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 smfrom sklearn.preprocessing import scalefrom sklearn.preprocessing import Normalizerfrom sklearn.preprocessing import StandardScaler, MinMaxScalerfrom sklearn.cluster import KMeans, SpectralClustering, MiniBatchKMeansfrom sklearn.compose import ColumnTransformerfrom sklearn.preprocessing import OneHotEncoderimport matplotlib.pyplot as pltimport pandas as pddf = 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 columnsfeatures = 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 question

from matplotlib.patches import Rectangle, Patch  # for creating a legend

from matplotlib.lines import Line2D

# beginning with 

features = trans.fit_transform(features)

# create the model and fit it to features

kmeans_model2 = KMeans(n_clusters=7, init='k-means++', random_state=0).fit(features)

# find the centers; there are 7

centers = np.array(kmeans_model2.cluster_centers_)

# unique markers for the labels

markers = ['o', 'v', 's', '*', 'p', 'd', 'h']

# get the model labels

labels = kmeans_model2.labels_

labels_unique = set(labels)

# unique colors for each label

colors = sns.color_palette('husl', n_colors=len(labels_unique))

# color map with labels and colors

cmap = dict(zip(labels_unique, colors))

# plot

# iterate through each group of 2 centers

for 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。 featurescenters

  • print当不再需要时，可以注释掉或删除负责的行。

特征 0

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, 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 1

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, 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2

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, 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 4

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:

[0.712, 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 5

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:

[0.164, 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 6

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, 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

# plot

plt.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 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()

正如各个地块所指出的那样，有很多重叠。