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# Clustering Algorithms - Hierarchical Clustering

## Introduction to Hierarchical Clustering

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 −

**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.

**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

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

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

As we discussed in the last step, the role of dendrogram starts 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

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

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

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()

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

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, the number of clusters would be two.

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)

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

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

The above diagram shows the two clusters from our datapoints.

### Example2

As we understood the concept of dendrograms from the simple example discussed above, let us 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] data.shape (768, 9) data.head()

slno. | preg | Plas | Pres | skin | test | mass | pedi | age | class |
---|---|---|---|---|---|---|---|---|---|

0 | 6 | 148 | 72 | 35 | 0 | 33.6 | 0.627 | 50 | 1 |

1 | 1 | 85 | 66 | 29 | 0 | 26.6 | 0.351 | 31 | 0 |

2 | 8 | 183 | 64 | 0 | 0 | 23.3 | 0.672 | 32 | 1 |

3 | 1 | 89 | 66 | 23 | 94 | 28.1 | 0.167 | 21 | 0 |

4 | 0 | 137 | 40 | 35 | 168 | 43.1 | 2.288 | 33 | 1 |

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=(10, 7)) plt.scatter(patient_data[:,0], patient_data[:,1], c=cluster.labels_, cmap='rainbow')