DBSCAN算法Python实现及原理

原创于 2023-08-16 11:32:12 发布 · 222 阅读

1 ·

CC 4.0 BY-SA版权

文章标签：

#算法 #python #开发语言

本文介绍了DBSCAN聚类算法的工作原理，包括中心点、边缘点和孤立点的概念，并提供了伪代码及Python示例。同时推荐了一个网站供读者观察不同聚类方法的动态演示。

摘要生成于 C知道，由 DeepSeek-R1 满血版支持，前往体验 >

首先推荐一个国外的网站

Visualizing DBSCAN Clustering (naftaliharris.com)这个网站不仅可以看DBSCAN还可以看K-means和系统聚类的动态演示

一、DBSCAN原理

DBSCAN主要将需要遍历的点分为3类：中心点，边缘点，孤立点

中心点：任意选取一个样本点，并在半径Eps中搜索是否存在minpoints个点，如果存在，则为中心点

边缘点：对于一个样本点，如果其在其本身的Eps半径内没有minpoints个点，但其在其余中心点的范围内，则称其为边缘点

孤立点：既不是中心点也不是边缘点

配上下面这个图可能会更好理解一下

那么算法本身其实也就逐渐明晰了：其实就是不断遍历寻找是否其满足在指定半径内有指定点，并将中心点及其包含的点作为一个簇（类），最后将同属一簇的绘上同一颜色展示，下面是wiki百科上有关DBSCAN伪代码的展示：

DBSCAN(D, eps, MinPts) {
C = 0
for each point P in dataset D {
if P is visited
continue next point
mark P as visited
NeighborPts = regionQuery(P, eps)
if sizeof(NeighborPts) < MinPts
mark P as NOISE
else {
C = next cluster
expandCluster(P, NeighborPts, C, eps, MinPts)
}
}
}
expandCluster(P, NeighborPts, C, eps, MinPts) {
add P to cluster C
for each point P' in NeighborPts { 
if P' is not visited {
mark P' as visited
NeighborPts' = regionQuery(P', eps)
if sizeof(NeighborPts') >= MinPts
NeighborPts = NeighborPts joined with NeighborPts'
}
if P' is not yet member of any cluster
add P' to cluster C
}
}
regionQuery(P, eps)
return all points within P's eps-neighborhood (including P)

那么跟着伪代码其实就很好写出具体代码了：

#encoding=gbk
import numpy as np
import matplotlib.pyplot as plt

def dbscan(data, eps, min_pts):
    labels = [0] * len(data)
    cluster_id = 0
    
    for i in range(len(data)):
        if labels[i] != 0:
            continue
        
        neighbors = get_neighbors(data, i, eps)
        if len(neighbors) < min_pts:
            labels[i] = -1  # noise point
        else:
            cluster_id += 1
            labels[i] = cluster_id
            expand_cluster(data, labels, i, neighbors, cluster_id, eps, min_pts)
    
    return labels

def expand_cluster(data, labels, point_idx, neighbors, cluster_id, eps, min_pts):
    for neighbor in neighbors:
        if labels[neighbor] == -1:
            labels[neighbor] = cluster_id
        elif labels[neighbor] == 0:
            labels[neighbor] = cluster_id
            new_neighbors = get_neighbors(data, neighbor, eps)
            if len(new_neighbors) >= min_pts:
                neighbors += new_neighbors

def get_neighbors(data, point_idx, eps):
    neighbors = []
    for i in range(len(data)):
        if np.linalg.norm(data[i] - data[point_idx]) < eps:
            neighbors.append(i)
    return neighbors

# 生成示例数据
np.random.seed(0)
#产生1000个2维数据
data = np.random.randn(1000, 2)
# 使用DBSCAN进行聚类
#选择圆半径和最低包含点个数
eps = 0.5
min_pts = 3
labels = dbscan(data, eps, min_pts)
##黑色作为孤立点
# 绘制聚类结果
plt.scatter(data[:, 0], data[:, 1], c=labels)
plt.show()

附上一张结果图：