机器学习——聚类

kMeans:

import numpy as np
import matplotlib.pyplot as plt
import sklearn.datasets as ds
import matplotlib.colors
from sklearn.cluster import KMeans


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


if __name__ == "__main__":
    N = 400
    centers = 4
    data, y = ds.make_blobs(N, n_features=2, centers=centers, random_state=2)
    data2, y2 = ds.make_blobs(N, n_features=2, centers=centers, cluster_std=(1,2.5,0.5,2), random_state=2)
    data3 = np.vstack((data[y == 0][:], data[y == 1][:50], data[y == 2][:20], data[y == 3][:5]))
    y3 = np.array([0] * 100 + [1] * 50 + [2] * 20 + [3] * 5)

    cls = KMeans(n_clusters=4, init='k-means++')
    y_hat = cls.fit_predict(data)
    y2_hat = cls.fit_predict(data2)
    y3_hat = cls.fit_predict(data3)

    m = np.array(((1, 1), (1, 3)))
    data_r = data.dot(m)
    y_r_hat = cls.fit_predict(data_r)

    matplotlib.rcParams['font.sans-serif'] = [u'SimHei']
    matplotlib.rcParams['axes.unicode_minus'] = False
    cm = matplotlib.colors.ListedColormap(list('rgbm'))

    plt.figure(figsize=(9, 10), facecolor='w')
    plt.subplot(421)
    plt.title(u'原始数据')
    plt.scatter(data[:, 0], data[:, 1], c=y, s=30, cmap=cm, edgecolors='none')
    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.subplot(422)
    plt.title(u'KMeans++聚类')
    plt.scatter(data[:, 0], data[:, 1], c=y_hat, s=30, cmap=cm, edgecolors='none')
    plt.xlim((x1_min, x1_max))
    plt.ylim((x2_min, x2_max))
    plt.grid(True)

    plt.subplot(423)
    plt.title(u'旋转后数据')
    plt.scatter(data_r[:, 0], data_r[:, 1], c=y, s=30, cmap=cm, edgecolors='none')
    x1_min, x2_min = np.min(data_r, axis=0)
    x1_max, x2_max = np.max(data_r, 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.subplot(424)
    plt.title(u'旋转后KMeans++聚类')
    plt.scatter(data_r[:, 0], data_r[:, 1], c=y_r_hat, s=30, cmap=cm, edgecolors='none')
    plt.xlim((x1_min, x1_max))
    plt.ylim((x2_min, x2_max))
    plt.grid(True)

    plt.subplot(425)
    plt.title(u'方差不相等数据')
    plt.scatter(data2[:, 0], data2[:, 1], c=y2, s=30, cmap=cm, edgecolors='none')
    x1_min, x2_min = np.min(data2, axis=0)
    x1_max, x2_max = np.max(data2, 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.subplot(426)
    plt.title(u'方差不相等KMeans++聚类')
    plt.scatter(data2[:, 0], data2[:, 1], c=y2_hat, s=30, cmap=cm, edgecolors='none')
    plt.xlim((x1_min, x1_max))
    plt.ylim((x2_min, x2_max))
    plt.grid(True)

    plt.subplot(427)
    plt.title(u'数量不相等数据')
    plt.scatter(data3[:, 0], data3[:, 1], s=30, c=y3, cmap=cm, edgecolors='none')
    x1_min, x2_min = np.min(data3, axis=0)
    x1_max, x2_max = np.max(data3, 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.subplot(428)
    plt.title(u'数量不相等KMeans++聚类')
    plt.scatter(data3[:, 0], data3[:, 1], c=y3_hat, s=30, cmap=cm, edgecolors='none')
    plt.xlim((x1_min, x1_max))
    plt.ylim((x2_min, x2_max))
    plt.grid(True)

    plt.tight_layout(2, rect=(0, 0, 1, 0.97))
    plt.suptitle(u'数据分布对KMeans聚类的影响', fontsize=18)
    # https://github.com/matplotlib/matplotlib/issues/829
    # plt.subplots_adjust(top=0.92)
    plt.show()

