Machine Learning 简明教程

Machine Learning - Hierarchical Clustering

层次聚类是另一种无监督学习算法，用于将具有相似特征的未标记数据点分组在一起。层次聚类算法分为以下两类：

Hierarchical clustering is another unsupervised learning algorithm that is used to group together the unlabeled data points having similar characteristics. Hierarchical clustering algorithms falls into following two categories −

  1. Agglomerative hierarchical algorithms − In agglomerative hierarchical algorithms, each data point is treated as a single cluster and then successively merge or agglomerate (bottom-up approach) the pairs of clusters. The hierarchy of the clusters is represented as a dendrogram or tree structure.

  2. Divisive hierarchical algorithms − On the other hand, in divisive hierarchical algorithms, all the data points are treated as one big cluster and the process of clustering involves dividing (Top-down approach) the one big cluster into various small clusters.

Steps to Perform Agglomerative Hierarchical Clustering

我们将解释最常用、最重要的层次聚类，即凝聚。执行此操作的步骤如下 −

We are going to explain the most used and important Hierarchical clustering i.e. agglomerative. The steps to perform the same is as follows −

  1. Step 1 − Treat each data point as single cluster. Hence, we will be having say K clusters at start. The number of data points will also be K at start.

  2. Step 2 − Now, in this step we need to form a big cluster by joining two closet datapoints. This will result in total of K-1 clusters.

  3. Step 3 − Now, to form more clusters we need to join two closet clusters. This will result in total of K-2 clusters.

  4. Step 4 − Now, to form one big cluster repeat the above three steps until K would become 0 i.e. no more data points left to join.

  5. Step 5 − At last, after making one single big cluster, dendrograms will be used to divide into multiple clusters depending upon the problem.

Role of Dendrograms in Agglomerative Hierarchical Clustering

正如我们在最后一步中讨论的那样，一旦形成大簇，树状图的作用就开始了。树状图将根据我们的问题将簇分割为多个相关数据点的簇。可以通过以下示例理解它 −

As we discussed in the last step, the role of dendrogram started once the big cluster is formed. Dendrogram will be used to split the clusters into multiple cluster of related data points depending upon our problem. It can be understood with the help of following example −

Example 1

为了理解，我们从导入所需的库开始，如下所示 −

To understand, let’s start with importing the required libraries as follows −

%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np

接下来，我们将绘制我们为此示例获取的数据点 −

Next, we will be plotting the datapoints we have taken for this example −

X = np.array([[7,8],[12,20],[17,19],[26,15],[32,37],[87,75],[73,85],
[62,80],[73,60],[87,96],])
labels = range(1, 11)
plt.figure(figsize=(10, 7))
plt.subplots_adjust(bottom=0.1)
plt.scatter(X[:,0],X[:,1], label='True Position')

for label, x, y in zip(labels, X[:, 0], X[:, 1]):
   plt.annotate(label,xy=(x, y), xytext=(-3, 3),textcoords='offset points', ha='right', va='bottom')
plt.show()

执行此代码时，它将生成以下绘图作为输出 −

When you execute this code, it will produce the following plot as the output −

random dots

从上图可以很容易地看出，我们的数据点有两个簇，但在现实世界的数据中，可能有数千个簇。

From the above diagram, it is very easy to see we have two clusters in our datapoints but in real-world data, there can be thousands of clusters.

接下来，我们将使用 Scipy 库绘制我们数据点的树状图 −

Next, we will be plotting the dendrograms of our datapoints by using Scipy library −

from scipy.cluster.hierarchy import dendrogram, linkage
from matplotlib import pyplot as plt
linked = linkage(X, 'single')
labelList = range(1, 11)
plt.figure(figsize=(10, 7))

dendrogram(linked, orientation='top',labels=labelList,
distance_sort='descending',show_leaf_counts=True)

plt.show()

它将生成以下图表 −

It will produce the following plot −

building

现在，一旦形成大簇，就会选择最长的垂直距离。然后，如以下图表所示，通过它绘制一条垂直线。由于水平线在两点交叉蓝色线，因此簇的数量为两个。

Now, once the big cluster is formed, the longest vertical distance is selected. A vertical line is then drawn through it as shown in the following diagram. As the horizontal line crosses the blue line at two points hence the number of clusters would be two.

red building

接下来，我们需要导入聚类类并调用其 fit_predict 方法来预测簇。我们正在导入 AgglomerativeClustering 库的 sklearn.cluster 类 −

Next, we need to import the class for clustering and call its fit_predict method to predict the cluster. We are importing AgglomerativeClustering class of sklearn.cluster library −

from sklearn.cluster import AgglomerativeClustering

cluster = AgglomerativeClustering(n_clusters=2, affinity='euclidean',
linkage='ward')

cluster.fit_predict(X)

接下来，使用以下代码绘制簇 −

Next, plot the cluster with the help of following code −

plt.scatter(X[:,0],X[:,1], c=cluster.labels_, cmap='rainbow')

下图显示了我们数据点中的两个簇。

The following diagram shows the two clusters from our datapoints.

random red dots

Example 2

由于我们从上述简单示例中了解了树状图的概念，让我们举一个另一个示例，在该示例中，我们使用层次聚类创建 Pima 印第安人糖尿病数据集中数据点的簇 −

As we understood the concept of dendrograms from the simple example above, let’s move to another example in which we are creating clusters of the data point in Pima Indian Diabetes Dataset by using hierarchical clustering −

import matplotlib.pyplot as plt
import pandas as pd
%matplotlib inline
import numpy as np

from pandas import read_csv
path = r"C:\pima-indians-diabetes.csv"
headernames = ['preg', 'plas', 'pres', 'skin', 'test', 'mass', 'pedi', 'age', 'class']
data = read_csv(path, names=headernames)
array = data.values
X = array[:,0:8]
Y = array[:,8]

patient_data = data.iloc[:, 3:5].values
import scipy.cluster.hierarchy as shc
plt.figure(figsize=(10, 7))
plt.title("Patient Dendograms")

dend = shc.dendrogram(shc.linkage(data, method='ward'))

from sklearn.cluster import AgglomerativeClustering
cluster = AgglomerativeClustering(n_clusters=4, affinity='euclidean', linkage='ward')
cluster.fit_predict(patient_data)

plt.figure(figsize=(7.2, 5.5))
plt.scatter(patient_data[:,0], patient_data[:,1], c=cluster.labels_,
cmap='rainbow')

运行此代码时，它会生成以下两个图表作为输出 −

When you run this code, it will produce the following two plots as the output −

green building
brown