Machine Learning 简明教程

Machine Learning - BIRCH Clustering

BIRCH（平衡迭代规约和集群层次）是一种分层聚类算法，设计为高效处理大型数据集。该算法通过递归地将数据划分为子簇，直到满足停止条件，从而构建一个类树的簇结构。

BIRCH (Balanced Iterative Reducing and Clustering hierarchies) is a hierarchical clustering algorithm that is designed to handle large datasets efficiently. The algorithm builds a treelike structure of clusters by recursively partitioning the data into subclusters until a stopping criterion is met.

BIRCH 使用两个主要数据结构来表示簇：聚类特征 (CF) 和子簇特征 (SCF)。CF 用于总结一组数据点的统计属性，而 SCF 用于表示子簇的结构。

BIRCH uses two main data structures to represent the clusters: Clustering Feature (CF) and Sub-Cluster Feature (SCF). CF is used to summarize the statistical properties of a set of data points, while SCF is used to represent the structure of subclusters.

BIRCH 聚类有三个主要步骤 −

BIRCH clustering has three main steps −

  1. Initialization − BIRCH constructs an empty tree structure and sets the maximum number of CFs that can be stored in a node.

  2. Clustering − BIRCH reads the data points one by one and adds them to the tree structure. If a CF is already present in a node, BIRCH updates the CF with the new data point. If there is no CF in the node, BIRCH creates a new CF for the data point. BIRCH then checks if the number of CFs in the node exceeds the maximum threshold. If the threshold is exceeded, BIRCH creates a new subcluster by recursively partitioning the CFs in the node.

  3. Refinement − BIRCH refines the tree structure by merging the subclusters that are similar based on a distance metric.

Implementation of BIRCH Clustering in Python

要在 Python 中实现 BIRCH 聚类，我们可以使用 scikit-learn 库。scikit-learn 库提供了一个实现了 BIRCH 算法的 BIRCH 类。

To implement BIRCH clustering in Python, we can use the scikit-learn library. The scikitlearn library provides a BIRCH class that implements the BIRCH algorithm.

下面是一个使用 BIRCH 类对数据集进行聚类的示例 −

Here is an example of how to use the BIRCH class to cluster a dataset −

Example

from sklearn.datasets import make_blobs
from sklearn.cluster import Birch
import matplotlib.pyplot as plt

# Generate sample data
X, y = make_blobs(n_samples=1000, centers=10, cluster_std=0.50,
random_state=0)

# Cluster the data using BIRCH
birch = Birch(threshold=1.5, n_clusters=4)
birch.fit(X)
labels = birch.predict(X)

# Plot the results
plt.figure(figsize=(7.5, 3.5))
plt.scatter(X[:, 0], X[:, 1], c=labels, cmap='winter')
plt.show()

在此示例中，我们首先使用 scikit-learn 的 make_blobs 函数生成一个样本数据集。然后，我们使用 BIRCH 算法对数据集进行聚类。对于 BIRCH 算法，我们使用阈值参数设置为 1.5，n_cluster 参数设置为 4，来实例化一个 Birch 对象。然后，我们使用 fit 方法将 Birch 对象与数据集进行匹配，并使用 predict 方法预测簇标签。最后，我们使用散点图绘制结果。

In this example, we first generate a sample dataset using the make_blobs function from scikit-learn. We then cluster the dataset using the BIRCH algorithm. For the BIRCH algorithm, we instantiate a Birch object with the threshold parameter set to 1.5 and the n_clusters parameter set to 4. We then fit the Birch object to the dataset using the fit method and predict the cluster labels using the predict method. Finally, we plot the results using a scatter plot.

当执行给定的程序时，将生成以下图表作为输出 −

When you execute the given program, it will produce the following plot as the output −

birch algorithm

Advantages of BIRCH Clustering

BIRCH 聚类比其他聚类算法具有优势，包括 −

BIRCH clustering has several advantages over other clustering algorithms, including −

  1. Scalability − BIRCH is designed to handle large datasets efficiently by using a treelike structure to represent the clusters.

  2. Memory efficiency − BIRCH uses CF and SCF data structures to summarize the statistical properties of the data points, which reduces the memory required to store the clusters.

  3. Fast clustering − BIRCH can cluster the data points quickly because it uses an incremental clustering approach.

Disadvantages of BIRCH Clustering

BIRCH 聚类还有一些缺点，包括 −

BIRCH clustering also has some disadvantages, including −

  1. Sensitivity to parameter settings − The performance of BIRCH clustering can be sensitive to the choice of parameters, such as the maximum number of CFs that can be stored in a node and the threshold value used to create subclusters.

  2. Limited ability to handle non-spherical clusters − BIRCH assumes that the clusters are spherical, which means it may not perform well on datasets with nonspherical clusters.

  3. Limited flexibility in the choice of distance metric − BIRCH uses the Euclidean distance metric by default, which may not be appropriate for all datasets.