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Python聚類算法之DBSACN實(shí)例分析

更新時(shí)間：2015年11月20日 11:23:06 作者：intergret

這篇文章主要介紹了Python聚類算法之DBSACN,結(jié)合實(shí)例形式詳細(xì)分析了DBSACN算法的原理與具體實(shí)現(xiàn)技巧,具有一定參考借鑒價(jià)值,需要的朋友可以參考下

本文實(shí)例講述了Python聚類算法之DBSACN。分享給大家供大家參考，具體如下：

DBSCAN：是一種簡單的，基于密度的聚類算法。本次實(shí)現(xiàn)中，DBSCAN使用了基于中心的方法。在基于中心的方法中，每個(gè)數(shù)據(jù)點(diǎn)的密度通過對(duì)以該點(diǎn)為中心以邊長為2*EPs的網(wǎng)格(鄰域)內(nèi)的其他數(shù)據(jù)點(diǎn)的個(gè)數(shù)來度量。根據(jù)數(shù)據(jù)點(diǎn)的密度分為三類點(diǎn):

核心點(diǎn)：該點(diǎn)在鄰域內(nèi)的密度超過給定的閥值MinPs。
邊界點(diǎn)：該點(diǎn)不是核心點(diǎn)，但是其鄰域內(nèi)包含至少一個(gè)核心點(diǎn)。
噪音點(diǎn)：不是核心點(diǎn)，也不是邊界點(diǎn)。

有了以上對(duì)數(shù)據(jù)點(diǎn)的劃分，聚合可以這樣進(jìn)行：各個(gè)核心點(diǎn)與其鄰域內(nèi)的所有核心點(diǎn)放在同一個(gè)簇中，把邊界點(diǎn)跟其鄰域內(nèi)的某個(gè)核心點(diǎn)放在同一個(gè)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")]
# 計(jì)算每個(gè)數(shù)據(jù)點(diǎn)相鄰的數(shù)據(jù)點(diǎn)，鄰域定義為以該點(diǎn)為中心以邊長為2*EPs的網(wǎng)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)
# 定義鄰域內(nèi)相鄰的數(shù)據(jù)點(diǎn)的個(gè)數(shù)大于4的為核心點(diǎn)
MinPts = 5
corePointIdx = [pointIdx for pointIdx,surPointIdxs in surroundPoints.iteritems() if len(surPointIdxs)>=MinPts]
# 鄰域內(nèi)包含某個(gè)核心點(diǎn)的非核心點(diǎn)，定義為邊界點(diǎn)
borderPointIdx = []
for pointIdx,surPointIdxs in surroundPoints.iteritems():
  if (pointIdx not in corePointIdx):
    for onesurPointIdx in surPointIdxs:
      if onesurPointIdx in corePointIdx:
        borderPointIdx.append(pointIdx)
        break
# 噪音點(diǎn)既不是邊界點(diǎn)也不是核心點(diǎn)
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))]
# 各個(gè)核心點(diǎn)與其鄰域內(nèi)的所有核心點(diǎn)放在同一個(gè)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]
# 邊界點(diǎn)跟其鄰域內(nèi)的某個(gè)核心點(diǎn)放在同一個(gè)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
# 取簇規(guī)模最大的5個(gè)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')
# 打印噪音點(diǎn)，黑色
pl.plot([eachpoint[0] for eachpoint in noisePoint], [eachpoint[1] for eachpoint in noisePoint], 'ok')  
pl.show()

運(yùn)行效果截圖如下：