# DBSCAN密度聚类

DBSCAN是一种基于密度的聚类算法，此类算法假设聚类结构能通过样本分布的紧密深度确定，从样本的密度角度来考量样本之间的可连接性，基于可连接样本不断扩张聚类簇以获得最终聚类结果。

**1）定义**

![img](https://img-blog.csdnimg.cn/20190302120515122.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2ppYW5nNDI1Nzc2MDI0,size_16,color_FFFFFF,t_70)

![img](https://images2015.cnblogs.com/blog/1042406/201612/1042406-20161222112847323-1346197243.png)

**2）DBSCAN算法流程**

![img](https://img-blog.csdnimg.cn/20190302113838430.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2ppYW5nNDI1Nzc2MDI0,size_16,color_FFFFFF,t_70)

![img](https://img-blog.csdnimg.cn/20190302113901586.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2ppYW5nNDI1Nzc2MDI0,size_16,color_FFFFFF,t_70)

## sklearn

> 在scikit-learn中，DBSCAN算法类为sklearn.cluster.DBSCAN
>
> sklearn API:<https://scikit-learn.org/stable/modules/generated/sklearn.cluster.DBSCAN.html#sklearn.cluster.DBSCAN>
>
> 参考中文参数介绍：<https://www.cnblogs.com/pinard/p/6217852.html>
>
> 部分参数：
>
> eps：ϵ-邻域的距离阈值，认值是0.5。
>
> min\_samples： 核心对象的ϵ-邻域的样本数阈值。默认值是5。min\_samples过大，则核心对象会过少，此时簇内部分本来是一类的样本可能会被标为噪音点，类别数也会变多。反之min\_samples过小的话，则会产生大量的核心对象，可能会导致类别数过少。
>
> metric：距离度量参数：欧式距离 “euclidean”、曼哈顿距离 “manhattan”、切比雪夫距离“chebyshev”、闵可夫斯基距离 “minkowski”、带权重闵可夫斯基距离 “wminkowski”、标准化欧式距离 “seuclidean”: 即对于各特征维度做了归一化以后的欧式距离。此时各样本特征维度的均值为0，方差为1、马氏距离“mahalanobis”。
>
> algorithm：最近邻搜索算法参数，‘brute’对应第一种蛮力实现，‘kd\_tree’对应第二种KD树实现，‘ball\_tree’对应第三种的球树实现， ‘auto’则会在上面三种算法中做权衡，选择一个拟合最好的最优算法
>
> leaf\_size：最近邻搜索算法参数，为使用KD树或者球树时， 停止建子树的叶子节点数量的阈值。这个值越小，则生成的KD树或者球树就越大，层数越深，建树时间越长，反之，则生成的KD树或者球树会小，层数较浅，建树时间较短。默认是30. 因为这个值一般只影响算法的运行速度和使用内存大小，因此一般情况下可以不管它。
>
> p: 最近邻距离度量参数。只用于闵可夫斯基距离和带权重闵可夫斯基距离中p值的选择，p=1为曼哈顿距离， p=2为欧式距离。如果使用默认的欧式距离不需要管这个参数。

```python
import numpy as np

from sklearn.cluster import DBSCAN
from sklearn import metrics
from sklearn.datasets.samples_generator import make_blobs
from sklearn.preprocessing import StandardScaler

# #############################################################################
# Generate sample data
centers = [[1, 1], [-1, -1], [1, -1]]
X, labels_true = make_blobs(n_samples=750, centers=centers, cluster_std=0.4,
                            random_state=0)
# 标准化
X = StandardScaler().fit_transform(X)

# #############################################################################
# 0.3邻域、10核心对象阈值
db = DBSCAN(eps=0.3, min_samples=10).fit(X)
# 全false
core_samples_mask = np.zeros_like(db.labels_, dtype=bool)
# 核心样本位置为True
core_samples_mask[db.core_sample_indices_] = True
labels = db.labels_

# 计算簇标签, 忽略噪点（label=-1)
n_clusters_ = np.unique(labels).shape[0] - (1 if -1 in labels else 0)
# 计算噪点数量
n_noise_ = labels[labels == -1].shape[0]

print('簇数量: %d' % n_clusters_)
print('噪点数量: %d' % n_noise_)

# #########################衡量指标####################################################
# reference：https://blog.csdn.net/sinat_26917383/article/details/70577710

# homogeneity_score(labels_true, labels_pred)集群标签的同质性度量，得分在0.0到1.0之间。1.0代表完全均匀的标签。
print("Homogeneity: %0.3f" % metrics.homogeneity_score(labels_true, labels))
# 集群标签的完整性度量。如果所有数据点都是同一簇的元素，则聚类结果满足完整性。得分在0.0到1.0之间。1.0代表完美的标签
print("Completeness: %0.3f" % metrics.completeness_score(labels_true, labels))
# 同质性和完整性的调和平均
print("V-measure: %0.3f" % metrics.v_measure_score(labels_true, labels))

# 兰德系数，[-1,1]越大意味着与真实情况越吻合
print("Adjusted Rand Index: %0.3f"
      % metrics.adjusted_rand_score(labels_true, labels))
# 互信息，也是衡量吻合度，[-1,1]
print("Adjusted Mutual Information: %0.3f"
      % metrics.adjusted_mutual_info_score(labels_true, labels))
# 轮廓系数，适用于实际类型未知情况，[-1,1]同类别样本越近，不同类样本距离越远分数越高
print("Silhouette Coefficient: %0.3f"
      % metrics.silhouette_score(X, labels))

# ################################绘图#############################################
# Plot result
import matplotlib.pyplot as plt

# Black removed and is used for noise instead.
unique_labels = set(labels)
colors = [plt.cm.Spectral(each)
          for each in np.linspace(0, 1, len(unique_labels))]
# 遍历类别、颜色列表，给不同的簇类画上不同的颜色
for k, col in zip(unique_labels, colors):
    # 噪点用黑色
    if k == -1:
        col = [0, 0, 0, 1]
    # 类别为k的bool矩阵
    class_member_mask = (labels == k)

    # 取类别为k，且core_samples_mask中为True(核心样本位置为True)的位置的样本
    # 既，核心样本markersize=14，比非核心样本大
    xy = X[class_member_mask & core_samples_mask]
    plt.plot(xy[:, 0], xy[:, 1], 'o', markerfacecolor=tuple(col),
             markeredgecolor='k', markersize=14)

    # ~ 取反：把1变为0,把0变为1
    #   取类别为k，且core_samples_mask中为False(非核心样本位置为False)的位置的样本
    # 既，非核心样本markersize=6，比核心样本小
    xy = X[class_member_mask & ~core_samples_mask]
    plt.plot(xy[:, 0], xy[:, 1], 'o', markerfacecolor=tuple(col),
             markeredgecolor='k', markersize=6)

plt.title('Estimated number of clusters: %d' % n_clusters_)
plt.show()

'''
output:

簇数量: 3
噪点数量: 18
Homogeneity: 0.953
Completeness: 0.883
V-measure: 0.917
Adjusted Rand Index: 0.952
Adjusted Mutual Information: 0.883
Silhouette Coefficient: 0.626
'''
```

![img](https://img-blog.csdnimg.cn/20190303182701896.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2ppYW5nNDI1Nzc2MDI0,size_16,color_FFFFFF,t_70)


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