及其应用"/>
4. DBSCAN方法及其应用
文章目录
- 1. DBSCAN密度聚类
- 2. 举例
- 应用实例
- 数据实例
- `DBSCAN`主要参数
- 根据上网时间聚类
- 根据上网时长聚类
- 输出
- 技巧
1. DBSCAN密度聚类
-
DBSCAN算法是一种基于密度的聚类算法。
- 聚类的时候不需要预先指定簇的个数。
- 最终的簇的个数不定。
-
DBSCAN算法将数据点分为三类。
- 核心点:在半径Eps内含有超过MinPts数目的点。
- 边界点:在半径Eps内点的数目小于MinPts,但是落在核心点的临域内。
- 噪音点:既不是核心点也不是边界点的点。
-
DBSCAN算法流程
- 将所有点标记为核心点、边界点或噪声点。
- 删除噪声点。
- 为距离在Eps之内的所有核心点之间赋予一条边。
- 每组连通的核心点形成一个簇。
- 将每个边界点指派到一个与之关联的核心点的簇中(哪一个核心点的半径范围之内)。
2. 举例
有如下13个样本点,使用DBSCAN进行聚类。
取Eps=3,MinPts=3,依 据DBSACN对所有点进行聚类 (曼哈顿距离)。
- 对每个点计算其邻域Eps=3内的点的集合。
- 集合内点的个数超过MinPts=3的点为核心点。
- 查看剩余点是否在核心点的邻域内,若在,则为边界点,否则为噪声点。
将距离不超过Eps=3的点相互连接,构成一个簇,核心点邻域内的点也会被加入到这个簇中。 则形成3个簇。
应用实例
现有大学校园网的日志数据,290条大学生的校园网使用情况数据,数据包 括用户ID,设备的MAC地址,IP地址,开始上网时间,停止上网时间,上 网时长,校园网套餐等。利用已有数据,分析学生上网的模式。目的:通过DBSCAN聚类,分析学生上网时间和上网时长的模式。
数据实例
数据链接
DBSCAN
主要参数
eps
:两个样本被看作邻居节点的最大距离。min_sample
:簇的样本数。metric
:距离计算方式。
根据上网时间聚类
import numpy as np
import sklearn.cluster as skc
from sklearn import metrics
import matplotlib.pyplot as pltmac2id = dict()
online_times = []
f = open('Data/TestData', encoding='utf-8')
for line in f:# 读取每条数据中的mac地址,# 开始上网时间,上网时长mac = line.split(',')[2]online_time = int(line.split(',')[6])start_time = int(line.split(',')[4].split(' ')[1].split(':')[0])# mac2id是一个字典:# key是mac地址# value是对应mac地址的上网时长以及开始上网时间(精度为小时)if mac not in mac2id:mac2id[mac] = len(online_times)online_times.append((start_time, online_time))else:online_times[mac2id[mac]] = [(start_time, online_time)]# -1:根据元素的个数自动计算此轴的长度
# X:上网时间
real_X = np.array(online_times).reshape((-1, 2))
X = real_X[:, 0:1]# 调用DBSCAN方法进行训练,
# labels为每个数据的簇标签db = skc.DBSCAN(eps=0.01, min_samples=20).fit(X)
labels = db.labels_# 打印数据被记上的标签,
# 计算标签为-1,即噪声数据的比例。print('Labels:')
print(labels)
raito = len(labels[labels[:] == -1]) / len(labels)
print('Noise raito:', format(raito, '.2%'))# 计算簇的个数并打印,评价聚类效果n_clusters_ = len(set(labels)) - (1 if -1 in labels else 0)
print('Estimated number of clusters: %d' % n_clusters_)
print("Silhouette Coefficient: %0.3f" % metrics.silhouette_score(X, labels))# 打印各簇标号以及各簇内数据for i in range(n_clusters_):print('Cluster ', i, ':')print(list(X[labels == i].flatten()))# 画直方图,分析实验结果plt.hist(X, 24)
plt.show()
###输出
Labels:
[ 0 -1 0 1 -1 1 0 1 2 -1 1 0 1 1 3 -1 -1 3 -1 1 1 -1 1 3 4-1 1 1 2 0 2 2 -1 0 1 0 0 0 1 3 -1 0 1 1 0 0 2 -1 1 31 -1 3 -1 3 0 1 1 2 3 3 -1 -1 -1 0 1 2 1 -1 3 1 1 2 3 01 -1 2 0 0 3 2 0 1 -1 1 3 -1 4 2 -1 -1 0 -1 3 -1 0 2 1 -1-1 2 1 1 2 0 2 1 1 3 3 0 1 2 0 1 0 -1 1 1 3 -1 2 1 31 1 1 2 -1 5 -1 1 3 -1 0 1 0 0 1 -1 -1 -1 2 2 0 1 1 3 00 0 1 4 4 -1 -1 -1 -1 4 -1 4 4 -1 4 -1 1 2 2 3 0 1 0 -1 10 0 1 -1 -1 0 2 1 0 2 -1 1 1 -1 -1 0 1 1 -1 3 1 1 -1 1 10 0 -1 0 -1 0 0 2 -1 1 -1 1 0 -1 2 1 3 1 1 -1 1 0 0 -1 00 3 2 0 0 5 -1 3 2 -1 5 4 4 4 -1 5 5 -1 4 0 4 4 4 5 44 5 5 0 5 4 -1 4 5 5 5 1 5 5 0 5 4 4 -1 4 4 5 4 0 54 -1 0 5 5 5 -1 4 5 5 5 5 4 4]
Noise raito: 22.15%
Estimated number of clusters: 6
Silhouette Coefficient: 0.710
Cluster 0 :
[22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22]
Cluster 1 :
[23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23]
