DBSCAN具有噪声的基于密度的聚类方法
- 简介
- 聚类:将原始数据分类 ( 数据集 -> 聚类算法 -> 数据分组 )
- 目的:希望将数据根据特征的密度找相似性,分为指定或者若干数据组
- 使用场景:
- 简单的如将同颜色的球分类,或将一个班的成绩分类为文科科目好的学生和理科科目好的学生
- 复杂的,图像特征识别等
- 概念解释:
- 主要有两个参数进行调节dist,minpoints。dist指点与点之间的距离,表示你想把密度多大的点聚合在一起。minpoints指符合上述密度的点至少有多少个。图片来源((五十)通俗易懂理解——DBSCAN聚类算法 - 知乎 (zhihu.com))
-
密度可达:除N点外都可达,密度直通:ABC
- 特点
- 本算法是无监督学习
-
- 代码实现和解释:
- 算法代码
#-*- coding:utf-8 -*- import math import numpy as np import pylab as pl #数据集:每三个是一组分别是西瓜的编号,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""" #数据处理 dataset是30个样本(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)] #计算欧几里得距离,a,b分别为两个元组 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): #初始化核心对象集合T,聚类个数k,聚类集合C, 未访问集合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) #开始聚类 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 #画图 def draw(C): colValue = ['r', 'y', 'g', 'b', 'c', 'k', 'm'] for i in range(len(C)): coo_X = [] #x坐标列表 coo_Y = [] #y坐标列表 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)
- 流程图载自(DBSCAN算法原理 - cheney-pro - 博客园 (cnblogs.com))
-
- 调用函数代码
- 算法代码
import numpy as np import pandas as pd import matplotlib.pyplot as plt from sklearn import datasets %matplotlib inline #生成数据 X=np.empty((100,2)) X[:,0]=np.random.uniform(0.,100.,size=100) X[:,1]=0.75*X[:,0]+3+np.random.normal(0,10,size=100) plt.scatter(X[:,0],X[:,1]) plt.show() df=pd.DataFrame(X,columns=['feature1','feature2']) df.plot.scatter('feature1','feature2') print(df) #调用DBSCAN接口完成聚类 from sklearn.cluster import dbscan # eps为邻域半径,min_samples为最少点数目 core_samples,cluster_ids = dbscan(X, eps = 10, min_samples=3) df = pd.DataFrame(np.c_[X,cluster_ids],columns = ['feature1','feature2','cluster_id']) df.plot.scatter('feature1','feature2', s = 100, c = list(df['cluster_id']),cmap = 'rainbow',colorbar = False, alpha = 0.6,title = 'DBSCAN cluster result')