聚类

import numpy as np


# 定义欧式距离
def euclidean_distance(x1, x2):
    distance = 0
    # 距离的平方项再开根号
    for i in range(len(x1)):
        distance += pow((x1[i] - x2[i]), 2)
    return np.sqrt(distance)


X = np.array([[0,2],[0,0],[1,0],[5,0],[5,2]])
print(euclidean_distance(X[0], X[4]))


# 定义中心初始化函数
def centroids_init(k, X):
    m, n = X.shape
    centroids = np.zeros((k, n))
    for i in range(k):
        # 每一次循环随机选择一个类别中心
        centroid = X[np.random.choice(range(m))]
        centroids[i] = centroid
    return centroids


# 定义样本的最近质心点所属的类别索引
def closest_centroid(sample, centroids):
    closest_i = 0
    closest_dist = float('inf')
    for i, centroid in enumerate(centroids):
        # 根据欧式距离判断，选择最小距离的中心点所属类别
        distance = euclidean_distance(sample, centroid)
        if distance < closest_dist:
            closest_i = i
            closest_dist = distance
    return closest_i


# 定义构建类别过程
def build_clusters(centroids, k, X):
    clusters = [[] for _ in range(k)]
    for x_i, x in enumerate(X):
        # 将样本划分到最近的类别区域
        centroid_i = closest_centroid(x, centroids)
        clusters[centroid_i].append(x_i)
    return clusters


# 根据上一步聚类结果计算新的中心点
def calculate_centroids(clusters, k, X):
    n = X.shape[1]
    centroids = np.zeros((k, n))
    # 以当前每个类样本的均值为新的中心点
    for i, cluster in enumerate(clusters):
        centroid = np.mean(X[cluster], axis=0)
        centroids[i] = centroid
    return centroids


# 获取每个样本所属的聚类类别
def get_cluster_labels(clusters, X):
    y_pred = np.zeros(X.shape[0])
    for cluster_i, cluster in enumerate(clusters):
        for X_i in cluster:
            y_pred[X_i] = cluster_i
    return y_pred


# 根据上述各流程定义kmeans算法流程
def kmeans(X, k, max_iterations):
    # 1.初始化中心点
    centroids = centroids_init(k, X)
    # 遍历迭代求解
    for _ in range(max_iterations):
        # 2.根据当前中心点进行聚类
        clusters = build_clusters(centroids, k, X)
        # 保存当前中心点
        prev_centroids = centroids
        # 3.根据聚类结果计算新的中心点
        centroids = calculate_centroids(clusters, k, X)
        # 4.设定收敛条件为中心点是否发生变化
        diff = centroids - prev_centroids
        if not diff.any():
            break
    # 返回最终的聚类标签
    return get_cluster_labels(clusters, X)


# 测试数据
X = np.array([[0, 2], [0, 0], [1, 0], [5, 0], [5, 2]])
# 设定聚类类别为2个，最大迭代次数为10次
labels = kmeans(X, 2, 10)
# 打印每个样本所属的类别标签
print(labels)

import time
import warnings

import numpy as np
import matplotlib.pyplot as plt

from sklearn import cluster, datasets, mixture
from sklearn.neighbors import kneighbors_graph
from sklearn.preprocessing import StandardScaler
from itertools import cycle, islice

np.random.seed(0)

# 生成数据集
n_samples = 1500
noisy_circles = datasets.make_circles(n_samples=n_samples, factor=.5,
                                      noise=.05)
noisy_moons = datasets.make_moons(n_samples=n_samples, noise=.05)
blobs = datasets.make_blobs(n_samples=n_samples, random_state=8)
no_structure = np.random.rand(n_samples, 2), None

random_state = 170
X, y = datasets.make_blobs(n_samples=n_samples, random_state=random_state)
transformation = [[0.6, -0.6], [-0.4, 0.8]]
X_aniso = np.dot(X, transformation)
aniso = (X_aniso, y)

varied = datasets.make_blobs(n_samples=n_samples,
                             cluster_std=[1.0, 2.5, 0.5],
                             random_state=random_state)

