Python基于聚類算法實現密度聚類(DBSCAN)計算【測試可用】

2020-01-04 13:41:56

字體：大中小

來源：轉載

供稿：網友

本文實例講述了Python基于聚類算法實現密度聚類(DBSCAN)計算。分享給大家供大家參考，具體如下：

算法思想

基于密度的聚類算法從樣本密度的角度考察樣本之間的可連接性，并基于可連接樣本不斷擴展聚類簇得到最終結果。

幾個必要概念：

ε-鄰域：對于樣本集中的xj, 它的ε-鄰域為樣本集中與它距離小于ε的樣本所構成的集合。
核心對象：若xj的ε-鄰域中至少包含MinPts個樣本，則xj為一個核心對象。
密度直達：若xj位于xi的ε-鄰域中，且xi為核心對象，則xj由xi密度直達。
密度可達：若樣本序列p1, p2, ……, pn。pi+1由pi密度直達，則p1由pn密度可達。

大致思想如下：

1. 初始化核心對象集合T為空，遍歷一遍樣本集D中所有的樣本，計算每個樣本點的ε-鄰域中包含樣本的個數，如果個數大于等于MinPts，則將該樣本點加入到核心對象集合中。初始化聚類簇數k = 0，初始化未訪問樣本集和為P = D。

2. 當T集合中存在樣本時執行如下步驟：

2.1記錄當前未訪問集合P_old = P
2.2從T中隨機選一個核心對象o,初始化一個隊列Q = [o]
2.3P = P-o(從T中刪除o)
2.4當Q中存在樣本時執行：
2.4.1取出隊列中的首個樣本q
2.4.2計算q的ε-鄰域中包含樣本的個數，如果大于等于MinPts，則令S為q的ε-鄰域與P的交集，
Q = Q+S, P = P-S
2.5 k = k + 1,生成聚類簇為Ck = P_old - P
2.6 T = T - Ck

3. 劃分為C= {C1, C2, ……, Ck}

Python代碼實現

#-*- coding:utf-8 -*-import mathimport numpy as npimport pylab as pl #數據集：每三個是一組分別是西瓜的編號，密度，含糖量data = """1,0.697,0.46,2,0.774,0.376,3,0.634,0.264,4,0.608,0.318,5,0.556,0.215,6,0.403,0.237,7,0.481,0.149,8,0.437,0.211,9,0.666,0.091,10,0.243,0.267,11,0.245,0.057,12,0.343,0.099,13,0.639,0.161,14,0.657,0.198,15,0.36,0.37,16,0.593,0.042,17,0.719,0.103,18,0.359,0.188,19,0.339,0.241,20,0.282,0.257,21,0.748,0.232,22,0.714,0.346,23,0.483,0.312,24,0.478,0.437,25,0.525,0.369,26,0.751,0.489,27,0.532,0.472,28,0.473,0.376,29,0.725,0.445,30,0.446,0.459"""#數據處理 dataset是30個樣本（密度，含糖量）的列表a = data.split(',')dataset = [(float(a[i]), float(a[i+1])) for i in range(1, len(a)-1, 3)]#計算歐幾里得距離,a,b分別為兩個元組def dist(a, b):  return math.sqrt(math.pow(a[0]-b[0], 2)+math.pow(a[1]-b[1], 2))#算法模型def DBSCAN(D, e, Minpts):  #初始化核心對象集合T,聚類個數k,聚類集合C, 未訪問集合P,  T = set(); k = 0; C = []; P = set(D)  for d in D:    if len([ i for i in D if dist(d, i) <= e]) >= Minpts:      T.add(d)  #開始聚類  while len(T):    P_old = P    o = list(T)[np.random.randint(0, len(T))]    P = P - set(o)    Q = []; Q.append(o)    while len(Q):      q = Q[0]      Nq = [i for i in D if dist(q, i) <= e]      if len(Nq) >= Minpts:        S = P & set(Nq)        Q += (list(S))        P = P - S      Q.remove(q)    k += 1    Ck = list(P_old - P)    T = T - set(Ck)    C.append(Ck)  return C#畫圖def draw(C):  colValue = ['r', 'y', 'g', 'b', 'c', 'k', 'm']  for i in range(len(C)):    coo_X = []  #x坐標列表    coo_Y = []  #y坐標列表    for j in range(len(C[i])):      coo_X.append(C[i][j][0])      coo_Y.append(C[i][j][1])    pl.scatter(coo_X, coo_Y, marker='x', color=colValue[i%len(colValue)], label=i)  pl.legend(loc='upper right')  pl.show()C = DBSCAN(dataset, 0.11, 5)draw(C)

本機測試運行結果圖：

Python,聚類算法,密度聚類,DBSCAN