并在此处查看更多奇特的方法: http://cran.r-project.org/web/views/Cluster.html
If your question is how can I produce a dendrogram to visualize the results of my cluster analysis, then you should start with these:http://www.statmethods.net/advstats/cluster.htmlhttp://www.r-tutor.com/gpu-computing/clustering/hierarchical-cluster-analysishttp://gastonsanchez.wordpress.com/2012/10/03/7-ways-to-plot-dendrograms-in-r/ And see here for more exotic methods: http://cran.r-project.org/web/views/Cluster.html
以下是一些示例:
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
对于高维数据来说，也是pvclust库，该库通过多尺度自举重采样为分层聚类计算p值.这是文档中的示例(不会像我的示例中那样处理低维数据):
Also for high-dimension data is the pvclust library which calculates p-values for hierarchical clustering via multiscale bootstrap resampling. Here's the example from the documentation (wont work on such low dimensional data as in my example):
library(pvclust)
library(MASS)
data(Boston)
boston.pv <- pvclust(Boston)
plot(boston.pv)
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