聚类算法之DBSCAN(具有噪声的基于密度的聚类方法)

# !/usr/bin/python
# -*- coding:utf-8 -*-

import numpy as np
import matplotlib.pyplot as plt
import sklearn.datasets as ds
import matplotlib.colors
from sklearn.cluster import DBSCAN
from sklearn.preprocessing import StandardScaler


def expand(a, b):
    d = (b - a) * 0.1
    return a-d, b+d


if __name__ == "__main__":
    N = 1000
    centers = [[1, 2], [-1, -1], [1, -1], [-1, 1]]
    #scikit中的make_blobs方法常被用来生成聚类算法的测试数据，直观地说，make_blobs会根据用户指定的特征数量、
    # 中心点数量、范围等来生成几类数据，这些数据可用于测试聚类算法的效果。
    #函数原型：sklearn.datasets.make_blobs(n_samples=100, n_features=2,
    # centers=3, cluster_std=1.0, center_box=(-10.0, 10.0), shuffle=True, random_state=None)[source]
    #参数解析：
    # n_samples是待生成的样本的总数。
    #
    # n_features是每个样本的特征数。
    #
    # centers表示类别数。
    #
    # cluster_std表示每个类别的方差，例如我们希望生成2类数据，其中一类比另一类具有更大的方差，可以将cluster_std设置为[1.0, 3.0]。
    data, y = ds.make_blobs(N, n_features=2, centers=centers, cluster_std=[0.5, 0.25, 0.7, 0.5], random_state=0)
    data = StandardScaler().fit_transform(data)
    # 数据1的参数：(epsilon, min_sample)
    params = ((0.2, 5), (0.2, 10), (0.2, 15), (0.3, 5), (0.3, 10), (0.3, 15))

    # 数据2
    # t = np.arange(0, 2*np.pi, 0.1)
    # data1 = np.vstack((np.cos(t), np.sin(t))).T
    # data2 = np.vstack((2*np.cos(t), 2*np.sin(t))).T
    # data3 = np.vstack((3*np.cos(t), 3*np.sin(t))).T
    # data = np.vstack((data1, data2, data3))
    # # # 数据2的参数：(epsilon, min_sample)
    # params = ((0.5, 3), (0.5, 5), (0.5, 10), (1., 3), (1., 10), (1., 20))

    matplotlib.rcParams['font.sans-serif'] = [u'SimHei']
    matplotlib.rcParams['axes.unicode_minus'] = False

    plt.figure(figsize=(12, 8), facecolor='w')
    plt.suptitle(u'DBSCAN聚类', fontsize=20)

    for i in range(6):
        eps, min_samples = params[i]
        #参数含义：
        #eps:半径，表示以给定点P为中心的圆形邻域的范围
        #min_samples:以点P为中心的邻域内最少点的数量
        #如果满足,以点P为中心,半径为EPS的邻域内点的个数不少于MinPts,则称点P为核心点
        model = DBSCAN(eps=eps, min_samples=min_samples)
        model.fit(data)
        y_hat = model.labels_

        core_indices = np.zeros_like(y_hat, dtype=bool)
        core_indices[model.core_sample_indices_] = True

        y_unique = np.unique(y_hat)
        n_clusters = y_unique.size - (1 if -1 in y_hat else 0)
        print y_unique, '聚类簇的个数为：', n_clusters

        # clrs = []
        # for c in np.linspace(16711680, 255, y_unique.size):
        #     clrs.append('#%06x' % c)
        plt.subplot(2, 3, i+1)
        clrs = plt.cm.Spectral(np.linspace(0, 0.8, y_unique.size))
        for k, clr in zip(y_unique, clrs):
            cur = (y_hat == k)
            if k == -1:
                plt.scatter(data[cur, 0], data[cur, 1], s=20, c='k')
                continue
            plt.scatter(data[cur, 0], data[cur, 1], s=30, c=clr, edgecolors='k')
            plt.scatter(data[cur & core_indices][:, 0], data[cur & core_indices][:, 1], s=60, c=clr, marker='o', edgecolors='k')
        x1_min, x2_min = np.min(data, axis=0)
        x1_max, x2_max = np.max(data, axis=0)
        x1_min, x1_max = expand(x1_min, x1_max)
        x2_min, x2_max = expand(x2_min, x2_max)
        plt.xlim((x1_min, x1_max))
        plt.ylim((x2_min, x2_max))
        plt.grid(True)
        plt.title(ur'$\epsilon$ = %.1f  m = %d，聚类数目：%d' % (eps, min_samples, n_clusters), fontsize=16)
    plt.tight_layout()
    plt.subplots_adjust(top=0.9)
    plt.show()