Course Content

Cluster Analysis in Python

1. K-Means Algorithm

Exploratory Data Analysis What is a K-Means Algorithm?Defining the Number of Clusters Case 1: Three Distinct Clusters Case 2: Four Distinct Clusters Clustering Weather Data February vs July Average Temperatures Visualizing the Dynamics Across Clusters

2. K-Medoids Algorithm

What is a K-Medoids Algorithm?Cluster Centers Silhouette Scores K-Medoids and the Weather Data Mean Yearly Temperatures Across Clusters Comparing the Dynamics

3. Hierarchical Clustering

What is a Hierarchical Clustering?Dendrograms Setting Parameters: Linkage Rand Index The Weather Data and Linkages Deciding the Number of Clusters Weather Data: Complete and Ward Linkages How Similar are the Results?

4. Spectral Clustering

What is a Spectral Clustering?Peculiarity of Spectral Clustering Setting Parameters: Affinity Defining the Number of Clusters Is 4 the Optimal Number of Clusters?Comparing the Trends Across Clusters

Silhouette Scores

Did you notice how the cluster's centers were placed in the previous chapter? That is where you can notice the key difference between K-Means and K-Medoids algorithm - in the second method the centers (medoids) have to be the data points, which makes this algorithm more useful in the case of 'uniformly' distributed points.

In the previous section, we used the total within sum of squares as defining factor for choosing the necessary number of clusters.

Consider the next metric we can use for number of clusters defining: silhouette score.

What is a Silhouette score?

The silhouette score - is the mean of all the silhouette scores calculated for each observation. There are two values calculated for each observation: mean intro-cluster distance (mean of all the distances between point and points within a predicted cluster) denoted as a, and mean nearest-cluster distance (mean of all the distances between point and all the points of the nearest cluster) denoted as b. Then, the value of (b-a)/max(a,b) is calculated for each point, and all the values are averaged. This will be the silhouette score for clustering into a certain number of clusters.

In Python, the silhouette score can be calculated by using the silhouette_score function from sklearn.metrics with two necessary parameters: the first is data used for fitting, and the second is the predicted model labels. Like for the total within sum of squares, we can also calculate the scores for a different number of clusters, then analyze the plot, and make the decision. But how should we interpret such a plot? Consider the example with random points, and two-dimensional data. The scatter plot of the data is shown below.

Let's use for loop to iterate over a different number of clusters, and then calculate the silhouette scores.


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# Import the libraries
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
from sklearn_extra.cluster import KMedoids
from sklearn.metrics import silhouette_score

# Read the data
data = pd.read_csv('https://codefinity-content-media.s3.eu-west-1.amazonaws.com/138ab9ad-aa37-4310-873f-0f62abafb038/model_data1.csv')

# Creating lists
n_cl = range(2, 9)
silhouettes = []

# Calculating silhouette scores for different number of clusters
for i in n_cl:
    model = KMedoids(n_clusters = i)
    model.fit(data)
    silhouettes.append(silhouette_score(data, model.labels_))
                      
# Visualize the results
g = sns.lineplot(x = n_cl, y = silhouettes)
g.set_xlabel('Number of clusters')
g.set_ylabel('Silhouette score')
plt.show()

The optimal number of clusters is the 'peak' of the line, where on both left and right sides are smaller values. In the chart above, the best choice is 3, but also 6 seems like an interesting choice. By the way, this method also applies to the K-Means algorithm.

Let's see how will the silhouette scores chart look for the 3-4 clusters points.

Task

Given a 2-D set of points data. The scatter plot of data is shown below.

You need to build a line plot number of clusters vs silhouette score for 2-8 clusters. Follow the next steps:

Import silhouette_score from sklearn.metrics and KMedoids from sklearn_extra.cluster.
Within the for loop:

Create KMedoids model with i clusters.
Fit the data to the model.
Add silhouette score to silhouettes list. Remember, the first parameter of the function is the data used for fitting.

Build a line plot with n_cl on the x-axis and silhouettes on the y-axis.

Switch to desktop for real-world practiceContinue from where you are using one of the options below

Everything was clear?

Thanks for your feedback!

Section 2. Chapter 3

Silhouette Scores

In the previous section, we used the total within sum of squares as defining factor for choosing the necessary number of clusters.

Consider the next metric we can use for number of clusters defining: silhouette score.

What is a Silhouette score?

Let's use for loop to iterate over a different number of clusters, and then calculate the silhouette scores.


