如何使用 Matplotlib 从多特征 kmeans 模型中绘制聚类和中心？

Question

我使用kmeans算法来确定数据集中的簇数。在下面的代码中，您可以看到我有多个特征，有些是分类的，有些不是。我对它们进行编码和缩放，然后我得到了我的最佳簇数。

您可以从这里下载数据：

import sklearn.metrics as sm

from sklearn.preprocessing import scale

from sklearn.preprocessing import Normalizer

from sklearn.preprocessing import StandardScaler, MinMaxScaler

from sklearn.cluster import KMeans, SpectralClustering, MiniBatchKMeans

from sklearn.compose import ColumnTransformer

from sklearn.preprocessing import OneHotEncoder

import matplotlib.pyplot as plt

import pandas as pd

df = pd.read_csv('dataset.csv')

print(df.columns)

features = df[['parcela', 'bruto', 'neto',

               'osnova', 'sipovi', 'nadzemno',

               'podzemno', 'tavanica', 'fasada']]

trans = ColumnTransformer(transformers=[('onehot', OneHotEncoder(), ['tavanica', 'fasada']),

                                        ('StandardScaler', Normalizer(), ['parcela', 'bruto', 'neto', 'osnova', 'nadzemno', 'podzemno', 'sipovi'])],

                          remainder='passthrough') # Default is to drop untransformed columns

features = trans.fit_transform(features)

Sum_of_squared_distances = []

for i in range(1,19):

     kmeans = KMeans(n_clusters = i, init = 'k-means++', random_state = 0)

     kmeans.fit(features)

     Sum_of_squared_distances.append(kmeans.inertia_)

plt.plot(range(1,19), Sum_of_squared_distances, 'bx-')

plt.xlabel('k')

plt.ylabel('Sum_of_squared_distances')

plt.title('Elbow Method For Optimal k')

plt.show()

