import random import numpy as np import matplotlib.pyplot as plt 生成随机坐标点 def generate_points(num_points): points = [] for i in range(num_points): x = random.uniform(-10, 10) y = random.uniform(-10, 10) points.append([x, y]) return points 计算欧几里得距离 def euclidean_distance(point1, point2): return np.sqrt(np.sum(np.square(np.array(point1) - np.array(point2)))) K-means算法实现 def kmeans(points, k, num_iterations=100): num_points = len(points) # 随机选择k个点作为初始聚类中心 centroids = random.sample(points, k) # 初始化聚类标签和距离 labels = np.zeros(num_points) distances = np.zeros((num_points, k)) for i in range(num_iterations): # 计算每个点到每个聚类中心的距离 for j in range(num_points): for l in range(k): distances[j][l] = euclidean_distance(points[j], centroids[l]) # 根据距离将点分配到最近的聚类中心 for j in range(num_points): labels[j] = np.argmin(distances[j]) # 更新聚类中心 for l in range(k): centroids[l] = np.mean([points[j] for j in range(num_points) if labels[j] == l], axis=0) return labels, centroids 生成坐标点 points = generate_points(100) 对点进行K-means聚类 k_values = [2, 3, 4] for k in k_values: labels, centroids = kmeans(points, k) # 绘制聚类结果 colors = [‘r’, ‘g’, ‘b’, ‘y’, ‘c’, ‘m’] for i in range(k): plt.scatter([points[j][0] for j in range(len(points)) if labels[j] == i], [points[j][1] for j in range(len(points)) if labels[j] == i], color=colors[i]) plt.scatter([centroid[0] for centroid in centroids], [centroid[1] for centroid in centroids], marker=‘x’, color=‘k’, s=100) plt.title(‘K-means clustering with k={}’.format(k)) plt.show()import numpy as np import pandas as pd import matplotlib.pyplot as plt from sklearn.cluster import KMeans from sklearn.datasets import load_iris 载入数据集 iris = load_iris() X = iris.data y = iris.target K-means聚类 kmeans = KMeans(n_clusters=3, random_state=0).fit(X) 可视化结果 plt.scatter(X[:, 0], X[:, 1], c=kmeans.labels_) plt.xlabel(‘Sepal length’) plt.ylabel(‘Sepal width’) plt.title(‘K-means clustering on iris dataset’) plt.show()对这个算法的结果用SSE，轮廓系数，方差比率准则，DBI几个指标分析

首先，我们需要定义这些指标：

1. SSE (Sum of Squared Errors)：误差平方和，表示每个点到其所属簇中心的距离的平方和，用于评估聚类效果的好坏。

2. 轮廓系数 (Silhouette Coefficient)：表示一个样本与其所属簇内其他样本的相似度，与其与最近簇的其他样本的相似度之间的比值，取值范围为[-1, 1]，越接近1表示聚类效果越好。

3. 方差比率准则 (Variance Ratio Criterion)：表示不同簇之间的距离与同一簇内部的距离的比值，用于评估聚类效果的好坏。

4. DBI (Davies-Bouldin Index)：表示不同簇之间的距离与同一簇内部的距离之和的比值，用于评估聚类效果的好坏。

接下来，我们分别用这些指标来评估上面两段代码实现的K-means算法的聚类效果。

对于第一段代码，我们可以在K-means算法的函数中添加计算SSE的代码，并在函数返回值中返回SSE的值。同时，我们可以使用sklearn库中的metrics模块来计算轮廓系数。方差比率准则的计算与SSE类似，只需要将距离平方和改为距离的平方和，即可得到方差比率准则的值。DBI的计算可以使用sklearn库中的metrics模块中的davies_bouldin_score函数来实现。

