聚类算法:DBSCAN

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：

    (1)核心点：该点在邻域内的密度超过给定的阀值MinPs。

   (2)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。

   (3)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。

根据该算法，实现如下代码：

# scoding=utf-8import pylab as plfrom 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 = 10surroundPoints = 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 = 5corePointIdx = [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 = 3finalGroup = 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()

因为DBSCAN使用簇的基于密度的定义，因此它是相对抗噪音的，并且能处理任意形状和大小的簇。但是如果簇的密度变化很大，例如ABCD四个簇，AB的密度大大大于CD，而且AB附近噪音的密度与簇CD的密度相当，这是当MinPs较大时，无法识别簇CD，簇CD和AB附近的噪音都被认为是噪音；当MinPs较小时，能识别簇CD，但AB跟其周围的噪音被识别为一个簇。这个问题可以基于共享最近邻(SNN)的聚类结局。