python中做层次聚类，使用scipy.cluster.hierarchy.fclusterdata方法

python机器学习包里面的cluster提供了很多聚类算法，其中ward_tree实现了凝聚层次聚类算法。

但是没有看明白ward_tree的返回值代表了什么含义，遂决定寻找别的实现方式。

经过查找，发现scipy.cluster.hierarchy.fclusterdata能够实现层次聚类。有关这个方法的介绍在：http://docs.scipy.org/doc/scipy/reference/generated/scipy.cluster.hierarchy.fclusterdata.html

以下是具体的python代码

#coding=utf8"""# Author: waleking# Created Time : 四  7/26 17:05:07 2012  Last Modified: 二  7/31 17:56:26 2012# File Name: hierachical.py# Description:使用sklearn的层次聚类方法，具体的是ward_tree方法测试数据采用iris数据，sklearn.datasets.load_iris()但是发现sklearn.cluster.ward_tree方法没有看懂,实验stackoverflow里面的代码http://stackoverflow.com/questions/9873840/cant-get-scipy-hierarchical-clustering-to-work"""import sklearn.datasets as datasetsimport scipy.cluster.hierarchy as hclusterimport numpy.random as randomimport numpy as npimport numpy.core.fromnumericimport timeimport matplotlib.pyplot as pltdef irisSample():iris=datasets.load_iris()irisdata=iris.dataresult=hcluster.fclusterdata(irisdata, criterion='maxclust',t=3)print("result is %s" % result)def gaussianSample():timeCheckin=time.clock()X=random.randn(100,100)X[:50,:100]+=10result=hcluster.fclusterdata(X, criterion='maxclust',t=2)print("hierachical clustering on sample with shape(%d,%d) cost %s seconds " % (np.shape(X)[0],np.shape(X)[1],time.clock()-timeCheckin))print("result is %s" % result)clusterA=[label for label in result if(label==1)]clusterB=[label for label in result if(label==2)]print("There are %d samples in cluster 1" %(len(clusterA)))print("ClusterA is %s" % clusterA)print("There are %d samples in cluster 2" %(len(clusterB)))print("ClusterB is %s" % clusterB)def testPerformanceByNum(start,end,increment):"""测试样本数对性能的影响"""mapPerformance=dict()for sampleNum in range(start,end,increment):X=random.randn(sampleNum,100)X[:50,:100]+=10timeCheckin=time.clock()result=hcluster.fclusterdata(X,criterion='maxclust',t=2)timeCost=time.clock()-timeCheckinmapPerformance[sampleNum]=timeCostreturn mapPerformancedef testPerformanceByDim(start,end,increment):"""测试维度对性能的影响"""mapPerformance=dict()for dim in range(start,end,increment):X=random.randn(100,dim)X[:50,:dim]+=10timeCheckin=time.clock()result=hcluster.fclusterdata(X,criterion='maxclust',t=2)timeCost=time.clock()-timeCheckinmapPerformance[dim]=timeCostreturn mapPerformancedef showPerformance(mapPerformance):"""画图，展现性能"""xAxisData=numpy.core.fromnumeric.sort(mapPerformance.keys())yAxisData=[mapPerformance[key] for key in xAxisData]plt.plot(xAxisData,yAxisData,'*-')plt.show()#irisSample()#gaussianSample()mapPerformance=testPerformanceByNum(100,3100,100)showPerformance(mapPerformance)mapPerformance=testPerformanceByDim(100,10100,100)showPerformance(mapPerformance)

我们测试了100维的数据的层次聚类，随机生成100个到3000个服从高斯分布的数据，让50个点的均值不同于其余的点。

测试的性能图如下：

我们又测试了固定样本数：100个样本，服从高斯分布，其中50个的均值不同于另外的50个。我们实验了维度从100变化到10000，得到性能图如下：

结论：层次聚类的时间复杂度是O(m^2 n)，和Andrew Ng在机器学习课程中的符号相同，其中样本数是m，维度是n，