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*里面的代码
http://*.com/questions/9873840/cant-get-scipy-hierarchical-clustering-to-work
"""
import sklearn.datasets as datasets
import scipy.cluster.hierarchy as hcluster
import numpy.random as random
import numpy as np
import numpy.core.fromnumeric
import time
import matplotlib.pyplot as plt
def irisSample():
iris=datasets.load_iris()
irisdata=iris.data
result=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]+=10
result=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]+=10
timeCheckin=time.clock()
result=hcluster.fclusterdata(X,criterion='maxclust',t=2)
timeCost=time.clock()-timeCheckin
mapPerformance[sampleNum]=timeCost
return mapPerformance
def 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]+=10
timeCheckin=time.clock()
result=hcluster.fclusterdata(X,criterion='maxclust',t=2)
timeCost=time.clock()-timeCheckin
mapPerformance[dim]=timeCost
return mapPerformance
def 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，