• 在图表上，肘部方法显示我的最佳聚类数为 7。

• 如何绘制 7 个集群？

  • 我想在图表上看到质心，以及具有 7 种不同颜色的簇的散点图。

Answer 1

给定图：kmeans 聚类质心，其中centers是一维。该centers数组有一个(3, 2)形状，带有xas(3, 1)和yas (3, 1)。针对这个一维中心展示的方法，已经适用于为中心的七个维度生成一个解决方案，由模型为这个问题生成。此问题中模型的返回值有七个维度，其中centers的形状是 7 组和值。(7, 14)14xy这个解决方案回答了这个问题，How to plot the clusters & centers?它不提供对模型结果的评论或解释，这需要在SE: Cross Validated或SE: Data Science中提出不同的问题。# uses the imports as shown in the questionfrom matplotlib.patches import Rectangle, Patch  # for creating a legendfrom matplotlib.lines import Line2D# beginning with features = trans.fit_transform(features)# create the model and fit it to featureskmeans_model2 = KMeans(n_clusters=7, init='k-means++', random_state=0).fit(features)# find the centers; there are 7centers = np.array(kmeans_model2.cluster_centers_)# unique markers for the labelsmarkers = ['o', 'v', 's', '*', 'p', 'd', 'h']# get the model labelslabels = kmeans_model2.labels_labels_unique = set(labels)# unique colors for each labelcolors = sns.color_palette('husl', n_colors=len(labels_unique))# color map with labels and colorscmap = dict(zip(labels_unique, colors))# plot# iterate through each group of 2 centersfor j in range(0, len(centers)*2, 2):    plt.figure(figsize=(6, 6))        x_features = features[:, j]    y_features = features[:, j+1]    x_centers = centers[:, j]    y_centers = centers[:, j+1]        # add the data for each label to the plot    for i, l in enumerate(labels):#         print(f'Label: {l}')  # uncomment as needed#         print(f'feature x coordinates for label:\n{x_features[i]}')  # uncomment as needed#         print(f'feature y coordinates for label:\n{y_features[i]}')  # uncomment as needed        plt.plot(x_features[i], y_features[i], color=colors[l], marker=markers[l], alpha=0.5)    # print values for given plot, rounded for easier interpretation; all 4 can be commented out    print(f'feature labels:\n{list(labels)}')    print(f'x_features:\n{list(map(lambda x: round(x, 3), x_features))}')    print(f'y_features:\n{list(map(lambda x: round(x, 3), y_features))}')    print(f'x_centers:\n{list(map(lambda x: round(x, 3), x_centers))}')    print(f'y_centers:\n{list(map(lambda x: round(x, 3), y_centers))}')        # add the centers    # this loop is to color the center marker to correspond to the color of the corresponding label.    for k in range(len(centers)):          plt.scatter(x_centers[k], y_centers[k], marker="X", color=colors[k])        # title    plt.title(f'Features: Dimension {int(j/2)}')        # create the rectangles for the legend    patches = [Patch(color=v, label=k) for k, v in cmap.items()]    # create centers marker for the legend    black_x = Line2D([], [], color='k', marker='X', linestyle='None', label='centers', markersize=10)    # add the legend    plt.legend(title='Labels', handles=patches + [black_x], bbox_to_anchor=(1.04, 0.5), loc='center left', borderaxespad=0, fontsize=15)        plt.show()绘图输出许多绘制的特征具有重叠的值和中心。和的x和y值已被打印出来，以便更容易地看到重叠，并确认绘制的值。 featurescentersprint当不再需要时，可以注释掉或删除负责的行。特征 0feature labels:[6, 1, 1, 1, 5, 5, 3, 4, 1, 0, 1, 5, 5, 1, 1, 1, 1, 1, 4, 1, 2, 0, 1, 3, 3, 4, 2, 2, 4, 3, 3, 2, 6, 3, 1, 2, 4, 6, 1, 4, 4, 1, 4, 5, 3, 1, 1, 1, 1, 1, 0, 1, 5, 5, 1, 1, 3, 3, 3, 1, 3, 1, 3, 3, 0, 1, 2, 2, 2, 6]x_features:[0.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.0, 0.0, 1.0, 1.0, 1.0, 0.0, 0.0, 1.0, 1.0, 0.0, 1.0, 0.