DBSCAN算法及sklearn实现

基本概念：(Density-Based Spatial Clustering of Application with Noiso)

1.核心对象：

若某个点的密度达到算法设定的阈值则其为核心点。（即r领域内的点数量不小于minPts）

2.ε-领域的距离阈值：

设定的半径r

3.直接密度可达：

若某点p在点q的r领域内，且q是核心点则p-q直接密度可达

4.密度可达：

若有一个点的序列q0、q1、 ...qk,对任意qi-qi-q是直接密度可达的，则称从q0到qk密度可达，这实际上是直接密度可达的"传播"。

5.密度相连：

若从某核心点p出发，点q和点k都是密度可达的，则称点q和点k是密度相连的

6.边界点：

属于某一类的非核心点,不能发展下线了

7.直接密度可达：

若某点p在点q的r领域内，且q是核心点则p-q直接密度可达

8.噪声点：

不属于任何一个类簇的点，从任何一个核心点出发都是密度不可达的

9.可视化展示：

A：核心对象

B,C：边界点

N：离群点

工作流程：

参数D：

输入数据集

参数ε：

指定半径

MinPts：

密度阈值

半径ε，可以根据K距离来设定：找突变点

K距离：

给定数据集P={p(i);i=0,1...n},计算点P(i)到集合D的子集S中所有点之间的距离，距离按照从小到大的顺序排序，d(k)就被称为k-距离。

MinPts:

k-距离中的k值，一般取得小一些，多次尝试，这儿有个聚类可视化好玩的网址点击这里，可以感受下，挺好玩的。

优势：

不需要指定簇个数

可以发现任意形状的簇

擅长找到离群点（检测任务）

劣势：

高维数据有些困难（可以做降维）

参数难以选择（参数对结果影响非常大）

Sklearn中效率很慢（数据消减策略）

kmeans-dbcan聚类对比

# beer dataset
import pandas as pd
beer = pd.read_csv('data.txt', sep=' ')
beer

X = beer[["calories","sodium","alcohol","cost"]]

# K-means clustering

from sklearn.cluster import KMeans
km = KMeans(n_clusters=3).fit(X)
km2 = KMeans(n_clusters=2).fit(X)

km.labels_

array([0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 2, 0, 0, 2, 1])

beer['cluster'] = km.labels_
beer['cluster2'] = km2.labels_
beer.sort_values('cluster')

from pandas.tools.plotting import scatter_matrix
%matplotlib inline
cluster_centers = km.cluster_centers_
cluster_centers_2 = km2.cluster_centers_

beer.groupby("cluster").mean()

beer.groupby("cluster2").mean()

centers = beer.groupby("cluster").mean().reset_index()

%matplotlib inline
import matplotlib.pyplot as plt
plt.rcParams['font.size'] = 14

import numpy as np
colors = np.array(['red', 'green', 'blue', 'yellow'])

plt.scatter(beer["calories"], beer["alcohol"],c=colors[beer["cluster"]])
plt.scatter(centers.calories, centers.alcohol, linewidths=3, marker='+', s=300, c='black')
plt.xlabel("Calories")
plt.ylabel("Alcohol")

scatter_matrix(beer[["calories","sodium","alcohol","cost"]],s=100, alpha=1, c=colors[beer["cluster"]], figsize=(10,10))
plt.suptitle("With 3 centroids initialized")

scatter_matrix(beer[["calories","sodium","alcohol","cost"]],s=100, alpha=1, c=colors[beer["cluster2"]], figsize=(10,10))
plt.suptitle("With 2 centroids initialized")

from sklearn.preprocessing import StandardScaler
scaler = StandardScaler()
X_scaled = scaler.fit_transform(X)
X_scaled

array([[ 0.38791334,  0.00779468,  0.43380786, -0.45682969],
       [ 0.6250656 ,  0.63136906,  0.62241997, -0.45682969],
       [ 0.82833896,  0.00779468, -3.14982226, -0.10269815],
       [ 1.26876459, -1.23935408,  0.90533814,  1.66795955],
       [ 0.65894449, -0.6157797 ,  0.71672602,  1.95126478],
       [ 0.42179223,  1.25494344,  0.3395018 , -1.5192243 ],
       [ 1.43815906,  1.41083704,  1.1882563 , -0.66930861],
       [ 0.55730781,  1.87851782,  0.43380786, -0.52765599],
       [-1.1366369 , -0.7716733 ,  0.05658363, -0.45682969],
       [-0.66233238, -1.08346049, -0.5092527 , -0.66930861],
       [ 0.25239776,  0.47547547,  0.3395018 , -0.38600338],
       [-1.03500022,  0.00779468, -0.13202848, -0.24435076],
       [ 0.08300329, -0.6157797 , -0.03772242,  0.03895447],
       [ 0.59118671,  0.63136906,  0.43380786,  1.88043848],
       [ 0.55730781, -1.39524768,  0.71672602,  2.0929174 ],
       [-2.18688263,  0.00779468, -1.82953748, -0.81096123],
       [ 0.21851887,  0.63136906,  0.15088969, -0.45682969],
       [ 0.38791334,  1.41083704,  0.62241997, -0.45682969],
       [-2.05136705, -1.39524768, -1.26370115, -0.24435076],
       [-1.20439469, -1.23935408, -0.03772242, -0.17352445]])

km = KMeans(n_clusters=3).fit(X_scaled)

beer["scaled_cluster"] = km.labels_
beer.sort_values("scaled_cluster")

beer.groupby("scaled_cluster").mean()

pd.scatter_matrix(X, c=colors[beer.scaled_cluster], alpha=1, figsize=(10,10), s=100)

from sklearn import metrics
score_scaled = metrics.silhouette_score(X,beer.scaled_cluster)
score = metrics.silhouette_score(X,beer.cluster)
print(score_scaled, score)

scores = []
for k in range(2,20):
    labels = KMeans(n_clusters=k).fit(X).labels_
    score = metrics.silhouette_score(X, labels)
    scores.append(score)
 
scores

[0.69176560340794857,
 0.67317750464557957,
 0.58570407211277953,
 0.42254873351720201,
 0.4559182167013377,
 0.43776116697963124,
 0.38946337473125997,
 0.39746405172426014,
 0.33061511213823314,
 0.34131096180393328,
 0.34597752371272478,
 0.31221439248428434,
 0.30707782144770296,
 0.31834561839139497,
 0.28495140011748982,
 0.23498077333071996,
 0.15880910174962809,
 0.084230513801511767]

plt.plot(list(range(2,20)), scores)
plt.xlabel("Number of Clusters Initialized")
plt.ylabel("Sihouette Score")

# DBSCAN clustering

from sklearn.cluster import DBSCAN
db = DBSCAN(eps=10, min_samples=2).fit(X)

labels = db.labels_

beer['cluster_db'] = labels
beer.sort_values('cluster_db')

beer.groupby('cluster_db').mean()