DBSCAN：是一种简单的，基于密度的聚类算法。本次实现中，DBSCAN使用了基于中心的方法。在基于中心的方法中，每个数据点的密度通过对以该点为中心以边长为2*EPs的网格(邻域)内的其他数据点的个数来度量。根据数据点的密度分为三类点:

核心点：该点在邻域内的密度超过给定的阀值MinPs。
边界点：该点不是核心点，但是其邻域内包含至少一个核心点。
噪音点：不是核心点，也不是边界点。

有了以上对数据点的划分，聚合可以这样进行：各个核心点与其邻域内的所有核心点放在同一个簇中，把边界点跟其邻域内的某个核心点放在同一个簇中。

# scoding=utf-8
import pylab as pl
from collections import defaultdict,Counter
points = [[int(eachpoint.split("#")[0]), int(eachpoint.split("#")[1])] for eachpoint in open("points","r")]
# 计算每个数据点相邻的数据点，邻域定义为以该点为中心以边长为2*EPs的网格
Eps = 10
surroundPoints = defaultdict(list)
for idx1,point1 in enumerate(points):
 for idx2,point2 in enumerate(points):
 if (idx1 < idx2):
 if(abs(point1[0]-point2[0])<=Eps and abs(point1[1]-point2[1])<=Eps):
 surroundPoints[idx1].append(idx2)
 surroundPoints[idx2].append(idx1)
# 定义邻域内相邻的数据点的个数大于4的为核心点
MinPts = 5
corePointIdx = [pointIdx for pointIdx,surPointIdxs in surroundPoints.iteritems() if len(surPointIdxs)>=MinPts]
# 邻域内包含某个核心点的非核心点，定义为边界点
borderPointIdx = []
for pointIdx,surPointIdxs in surroundPoints.iteritems():
 if (pointIdx not in corePointIdx):
 for onesurPointIdx in surPointIdxs:
 if onesurPointIdx in corePointIdx:
 borderPointIdx.append(pointIdx)
 break
# 噪音点既不是边界点也不是核心点
noisePointIdx = [pointIdx for pointIdx in range(len(points)) if pointIdx not in corePointIdx and pointIdx not in borderPointIdx]
corePoint = [points[pointIdx] for pointIdx in corePointIdx] 
borderPoint = [points[pointIdx] for pointIdx in borderPointIdx]
noisePoint = [points[pointIdx] for pointIdx in noisePointIdx]
# pl.plot([eachpoint[0] for eachpoint in corePoint], [eachpoint[1] for eachpoint in corePoint], 'or')
# pl.plot([eachpoint[0] for eachpoint in borderPoint], [eachpoint[1] for eachpoint in borderPoint], 'oy')
# pl.plot([eachpoint[0] for eachpoint in noisePoint], [eachpoint[1] for eachpoint in noisePoint], 'ok')
groups = [idx for idx in range(len(points))]
# 各个核心点与其邻域内的所有核心点放在同一个簇中
for pointidx,surroundIdxs in surroundPoints.iteritems():
 for oneSurroundIdx in surroundIdxs:
 if (pointidx in corePointIdx and oneSurroundIdx in corePointIdx and pointidx < oneSurroundIdx):
 for idx in range(len(groups)):
 if groups[idx] == groups[oneSurroundIdx]:
 groups[idx] = groups[pointidx]
# 边界点跟其邻域内的某个核心点放在同一个簇中
for pointidx,surroundIdxs in surroundPoints.iteritems():
 for oneSurroundIdx in surroundIdxs:
 if (pointidx in borderPointIdx and oneSurroundIdx in corePointIdx):
 groups[pointidx] = groups[oneSurroundIdx]
 break
# 取簇规模最大的5个簇
wantGroupNum = 3
finalGroup = Counter(groups).most_common(3)
finalGroup = [onecount[0] for onecount in finalGroup]
group1 = [points[idx] for idx in xrange(len(points)) if groups[idx]==finalGroup[0]]
group2 = [points[idx] for idx in xrange(len(points)) if groups[idx]==finalGroup[1]]
group3 = [points[idx] for idx in xrange(len(points)) if groups[idx]==finalGroup[2]]
pl.plot([eachpoint[0] for eachpoint in group1], [eachpoint[1] for eachpoint in group1], 'or')
pl.plot([eachpoint[0] for eachpoint in group2], [eachpoint[1] for eachpoint in group2], 'oy')
pl.plot([eachpoint[0] for eachpoint in group3], [eachpoint[1] for eachpoint in group3], 'og')
# 打印噪音点，黑色
pl.plot([eachpoint[0] for eachpoint in noisePoint], [eachpoint[1] for eachpoint in noisePoint], 'ok') 
pl.show()

运行效果截图如下：

希望本文所述对大家Python程序设计有所帮助。