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0]y_features:[1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 0.0, 0.0, 0.0, 1.0, 1.0, 0.0, 0.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0]x_centers:[1.0, 1.0, 0.0, 1.0, 1.0, 1.0, 0.0]y_centers:[0.0, 0.0, 1.0, 0.0, -0.0, -0.0, 1.0]特点 1feature labels:[6, 1, 1, 1, 5, 5, 3, 4, 1, 0, 1, 5, 5, 1, 1, 1, 1, 1, 4, 1, 2, 0, 1, 3, 3, 4, 2, 2, 4, 3, 3, 2, 6, 3, 1, 2, 4, 6, 1, 4, 4, 1, 4, 5, 3, 1, 1, 1, 1, 1, 0, 1, 5, 5, 1, 1, 3, 3, 3, 1, 3, 1, 3, 3, 0, 1, 2, 2, 2, 6]x_features:[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0]y_features:[1.0, 1.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 1.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 1.0, 0.0, 0.0, 1.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.0, 1.0, 0.0, 0.0, 1.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0]x_centers:[1.0, -0.0, -0.0, -0.0, -0.0, 0.0, 0.0]y_centers:[0.0, 1.0, 0.0, -0.0, 0.0, 0.0, 1.0]特征2feature labels:[6, 1, 1, 1, 5, 5, 3, 4, 1, 0, 1, 5, 5, 1, 1, 1, 1, 1, 4, 1, 2, 0, 1, 3, 3, 4, 2, 2, 4, 3, 3, 2, 6, 3, 1, 2, 4, 6, 1, 4, 4, 1, 4, 5, 3, 1, 1, 1, 1, 1, 0, 1, 5, 5, 1, 1, 3, 3, 3, 1, 3, 1, 3, 3, 0, 1, 2, 2, 2, 6]x_features:[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 0.0, 1.0, 0.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0]y_features:[0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]x_centers:[0.0, -0.0, 0.125, 1.0, 0.0, 0.0, 0.0]y_centers:[0.0, -0.0, 0.0, 0.0, 0.0, 1.0, 0.0]特色三feature labels:[6, 1, 1, 1, 5, 5, 3, 4, 1, 0, 1, 5, 5, 1, 1, 1, 1, 1, 4, 1, 2, 0, 1, 3, 3, 4, 2, 2, 4, 3, 3, 2, 6, 3, 1, 2, 4, 6, 1, 4, 4, 1, 4, 5, 3, 1, 1, 1, 1, 1, 0, 1, 5, 5, 1, 1, 3, 3, 3, 1, 3, 1, 3, 3, 0, 1, 2, 2, 2, 6]x_features:[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 1.0, 0.0, 0.0, 1.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 0.0, 0.0]y_features:[0.298, 0.193, 0.18, 0.336, 0.181, 0.174, 0.197, 0.23, 0.175, 0.212, 0.196, 0.186, 0.2, 0.15, 0.141, 0.304, 0.108, 0.101, 0.304, 0.105, 0.459, 0.18, 0.16, 0.224, 0.216, 0.246, 0.139, 0.111, 0.227, 0.177, 0.159, 0.25, 0.298, 0.223, 0.335, 0.431, 0.17, 0.381, 0.255, 0.222, 0.296, 0.156, 0.202, 0.145, 0.195, 0.15, 0.141, 0.18, 0.336, 0.175, 0.212, 0.196, 0.186, 0.2, 0.15, 0.141, 0.177, 0.177, 0.177, 0.177, 0.177, 0.177, 0.224, 0.224, 0.18, 0.16, 0.222, 0.202, 0.18, 0.336]x_centers:[0.0, -0.0, 0.875, -0.0, 1.0, 0.0, 0.0]y_centers:[0.196, 0.188, 0.249, 0.196, 0.237, 0.182, 0.328]特点 4feature labels:[6, 1, 1, 1, 5, 5, 3, 4, 1, 0, 1, 5, 5, 1, 1, 1, 1, 1, 4, 1, 2, 0, 1, 3, 3, 4, 2, 2, 4, 3, 3, 2, 6, 3, 1, 2, 4, 6, 1, 4, 4, 1, 4, 5, 3, 1, 1, 1, 1, 1, 0, 1, 5, 5, 1, 1, 3, 3, 3, 1, 3, 1, 3, 3, 0, 1, 2, 2, 2, 6]x_features:[0.712, 0.741, 0.763, 0.704, 0.749, 0.741, 0.754, 0.735, 0.744, 0.738, 0.743, 0.747, 0.758, 0.759, 0.749, 0.714, 0.766, 0.748, 0.728, 0.755, 0.681, 0.752, 0.762, 0.734, 0.721, 0.747, 0.749, 0.756, 0.737, 0.748, 0.742, 0.724, 0.712, 0.733, 0.73, 0.688, 0.722, 0.705, 0.777, 0.749, 0.733, 0.744, 0.733, 0.764, 0.739, 0.76, 0.749, 0.763, 0.704, 0.744, 0.738, 0.743, 0.747, 0.758, 0.759, 0.749, 0.748, 0.748, 0.748, 0.748, 0.748, 0.748, 0.734, 0.734, 0.752, 0.762, 0.749, 0.733, 0.763, 0.704]y_features:[0.614, 0.636, 0.612, 0.601, 0.631, 0.64, 0.62, 0.624, 0.636, 0.633, 0.632, 0.63, 0.61, 0.629, 0.641, 0.616, 0.629, 0.65, 0.601, 0.644, 0.539, 0.628, 