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()