实验结果：

AgglomerativeClustering:

import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
from sklearn.cluster import AgglomerativeClustering
from sklearn.neighbors import kneighbors_graph
import sklearn.datasets as ds
import warnings


def extend(a, b):
    return 1.05*a-0.05*b, 1.05*b-0.05*a


if __name__ == '__main__':
    warnings.filterwarnings(action='ignore', category=UserWarning)
    np.set_printoptions(suppress=True)
    np.random.seed(0)
    n_clusters = 4
    N = 400
    data1, y1 = ds.make_blobs(n_samples=N, n_features=2, centers=((-1, 1), (1, 1), (1, -1), (-1, -1)),
                              cluster_std=(0.1, 0.2, 0.3, 0.4), random_state=0)
    data1 = np.array(data1)
    n_noise = int(0.1*N)
    r = np.random.rand(n_noise, 2)
    data_min1, data_min2 = np.min(data1, axis=0)
    data_max1, data_max2 = np.max(data1, axis=0)
    r[:, 0] = r[:, 0] * (data_max1-data_min1) + data_min1
    r[:, 1] = r[:, 1] * (data_max2-data_min2) + data_min2
    data1_noise = np.concatenate((data1, r), axis=0)
    y1_noise = np.concatenate((y1, [4]*n_noise))

    data2, y2 = ds.make_moons(n_samples=N, noise=.05)
    data2 = np.array(data2)
    n_noise = int(0.1 * N)
    r = np.random.rand(n_noise, 2)
    data_min1, data_min2 = np.min(data2, axis=0)
    data_max1, data_max2 = np.max(data2, axis=0)
    r[:, 0] = r[:, 0] * (data_max1 - data_min1) + data_min1
    r[:, 1] = r[:, 1] * (data_max2 - data_min2) + data_min2
    data2_noise = np.concatenate((data2, r), axis=0)
    y2_noise = np.concatenate((y2, [3] * n_noise))

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

    cm = mpl.colors.ListedColormap(['r', 'g', 'b', 'm', 'c'])
    plt.figure(figsize=(14, 12), facecolor='w')
    plt.cla()
    linkages = ("ward", "complete", "average")
    for index, (n_clusters, data, y) in enumerate(((4, data1, y1), (4, data1_noise, y1_noise),
                                                   (2, data2, y2), (2, data2_noise, y2_noise))):
        plt.subplot(4, 4, 4*index+1)
        plt.scatter(data[:, 0], data[:, 1], c=y, cmap=cm)
        plt.title('Prime', fontsize=17)
        plt.grid(b=True, ls=':')
        data_min1, data_min2 = np.min(data, axis=0)
        data_max1, data_max2 = np.max(data, axis=0)
        plt.xlim(extend(data_min1, data_max1))
        plt.ylim(extend(data_min2, data_max2))

        connectivity = kneighbors_graph(data, n_neighbors=7, mode='distance', metric='minkowski', p=2, include_self=True)
        connectivity = 0.5 * (connectivity + connectivity.T)
        for i, linkage in enumerate(linkages):
            ac = AgglomerativeClustering(n_clusters=n_clusters, affinity='euclidean',
                                         connectivity=connectivity, linkage=linkage)
            ac.fit(data)
            y = ac.labels_
            plt.subplot(4, 4, i+2+4*index)
            plt.scatter(data[:, 0], data[:, 1], c=y, cmap=cm)
            plt.title(linkage, fontsize=17)
            plt.grid(b=True, ls=':')
            plt.xlim(extend(data_min1, data_max1))
            plt.ylim(extend(data_min2, data_max2))
    plt.suptitle(u'层次聚类的不同合并策略', fontsize=20)
    plt.tight_layout(0.5, rect=(0, 0, 1, 0.95))
    plt.show()

实验结果：