0.623, 0.627, 0.65, 0.603, 0.641, 0.641, 0.616, 0.632, 0.648, 0.631, 0.614, 0.624, 0.58, 0.562, 0.666, 0.587, 0.565, 0.616, 0.591, 0.646, 0.642, 0.625, 0.631, 0.629, 0.641, 0.612, 0.601, 0.636, 0.633, 0.632, 0.63, 0.61, 0.629, 0.641, 0.632, 0.632, 0.632, 0.632, 0.632, 0.632, 0.627, 0.627, 0.628, 0.623, 0.616, 0.642, 0.612, 0.601]x_centers:[0.745, 0.747, 0.73, 0.741, 0.735, 0.752, 0.708]y_centers:[0.63, 0.625, 0.611, 0.632, 0.62, 0.625, 0.604]特点 5feature labels:[6, 1, 1, 1, 5, 5, 3, 4, 1, 0, 1, 5, 5, 1, 1, 1, 1, 1, 4, 1, 2, 0, 1, 3, 3, 4, 2, 2, 4, 3, 3, 2, 6, 3, 1, 2, 4, 6, 1, 4, 4, 1, 4, 5, 3, 1, 1, 1, 1, 1, 0, 1, 5, 5, 1, 1, 3, 3, 3, 1, 3, 1, 3, 3, 0, 1, 2, 2, 2, 6]x_features:[0.164, 0.096, 0.103, 0.171, 0.091, 0.106, 0.094, 0.132, 0.105, 0.098, 0.102, 0.101, 0.115, 0.079, 0.095, 0.135, 0.075, 0.088, 0.126, 0.063, 0.186, 0.088, 0.075, 0.134, 0.107, 0.134, 0.09, 0.072, 0.16, 0.097, 0.073, 0.123, 0.165, 0.154, 0.133, 0.158, 0.084, 0.11, 0.105, 0.1, 0.164, 0.075, 0.1, 0.075, 0.135, 0.069, 0.095, 0.103, 0.171, 0.105, 0.098, 0.102, 0.101, 0.115, 0.079, 0.095, 0.097, 0.097, 0.097, 0.097, 0.097, 0.097, 0.134, 0.134, 0.088, 0.075, 0.1, 0.1, 0.103, 0.171]y_features:[0.001, 0.002, 0.001, 0.001, 0.001, 0.002, 0.002, 0.001, 0.001, 0.001, 0.001, 0.005, 0.002, 0.001, 0.002, 0.001, 0.002, 0.001, 0.001, 0.002, 0.0, 0.001, 0.001, 0.002, 0.0, 0.001, 0.001, 0.002, 0.002, 0.002, 0.0, 0.001, 0.001, 0.001, 0.004, 0.004, 0.001, 0.002, 0.001, 0.001, 0.002, 0.0, 0.001, 0.001, 0.001, 0.001, 0.0, 0.001, 0.001, 0.001, 0.0, 0.0, 0.003, 0.001, 0.001, 0.001, 0.001, 0.001, 0.001, 0.0, 0.002, 0.001, 0.001, 0.0, 0.001, 0.001, 0.002, 0.002, 0.002, 0.001]x_centers:[0.093, 0.1, 0.116, 0.112, 0.125, 0.101, 0.152]y_centers:[0.001, 0.001, 0.002, 0.001, 0.001, 0.002, 0.001]特征 6feature labels:[6, 1, 1, 1, 5, 5, 3, 4, 1, 0, 1, 5, 5, 1, 1, 1, 1, 1, 4, 1, 2, 0, 1, 3, 3, 4, 2, 2, 4, 3, 3, 2, 6, 3, 1, 2, 4, 6, 1, 4, 4, 1, 4, 5, 3, 1, 1, 1, 1, 1, 0, 1, 5, 5, 1, 1, 3, 3, 3, 1, 3, 1, 3, 3, 0, 1, 2, 2, 2, 6]x_features:[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.002, 0.0, 0.0, 0.001, 0.0, 0.001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001, 0.001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]y_features:[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]x_centers:[0.0, 0.0, 0.0, 0.0, 0.0, 0.001, 0.0]y_centers:[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]在一个图上更新所有维度根据 OP 的要求# plotplt.figure(figsize=(16, 8))for j in range(0, len(centers)*2, 2):        x_features = features[:, j]    y_features = features[:, j+1]    x_centers = centers[:, j]    y_centers = centers[:, j+1]        # add the data for each label to the plot    for i, l in enumerate(labels):        plt.plot(x_features[i], y_features[i], marker=markers[int(j/2)], color=colors[int(j/2)], alpha=0.5)    # add the centers    for k in range(len(centers)):          plt.scatter(x_centers[k], y_centers[k], marker="X", color=colors[int(j/2)])# create the rectangles for the legendpatches = [Patch(color=v, label=k) for k, v in cmap.items()]# create centers marker for the legendblack_x = Line2D([], [], color='k', marker='X', linestyle='None', label='centers', markersize=10)# add the legendplt.legend(title='Labels', handles=patches + [black_x], bbox_to_anchor=(1.04, 0.5), loc='center left', borderaxespad=0, fontsize=15)    plt.show()正如各个地块所指出的那样，有很多重叠。