13 聚类算法 - 谱聚类

需求 使用scikit的相关API创建模拟数据，然后使用谱聚类算法进行数据聚类操作，并比较算法在不同参数情况下的聚类效果。

相关API：https://scikit-learn.org/stable/modules/generated/sklearn.cluster.SpectralClustering.html

常规操作：

import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
import sklearn.datasets as ds
import matplotlib.colors
import warnings
from sklearn.cluster import SpectralClustering#引入谱聚类
from sklearn.preprocessing import StandardScaler
from sklearn.metrics import euclidean_distances

## 设置属性防止中文乱码及拦截异常信息
mpl.rcParams['font.sans-serif'] = [u'SimHei']
mpl.rcParams['axes.unicode_minus'] = False

warnings.filterwarnings('ignore', category=FutureWarning)

1、创建模拟数据

N = 1000
centers = [[1, 2], [-1, -1], [1, -1], [-1, 1]]
#符合高斯分布的数据集
data1, y1 = ds.make_blobs(N, n_features=2, centers=centers, 
    cluster_std=(0.75,0.5,0.3,0.25), random_state=0)
data1 = StandardScaler().fit_transform(data1)
dist1 = euclidean_distances(data1, squared=True)

2、 数据2 - 圆形数据集

t = np.arange(0, 2 * np.pi, 0.1)
data2_1 = np.vstack((np.cos(t), np.sin(t))).T
data2_2 = np.vstack((2*np.cos(t), 2*np.sin(t))).T
data2_3 = np.vstack((3*np.cos(t), 3*np.sin(t))).T
data2 = np.vstack((data2_1, data2_2, data2_3))
y2 = np.vstack(([0] * len(data2_1), [1] * len(data2_2), [2] * len(data2_3)))

datasets = [(data1, y1), (data2, y2.ravel())]

---

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

---

3、画图

colors = ['r', 'g', 'b', 'y']
cm = mpl.colors.ListedColormap(colors)

for i,(X, y) in enumerate(datasets):
    x1_min, x2_min = np.min(X, axis=0)
    x1_max, x2_max = np.max(X, axis=0)
    x1_min, x1_max = expandBorder(x1_min, x1_max)
    x2_min, x2_max = expandBorder(x2_min, x2_max)
    n_clusters = len(np.unique(y))
    plt.figure(figsize=(12, 8), facecolor='w')
    plt.suptitle(u'谱聚类--数据%d' % (i+1), fontsize=20)
    plt.subplots_adjust(top=0.9,hspace=0.35)

    #谱聚类的建模
    gamma_list = [0.1,5,10]
    nclusters = [4,3]
    for i, ncluster in enumerate(nclusters):
        for j,gamma_value in enumerate(gamma_list):
            spectral = SpectralClustering(n_clusters=ncluster,
                gamma = gamma_value, affinity='laplacian',assign_labels='kmeans')
            y_hat = spectral.fit_predict(X)
            unique_y_hat = np.unique(y_hat)


            ## 开始画图
            plt.subplot(2,3,j+1)
            for k, col in zip(unique_y_hat, colors):
                cur = (y_hat == k)
                plt.scatter(X[cur, 0], X[cur, 1], s=40, c=col, edgecolors='k')
            plt.xlim((x1_min, x1_max))
            plt.ylim((x2_min, x2_max))
            plt.grid(True)
            plt.title('$\gamma$ = %.2f ，聚类簇数目：%d' % (gamma_value, n_clusters), 
                fontsize=16)

    plt.subplot(234)
    plt.scatter(X[:, 0], X[:,1], c=y, s=30, cmap=cm, edgecolors='none')
    plt.xlim((x1_min, x1_max))
    plt.ylim((x2_min, x2_max))
    plt.title('原始数据，聚类簇数目:%d' % len(np.unique(y)))
    plt.grid(True)
    plt.show()