Scipy.cluster.hierarchy.fclusterdata + 距离度量

Question

1) 我正在使用scipy的hcluster模块。

所以我控制的变量是阈值变量。如何知道每个阈值下我的性能？即在Kmeans中，这种性能将是所有点到它们的质心的总和。当然，由于更多的簇=一般距离更小，因此必须进行调整。

对于这个问题，hcluster有没有可以观察的方法呢？

2) 我意识到fclusterdata有大量可用的度量标准。我基于关键词的tf-idf对文本文档进行聚类。问题是，有些文档比其他文档长，而我认为余弦是解决长度问题的好方法，因为如果内容保持一致，文档越长，它在n维场中的“方向”应该保持不变。还有其他人能建议的方法吗？我如何评估？

谢谢

- disappearedng

Answer 1

对于聚类中的x，可以像K-means一样计算|x-簇中心|的平均距离。以下是暴力计算方法。（它必须是scipy.cluster或scipy.spatial.distance的内置函数，但我也找不到。）

关于你的问题2，我不清楚。如果有好的层次聚类教程链接，请分享。

#!/usr/bin/env python
""" cluster cities: pdist linkage fcluster plot
    util: clusters() avdist()
"""

from __future__ import division
import sys
import numpy as np
import scipy.cluster.hierarchy as hier  # $scipy/cluster/hierarchy.py
import scipy.spatial.distance as dist
import pylab as pl
from citiesin import citiesin  # 1000 US cities

__date__ = "27may 2010 denis"

def clusterlists(T):
    """ T = hier.fcluster( Z, t ) e.g. [a b a b a c]
        -> [ [0 2 4] [1 3] [5] ] sorted by len
    """
    clists = [ [] for j in range( max(T) + 1 )]
    for j, c in enumerate(T):
        clists[c].append( j )
    clists.sort( key=len, reverse=True )
    return clists[:-1]  # clip the []

def avdist( X, to=None ):
    """ av dist X vecs to "to", None: mean(X) """
    if to is None:
        to = np.mean( X, axis=0 )
    return np.mean( dist.cdist( X, [to] ))

#...............................................................................
Ndata = 100
method = "average"
t = 0
crit = "maxclust"
    # 'maxclust': Finds a minimum threshold `r` so that the cophenetic distance
    # between any two original observations in the same flat cluster
    # is no more than `r` and no more than `t` flat clusters are formed.
    # but t affects cluster sizes only weakly ?
    # t 25: [10, 9, 8, 7, 6
    # t 20: [12, 11, 10, 9, 7
plot = 0
seed = 1

exec "\n".join( sys.argv[1:] )  # Ndata= t= ...
np.random.seed(seed)
np.set_printoptions( 2, threshold=100, edgeitems=10, suppress=True )  # .2f
me = __file__.split('/') [-1]

    # biggest US cities --
cities = np.array( citiesin( n=Ndata )[0] )  # N,2

if t == 0:  t = Ndata // 4

#...............................................................................
print "# %s  Ndata=%d  t=%d  method=%s  crit=%s " % (me, Ndata, t, method, crit)

Y = dist.pdist( cities )  # n*(n-1) / 2
Z = hier.linkage( Y, method )  # n-1
T = hier.fcluster( Z, t, criterion=crit )  # n

clusters = clusterlists(T)
print "cluster sizes:", map( len, clusters )
print "# average distance to centre in the biggest clusters:"
for c in clusters:
    if len(c) < len(clusters[0]) // 3:  break
    cit = cities[c].T
    print "%.2g %s" % (avdist(cit.T), cit)
    if plot:
        pl.plot( cit[0], cit[1] )

if plot:
    pl.title( "scipy.cluster.hierarchy of %d US cities, %s t=%d" % (
        Ndata, crit, t) )
    pl.grid(False)
    if plot >= 2:
        pl.savefig( "cities-%d-%d.png" % (Ndata, t), dpi=80 )
    pl.show()

- denis