              12345678910111213141516171819202122232425
            
# Import the libraries
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
from sklearn_extra.cluster import KMedoids
from sklearn.metrics import silhouette_score

# Read the data
data = pd.read_csv('https://codefinity-content-media.s3.eu-west-1.amazonaws.com/138ab9ad-aa37-4310-873f-0f62abafb038/model_data1.csv')

# Creating lists
n_cl = range(2, 9)
silhouettes = []

# Calculating silhouette scores for different number of clusters
for i in n_cl:
    model = KMedoids(n_clusters = i)
    model.fit(data)
    silhouettes.append(silhouette_score(data, model.labels_))
                      
# Visualize the results
g = sns.lineplot(x = n_cl, y = silhouettes)
g.set_xlabel('Number of clusters')
g.set_ylabel('Silhouette score')
plt.show()

Let's see how will the silhouette scores chart look for the 3-4 clusters points.

Task

Given a 2-D set of points data. The scatter plot of data is shown below.

You need to build a line plot number of clusters vs silhouette score for 2-8 clusters. Follow the next steps:

Import silhouette_score from sklearn.metrics and KMedoids from sklearn_extra.cluster.
Within the for loop:

Create KMedoids model with i clusters.
Fit the data to the model.
Add silhouette score to silhouettes list. Remember, the first parameter of the function is the data used for fitting.

Build a line plot with n_cl on the x-axis and silhouettes on the y-axis.

Switch to desktop for real-world practiceContinue from where you are using one of the options below

Everything was clear?

Thanks for your feedback!

Section 2. Chapter 3

Silhouette Scores

In the previous section, we used the total within sum of squares as defining factor for choosing the necessary number of clusters.

Consider the next metric we can use for number of clusters defining: silhouette score.

What is a Silhouette score?

Let's use for loop to iterate over a different number of clusters, and then calculate the silhouette scores.


              12345678910111213141516171819202122232425
            
# Import the libraries
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
from sklearn_extra.cluster import KMedoids
from sklearn.metrics import silhouette_score

# Read the data
data = pd.read_csv('https://codefinity-content-media.s3.eu-west-1.amazonaws.com/138ab9ad-aa37-4310-873f-0f62abafb038/model_data1.csv')

# Creating lists
n_cl = range(2, 9)
silhouettes = []

# Calculating silhouette scores for different number of clusters
for i in n_cl:
    model = KMedoids(n_clusters = i)
    model.fit(data)
    silhouettes.append(silhouette_score(data, model.labels_))
                      
# Visualize the results
g = sns.lineplot(x = n_cl, y = silhouettes)
g.set_xlabel('Number of clusters')
g.set_ylabel('Silhouette score')
plt.show()

Let's see how will the silhouette scores chart look for the 3-4 clusters points.

Task

Given a 2-D set of points data. The scatter plot of data is shown below.

You need to build a line plot number of clusters vs silhouette score for 2-8 clusters. Follow the next steps:

Import silhouette_score from sklearn.metrics and KMedoids from sklearn_extra.cluster.
Within the for loop:

Create KMedoids model with i clusters.
Fit the data to the model.
Add silhouette score to silhouettes list. Remember, the first parameter of the function is the data used for fitting.

Build a line plot with n_cl on the x-axis and silhouettes on the y-axis.

Switch to desktop for real-world practiceContinue from where you are using one of the options below

Everything was clear?

Thanks for your feedback!

In the previous section, we used the total within sum of squares as defining factor for choosing the necessary number of clusters.

Consider the next metric we can use for number of clusters defining: silhouette score.

What is a Silhouette score?

Let's use for loop to iterate over a different number of clusters, and then calculate the silhouette scores.


              12345678910111213141516171819202122232425
            
# Import the libraries
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
from sklearn_extra.cluster import KMedoids
from sklearn.metrics import silhouette_score

# Read the data
data = pd.read_csv('https://codefinity-content-media.s3.eu-west-1.amazonaws.com/138ab9ad-aa37-4310-873f-0f62abafb038/model_data1.csv')

# Creating lists
n_cl = range(2, 9)
silhouettes = []

# Calculating silhouette scores for different number of clusters
for i in n_cl:
    model = KMedoids(n_clusters = i)
    model.fit(data)
    silhouettes.append(silhouette_score(data, model.labels_))
                      
# Visualize the results
g = sns.lineplot(x = n_cl, y = silhouettes)
g.set_xlabel('Number of clusters')
g.set_ylabel('Silhouette score')
plt.show()

Let's see how will the silhouette scores chart look for the 3-4 clusters points.

Task

Given a 2-D set of points data. The scatter plot of data is shown below.

You need to build a line plot number of clusters vs silhouette score for 2-8 clusters. Follow the next steps:

Import silhouette_score from sklearn.metrics and KMedoids from sklearn_extra.cluster.
Within the for loop:

Create KMedoids model with i clusters.
Fit the data to the model.
Add silhouette score to silhouettes list. Remember, the first parameter of the function is the data used for fitting.

Build a line plot with n_cl on the x-axis and silhouettes on the y-axis.

Switch to desktop for real-world practiceContinue from where you are using one of the options below

Section 2. Chapter 3

Switch to desktop for real-world practiceContinue from where you are using one of the options below