Cluster 2 :
[20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20]
Cluster 3 :
[21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21]
Cluster 4 :
[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]
Cluster 5 :
[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]
根据上网时长聚类
import numpy as np
import sklearn.cluster as skc
from sklearn import metrics
import matplotlib.pyplot as pltmac2id = dict()
online_times = []
f = open('Data/TestData', encoding='utf-8')
for line in f:# 读取每条数据中的mac地址,# 开始上网时间,上网时长mac = line.split(',')[2]online_time = int(line.split(',')[6])start_time = int(line.split(',')[4].split(' ')[1].split(':')[0])# mac2id是一个字典:# key是mac地址# value是对应mac地址的上网时长以及开始上网时间(精度为小时)if mac not in mac2id:mac2id[mac] = len(online_times)online_times.append((start_time, online_time))else:online_times[mac2id[mac]] = [(start_time, online_time)]# -1:根据元素的个数自动计算此轴的长度
# X:上网时间
real_X = np.array(online_times).reshape((-1, 2))
X = np.log(1 + real_X[:, 1:])# 调用DBSCAN方法进行训练 ,
# labels为每个数据的簇标签db = skc.DBSCAN(eps=0.14, min_samples=10).fit(X)
labels = db.labels_print('Lables:')
print(labels)
raito = len(labels[labels[:] == -1]) / len(labels)
print('Noise raito:', format(raito, '.2%'))# Number of cluster in lables, ignoring noise if present.
n_clusters_ = len(set(labels)) - (1 if -1 in labels else 0)print('Estimated number of clusters: %d' % n_clusters_)
print('Silhouette Coefficient: %0.3f' % metrics.silhouette_score(X, labels))# 统计每一个簇内的样本个数 , 均值,标准差for i in range(n_clusters_):print('Cluster ', i, ':')count = len(X[labels == i])mean = np.mean(real_X[labels == i][:, 1])std = np.std(real_X[labels == i][:, 1])print('\t number of sample: ', count)print('\t mean of sample : ', format(mean, '.1f'))print('\t std of sample : ', format(std, '.1f'))
输出
Lables:
[ 0 1 0 4 1 2 0 2 0 3 -1 0 -1 -1 0 3 1 0 3 2 2 1 2 0 11 -1 -1 0 0 0 0 1 0 -1 0 0 0 2 0 1 0 -1 -1 0 0 0 3 2 0-1 1 0 1 0 0 -1 2 0 0 0 1 3 3 0 2 0 -1 3 0 0 2 0 0 02 1 -1 0 0 0 0 0 0 1 -1 0 3 1 0 1 1 0 1 0 1 0 0 -1 11 0 0 2 0 0 0 2 2 0 0 0 -1 0 0 4 0 1 2 -1 0 1 0 2 0-1 -1 -1 0 1 1 3 -1 0 1 0 2 0 0 2 1 1 0 0 0 0 4 -1 0 00 0 2 0 0 0 0 -1 2 0 0 0 0 4 0 0 -1 0 2 0 0 -1 0 1 40 0 -1 1 1 0 0 2 0 0 3 -1 -1 -1 1 0 0 2 1 0 -1 -1 3 2 20 0 3 0 1 0 0 0 3 2 0 -1 0 1 -1 -1 0 2 2 1 4 0 0 1 02 0 0 0 0 1 1 0 0 1 0 4 -1 -1 0 0 0 -1 -1 1 -1 4 -1 0 22 -1 2 1 2 -1 0 -1 0 2 2 1 -1 0 1 2 -1 -1 1 -1 2 -1 -1 1 42 3 1 0 4 0 0 4 2 4 0 0 2 -1]
Noise raito: 16.96%
Estimated number of clusters: 5
Silhouette Coefficient: 0.227
Cluster 0 :number of sample: 128mean of sample : 5864.3std of sample : 3498.1
Cluster 1 :number of sample: 46mean of sample : 36835.1std of sample : 11314.1
Cluster 2 :number of sample: 40mean of sample : 843.2std of sample : 242.9
Cluster 3 :number of sample: 14mean of sample : 16581.6std of sample : 1186.7
Cluster 4 :number of sample: 12mean of sample : 338.4std of sample : 31.9
技巧
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4. DBSCAN方法及其应用
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