学习笔记1

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前言

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聚类算法部分的论文学习笔记
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一、DBSAN聚类算法

1、输入：样本数据
输出：聚类结果
1）、计算样本中各个点与其他点之间的欧几里得距离：
2）、两个点 A= (a[1]，a[2]，…，a[n]) 和 B = (b[1]，b[2]，…，b[n]) 之间的
距离ρ(A，B)定义为下面的公式 3-4；
3）、获得每一个点的 K 距离，并将 K 距离排序
4）、确定半径 eps 的值；
5）、计算中心点，建立所有中心点之间间隔小于半径 eps 的映射；
6）、根据得到的核心点和半径 eps，计算出和核心点联通的点和离群的点；
7）、将能够联通，以及距离小于半径的点，生成一个集合，即一个簇。

二、使用步骤

1.引入库

代码如下（示例）：

from sklearn import datasets
import numpy as np
import random
import matplotlib.pyplot as plt
import time
import copy

2.读入数据

代码如下（示例）：

def find_neighbor(j, x, eps):#确定邻域
    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()

3.完整代码

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()