# 设置聚类参数
plt.figure(figsize=(9 * 2 + 3, 12.5))
plt.subplots_adjust(left=.02, right=.98, bottom=.001, top=.96, wspace=.05,
                    hspace=.01)

plot_num = 1

default_base = {'quantile': .3,
                'eps': .3,
                'damping': .9,
                'preference': -200,
                'n_neighbors': 10,
                'n_clusters': 3,
                'min_samples': 20,
                'xi': 0.05,
                'min_cluster_size': 0.1}

datasets = [
    (noisy_circles, {'damping': .77, 'preference': -240,
                     'quantile': .2, 'n_clusters': 2,
                     'min_samples': 20, 'xi': 0.25}),
    (noisy_moons, {'damping': .75, 'preference': -220, 'n_clusters': 2}),
    (varied, {'eps': .18, 'n_neighbors': 2,
              'min_samples': 5, 'xi': 0.035, 'min_cluster_size': .2}),
    (aniso, {'eps': .15, 'n_neighbors': 2,
             'min_samples': 20, 'xi': 0.1, 'min_cluster_size': .2}),
    (blobs, {}),
    (no_structure, {})]

for i_dataset, (dataset, algo_params) in enumerate(datasets):
    params = default_base.copy()
    params.update(algo_params)

    X, y = dataset

    # 数据标准归一化
    X = StandardScaler().fit_transform(X)

    bandwidth = cluster.estimate_bandwidth(X, quantile=params['quantile'])

    connectivity = kneighbors_graph(
        X, n_neighbors=params['n_neighbors'], include_self=False)

    connectivity = 0.5 * (connectivity + connectivity.T)

    # 创建聚类对象
    ms = cluster.MeanShift(bandwidth=bandwidth, bin_seeding=True)
    two_means = cluster.MiniBatchKMeans(n_clusters=params['n_clusters'])
    ward = cluster.AgglomerativeClustering(
        n_clusters=params['n_clusters'], linkage='ward',
        connectivity=connectivity)
    spectral = cluster.SpectralClustering(
        n_clusters=params['n_clusters'], eigen_solver='arpack',
        affinity="nearest_neighbors")
    dbscan = cluster.DBSCAN(eps=params['eps'])
    affinity_propagation = cluster.AffinityPropagation(
        damping=params['damping'], preference=params['preference'])
    average_linkage = cluster.AgglomerativeClustering(
        linkage="average", affinity="cityblock",
        n_clusters=params['n_clusters'], connectivity=connectivity)
    birch = cluster.Birch(n_clusters=params['n_clusters'])
    gmm = mixture.GaussianMixture(
        n_components=params['n_clusters'], covariance_type='full')

    clustering_algorithms = (
        ('MiniBatchKMeans', two_means),
        ('AffinityPropagation', affinity_propagation),
        ('MeanShift', ms),
        ('SpectralClustering', spectral),
        ('Ward', ward),
        ('AgglomerativeClustering', average_linkage),
        ('DBSCAN', dbscan),
        ('Birch', birch),
        ('GaussianMixture', gmm)
    )

    for name, algorithm in clustering_algorithms:
        t0 = time.time()

        with warnings.catch_warnings():
            warnings.filterwarnings(
                "ignore",
                message="the number of connected components of the " +
                        "connectivity matrix is [0-9]{1,2}" +
                        " > 1. Completing it to avoid stopping the tree early.",
                category=UserWarning)
            warnings.filterwarnings(
                "ignore",
                message="Graph is not fully connected, spectral embedding" +
                        " may not work as expected.",
                category=UserWarning)
            algorithm.fit(X)

        t1 = time.time()
        if hasattr(algorithm, 'labels_'):
            y_pred = algorithm.labels_.astype(np.int)
        else:
            y_pred = algorithm.predict(X)

        plt.subplot(len(datasets), len(clustering_algorithms), plot_num)
        if i_dataset == 0:
            plt.title(name, size=18)

        colors = np.array(list(islice(cycle(['#377eb8', '#ff7f00', '#4daf4a',
                                             '#f781bf', '#a65628', '#984ea3',
                                             '#999999', '#e41a1c', '#dede00']),
                                      int(max(y_pred) + 1))))

        colors = np.append(colors, ["#000000"])
        plt.scatter(X[:, 0], X[:, 1], s=10, color=colors[y_pred])

        plt.xlim(-2.5, 2.5)
        plt.ylim(-2.5, 2.5)
        plt.xticks(())
        plt.yticks(())
        plt.text(.99, .01, ('%.2fs' % (t1 - t0)).lstrip('0'), transform=plt.gca().transAxes, size=15,
                 horizontalalignment='right')
        plot_num += 1

plt.show()