原理
DBSCAN是一种基于密度的聚类算法，这类密度聚类算法一般假定类别可以通过样本分布的紧密程度决定。同一类别的样本，他们之间的紧密相连的，也就是说，在该类别任意样本周围不远处一定有同类别的样本存在。
通过将紧密相连的样本划为一类，这样就得到了一个聚类类别。通过将所有各组紧密相连的样本划为各个不同的类别，则我们就得到了最终的所有聚类类别结果。
一些概念
x1是核心对象，x2由x1密度直达，x3由x1密度可达，x3与x4密度相连
伪码
python代码
代码语言：javascript复制from sklearn import datasets
import numpy as np
import random
import matplotlib.pyplot as plt
import time
import copy
def find_neighbor(j, x, eps):
N = list()
for i in range(x.shape[0]):
temp = np.sqrt(np.sum(np.square(x[j]-x[i]))) # 计算欧式距离
if temp <= eps:
N.append(i)
return set(N)
def DBSCAN(X, eps, min_Pts):
k = -1
neighbor_list = [] # 用来保存每个数据的邻域
omega_list = [] # 核心对象集合
gama = set([x for x in range(len(X))]) # 初始时将所有点标记为未访问
cluster = [-1 for _ in range(len(X))] # 聚类
for i in range(len(X)):
neighbor_list.append(find_neighbor(i, X, eps))
if len(neighbor_list[-1]) >= min_Pts:
omega_list.append(i) # 将样本加入核心对象集合
omega_list = set(omega_list) # 转化为集合便于操作
while len(omega_list) > 0:
gama_old = copy.deepcopy(gama)
j = random.choice(list(omega_list)) # 随机选取一个核心对象
k = k 1
Q = list()
Q.append(j)
gama.remove(j)
while len(Q) > 0:
q = Q[0]
Q.remove(q)
if len(neighbor_list[q]) >= min_Pts:
delta = neighbor_list[q] & gama
deltalist = list(delta)
for i in range(len(delta)):
Q.append(deltalist[i])
gama = gama - delta
Ck = gama_old - gama
Cklist = list(Ck)
for i in range(len(Ck)):
cluster[Cklist[i]] = k
omega_list = omega_list - Ck
return cluster
X1, y1 = datasets.make_circles(n_samples=2000, factor=.6, noise=.02)
X2, y2 = datasets.make_blobs(n_samples=400, n_features=2, centers=[[1.2, 1.2]], cluster_std=[[.1]], random_state=9)
X = np.concatenate((X1, X2))
eps = 0.08
min_Pts = 10
begin = time.time()
C = DBSCAN(X, eps, min_Pts)
end = time.time()
plt.figure()
plt.scatter(X[:, 0], X[:, 1], c=C)
plt.show()效果
选用iris鸢尾花数据集更改
代码语言：javascript复制from sklearn.datasets import load_iris
X = load_iris().data缺点
参数敏感Eps , MinPts ,若选取不当 ,会造成聚类质量下降。
