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    <p>Below is a little test bench to see how fast <a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.spatial.cKDTree.html" rel="nofollow">scipy.spatial.cKDTree</a> is on your data, and to get a rough idea of how the distances between nearby points scatter.</p> <p>A nice way to run K-cluster for various K is to build an MST of nearest pairs, and remove the K-1 longest; see <a href="http://www.cs.princeton.edu/~wayne/kleinberg-tardos/04greedy-2x2.pdf" rel="nofollow">Wayne, Greedy Algorithms</a> .</p> <p>Visualizing the clusters would be fun -- project to 2d with PCA ?</p> <p>(Just curious, is your K 10, 100, 1000 ?)</p> <p>Added 17 Dec: real runtimes: 100000 x 5 10 sec, 500000 x 5 60sec</p> <pre><code>#!/usr/bin/env python # time scipy.spatial.cKDTree build, query from __future__ import division import random import sys import time import numpy as np from scipy.spatial import cKDTree as KDTree # http://docs.scipy.org/doc/scipy/reference/spatial.html # $scipy/spatial/kdtree.py is slow but clean, 0.9 has cython __date__ = "2010-12-17 dec denis" def clumpiness( X, nbin=10 ): """ how clumpy is X ? histogramdd av, max """ # effect on kdtree time ? not much N, dim = X.shape histo = np.histogramdd( X, nbin )[0] .astype(int) # 10^dim n0 = histo.size - histo.astype(bool).sum() # uniform: 1/e^lambda print "clumpiness: %d of %d^%d data bins are empty av %.2g max %d" % ( n0, nbin, dim, histo.mean(), histo.max()) #............................................................................... N = 100000 nask = 0 # 0: ask all N dim = 5 rnormal = .9 # KDtree params -- nnear = 2 # k=nnear+1, self leafsize = 10 eps = 1 # approximate nearest, dist &lt;= (1 + eps) * true nearest seed = 1 exec "\n".join( sys.argv[1:] ) # run this.py N= ... np.random.seed(seed) np.set_printoptions( 2, threshold=200, suppress=True ) # .2f nask = nask or N print "\nkdtree: dim=%d N=%d nask=%d nnear=%d rnormal=%.2g leafsize=%d eps=%.2g" % ( dim, N, nask, nnear, rnormal, leafsize, eps) if rnormal &gt; 0: # normal point cloud, .9 =&gt; many near 1 1 1 axis cov = rnormal * np.ones((dim,dim)) + (1 - rnormal) * np.eye(dim) data = np.abs( np.random.multivariate_normal( np.zeros(dim), cov, N )) % 1 # % 1: wrap to unit cube else: data = np.random.uniform( size=(N,dim) ) clumpiness(data) ask = data if nask == N else random.sample( data, sample ) t = time.time() #............................................................................... datatree = KDTree( data, leafsize=leafsize ) # build the tree print "%.1f sec to build KDtree of %d points" % (time.time() - t, N) t = time.time() distances, ix = datatree.query( ask, k=nnear+1, eps=eps ) print "%.1f sec to query %d points" % (time.time() - t, nask) distances = distances[:,1:] # [:,0] is all 0, point to itself avdist = distances.mean( axis=0 ) maxdist = distances.max( axis=0 ) print "distances to %d nearest: av" % nnear, avdist, "max", maxdist # kdtree: dim=5 N=100000 nask=100000 nnear=2 rnormal=0.9 leafsize=10 eps=1 # clumpiness: 42847 of 10^5 data bins are empty av 1 max 21 # 0.4 sec to build KDtree of 100000 points # 10.1 sec to query 100000 points # distances to 2 nearest: av [ 0.07 0.08] max [ 0.15 0.18] # kdtree: dim=5 N=500000 nask=500000 nnear=2 rnormal=0.9 leafsize=10 eps=1 # clumpiness: 2562 of 10^5 data bins are empty av 5 max 80 # 2.5 sec to build KDtree of 500000 points # 60.1 sec to query 500000 points # distances to 2 nearest: av [ 0.05 0.06] max [ 0.13 0.13] # run: 17 Dec 2010 15:23 mac 10.4.11 ppc </code></pre>
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