Machine Learning 简明教程

Machine Learning - K-Medoids Clustering

K-Medoids Clustering - Algorithm

K 型 medoids 聚类算法可以总结如下：-

The K-medoids clustering algorithm can be summarized as follows −

Initialize k medoids − Select k random data points from the dataset as the initial medoids.
Assign data points to medoids − Assign each data point to the nearest medoid.
Update medoids − For each cluster, select the data point that minimizes the sum of distances to all the other data points in the cluster, and set it as the new medoid.
Repeat steps 2 and 3 until convergence or a maximum number of iterations is reached.

Implementation in Python

要在 Python 中实施 K 型 medoids 聚类，我们可以使用 scikit-learn 库。 scikit-learn 库提供了 KMedoids 类，该类可用于在数据集上执行 K 型 medoids 聚类。

To implement K-medoids clustering in Python, we can use the scikit-learn library. The scikit-learn library provides the KMedoids class, which can be used to perform K-medoids clustering on a dataset.

首先，我们需要导入所需的库：-

First, we need to import the required libraries −

from sklearn_extra.cluster import KMedoids
from sklearn.datasets import make_blobs
import matplotlib.pyplot as plt

接下来，我们使用 scikit-learn 中的 make_blobs() 函数生成示例数据集：-

Next, we generate a sample dataset using the make_blobs() function from scikit-learn −

X, y = make_blobs(n_samples=500, centers=3, random_state=42)

在此，我们生成一个包含 500 个数据点和 3 个群集的数据集。

Here, we generate a dataset with 500 data points and 3 clusters.

接下来，我们初始化 KMedoids 类并拟合数据 −

Next, we initialize the KMedoids class and fit the data −

kmedoids = KMedoids(n_clusters=3, random_state=42)
kmedoids.fit(X)

在此，我们设置群集数为 3 并使用 random_state 参数以确保可重现性。

Here, we set the number of clusters to 3 and use the random_state parameter to ensure reproducibility.

最后，我们可使用散点图可视化群集结果 −

Finally, we can visualize the clustering results using a scatter plot −

plt.figure(figsize=(7.5, 3.5))
plt.scatter(X[:, 0], X[:, 1], c=kmedoids.labels_, cmap='viridis')
plt.scatter(kmedoids.cluster_centers_[:, 0],
kmedoids.cluster_centers_[:, 1], marker='x', color='red')
plt.show()

Example

以下是完整的 Python 实现代码 −

Here is the complete implementation in Python −

from sklearn_extra.cluster import KMedoids
from sklearn.datasets import make_blobs
import matplotlib.pyplot as plt

# Generate sample data
X, y = make_blobs(n_samples=500, centers=3, random_state=42)

# Cluster the data using KMedoids
kmedoids = KMedoids(n_clusters=3, random_state=42)
kmedoids.fit(X)

# Plot the results
plt.figure(figsize=(7.5, 3.5))
plt.scatter(X[:, 0], X[:, 1], c=kmedoids.labels_, cmap='viridis')
plt.scatter(kmedoids.cluster_centers_[:, 0],
kmedoids.cluster_centers_[:, 1], marker='x', color='red')
plt.show()

在此，我们以散点图形式绘制数据点，并根据其群集标签进行着色。我们还将质心绘制为红十字。

Here, we plot the data points as a scatter plot and color them based on their cluster labels. We also plot the medoids as red crosses.

K-Medoids Clustering - Advantages

以下是使用 K-medoids 群集的优势 −

Here are the advantages of using K-medoids clustering −

Robust to outliers and noise − K-medoids clustering is more robust to outliers and noise than K-means clustering because it uses a representative data point, called a medoid, to represent the center of the cluster.
Can handle non-Euclidean distance metrics − K-medoids clustering can be used with any distance metric, including non-Euclidean distance metrics, such as Manhattan distance and cosine similarity.
Computationally efficient − K-medoids clustering has a computational complexity of O(k*n^2), which is lower than the computational complexity of K-means clustering.

K-Medoids Clustering - Disadvantages

使用 K-medoids 群集的劣势如下 −

The disadvantages of using K-medoids clustering are as follows −

Sensitive to the choice of k − The performance of K-medoids clustering can be sensitive to the choice of k, the number of clusters.
Not suitable for high-dimensional data − K-medoids clustering may not perform well on high-dimensional data because the medoid selection process becomes computationally expensive.