代码如下所示：

import random import numpy as np import matplotlib.pyplot as plt from sklearn.metrics import silhouette_score from sklearn.metrics import davies_bouldin_score  # 生成随机坐标点 def generate_points(num_points):     points = []     for i in range(num_points):         x = random.uniform(-10, 10)         y = random.uniform(-10, 10)         points.append([x, y])     return points   # 计算欧几里得距离 def euclidean_distance(point1, point2):     return np.sqrt(np.sum(np.square(np.array(point1) - np.array(point2))))   # K-means算法实现 def kmeans(points, k, num_iterations=100):     num_points = len(points)     # 随机选择k个点作为初始聚类中心     centroids = random.sample(points, k)     # 初始化聚类标签和距离     labels = np.zeros(num_points)     distances = np.zeros((num_points, k))     sse = 0     for i in range(num_iterations):         # 计算每个点到每个聚类中心的距离         for j in range(num_points):             for l in range(k):                 distances[j][l] = euclidean_distance(points[j], centroids[l])         # 根据距离将点分配到最近的聚类中心         for j in range(num_points):             labels[j] = np.argmin(distances[j])         # 更新聚类中心         for l in range(k):             centroids[l] = np.mean([points[j] for j in range(num_points) if labels[j] == l], axis=0)         # 计算SSE         sse = np.sum(np.square(distances[np.arange(num_points), labels]))     # 计算轮廓系数     silhouette = silhouette_score(points, labels)     # 计算方差比率准则     var_ratio = np.sum(np.min(distances, axis=1)) / sse     # 计算DBI     dbi = davies_bouldin_score(points, labels)     return labels, centroids, sse, silhouette, var_ratio, dbi   # 生成坐标点 points = generate_points(100)   # 对点进行K-means聚类 k_values = [2, 3, 4] for k in k_values:     labels, centroids, sse, silhouette, var_ratio, dbi = kmeans(points, k)     # 绘制聚类结果     colors = ['r', 'g', 'b', 'y', 'c', 'm']     for i in range(k):         plt.scatter([points[j][0] for j in range(len(points)) if labels[j] == i],                    [points[j][1] for j in range(len(points)) if labels[j] == i], color=colors[i])     plt.scatter([centroid[0] for centroid in centroids],                 [centroid[1] for centroid in centroids], marker='x', color='k', s=100)     plt.title('K-means clustering with k={}'.format(k))     plt.show()     print('SSE: {:.2f}'.format(sse))     print('Silhouette: {:.2f}'.format(silhouette))     print('Variance Ratio Criterion: {:.2f}'.format(var_ratio))     print('DBI: {:.2f}'.format(dbi)) 

对于第二段代码，我们可以使用sklearn库中的metrics模块来计算SSE、轮廓系数和DBI，方差比率准则的计算方法与第一段代码相同。

代码如下所示：

import numpy as np import pandas as pd import matplotlib.pyplot as plt from sklearn.cluster import KMeans from sklearn.datasets import load_iris from sklearn.metrics import silhouette_score from sklearn.metrics import davies_bouldin_score  # 载入数据集 iris = load_iris() X = iris.data y = iris.target   # K-means聚类 kmeans = KMeans(n_clusters=3, random_state=0).fit(X)   # 计算SSE sse = np.sum(np.square(X - kmeans.cluster_centers_[kmeans.labels_]))   # 计算轮廓系数 silhouette = silhouette_score(X, kmeans.labels_)   # 计算方差比率准则 var_ratio = kmeans.inertia_ / sse   # 计算DBI dbi = davies_bouldin_score(X, kmeans.labels_)   # 可视化结果 plt.scatter(X[:, 0], X[:, 1], c=kmeans.labels_) plt.xlabel('Sepal length') plt.ylabel('Sepal width') plt.title('K-means clustering on iris dataset') plt.show() print('SSE: {:.2f}'.format(sse)) print('Silhouette: {:.2f}'.format(silhouette)) print('Variance Ratio Criterion: {:.2f}'.format(var_ratio)) print('DBI: {:.2f}'.format(dbi)) 

通过这些指标的计算，我们可以得到K-means算法的聚类效果的好坏。一般来说，SSE和轮廓系数越小，方差比率准则越大，DBI越小，则聚类效果越好。