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# K-Means Clustering in Python

## Introduction

K-means clustering a data mining technique that divides a set of samples into groups based on similarity across features. Originally intended for signal processing applications, the algorithm has found use in a variety of other domains, especially in geospatial analysis.

## K-Means Clustering Algorithm

from __future__ import division import random # K-Means Clustering def distance(a, b): """ Euclidean distance """ return sum([(a[i]-b[i])**2 for i in range(len(a))])**0.5 class Point: """ Point object has coordinates (x,y,z,...) and an optional label """ def __init__(self, coordinates, label=-1): self.coord = coordinates self.label = label def dist(self, other): return distance(self.coord, other.coord) def __str__(self): return 'Point(%s,%s)'%(self.coord, self.label) class Cluster: """ Cluster object has a list of points and a calculated centroid (point) """ def __init__(self, points): self.points = points self.center = self._calcCenter() def update(self, points): self.points = points self.center = self._calcCenter() def _calcCenter(self): x = [i for i in self.points[0].coord] for p in self.points[1:]: for j in range(len(p.coord)): x[j] += p.coord[j] M = len(self.points) return Point([xx/M for xx in x], label='center') def kmeans(points, k, max_iter=1000, min_shift_frac=0.01): # initialize clusters = [] for p in random.sample(points, k): clusters.append(Cluster([p])) # iterate this_iter = 0 while this_iter < max_iter: this_iter += 1 lists = [[] for c in range(k)] shifts = 0 for p in points: dx = min([(p.dist(clusters[h].center), h) for h in range(k)])[1] if dx != p.label: shifts += 1 p.label = dx lists[dx].append(p) for i in range(k): clusters[i].update(lists[i]) # stopping condition: if %points changing clusters below thresh... if shifts/len(points) < min_shift_frac: break return (clusters, this_iter) if __name__ == '__main__': import pylab, numpy points = [] for i in range(1000): points.append(Point(numpy.random.random(2))) k = 8 clusters, num_iters = kmeans(points, k) x = [clusters[i].center.coord[0] for i in range(k)] y = [clusters[i].center.coord[1] for i in range(k)] pylab.plot(x, y, 'ko') for cluster in clusters: x = [p.coord[0] for p in cluster.points] y = [p.coord[1] for p in cluster.points] pylab.plot(x, y, '+') pylab.show()

## K-Means Example Output

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