Зміст курсу

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

Dendrograms

In the previous sections, we used two metrics to help us to define the number of clusters in data. These were the total within sum of squares, and silhouette score. Both of the methods equally work either with K-Means, either K-Medoids methods. But these are not applicable for Hierarchical clustering.

As was mentioned in the previous chapter, at each step some metric is used to decide whether the clusters should be merged or not. This process can continue up to one single cluster with all the points. So, how to choose where should we stop? The dendrogram is the solution! The dendrogram visualizes the distances between the points.

To build a dendrogram in Python, firstly you need to calculate all the distances between the points of your data. It can be easily done with the linkage function from the scipy.cluster.hierarchy library. This function requires the numerical data matrix (DataFrame) as the first parameter. Also, there is parameters method (by default 'single') and metric (by default 'euclidean') that can be changed, but we will consider that later. After computing the distances, you can visualize them by using the dendrogram function from the same library (scipy.cluster.hierarchy) passing the distances matrix (computed with the linkage function) as a parameter. This function also has multiple additional parameters that can be changed, but they will be considered later. Watch out for the example below!


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# Import the libraries
import pandas as pd
import matplotlib.pyplot as plt
from scipy.cluster.hierarchy import linkage, dendrogram

# Read the data
data = pd.read_csv('https://codefinity-content-media.s3.eu-west-1.amazonaws.com/138ab9ad-aa37-4310-873f-0f62abafb038/train_data1.csv')

# Compute the distances
dist = linkage(data)

# Build the dendrogram
dendrogram(dist)
plt.show()

How should you read this plot? The division there was so obvious that algorithms automatically colored the nodes with 2 colors. The height of the vertical line - is the distance between points and/or clusters. The higher it is, the more distinct clusters are. There you can see that the maximum distances within orange and green areas are 1, while the distance between them significantly higher. Remember, there is no correct answer to the clustering problems. The labels on the x-axis are the values' indices, and they can be customized.

Завдання

Given the 2-D set of points data (training dataset). The scatter plot is shown below.

[object Object]

Build the dendrogram for this data. Follow the next steps:

Import dendrogram and linkage from scipy.cluster.hierarchy.
Compute the distances of data points using the linkage function. Save the result within the dist variable.
Build a dendrogram visualizing the dist. Do not set any additional parameters.

Завдання

Given the 2-D set of points data (training dataset). The scatter plot is shown below.

[object Object]

Build the dendrogram for this data. Follow the next steps:

Import dendrogram and linkage from scipy.cluster.hierarchy.
Compute the distances of data points using the linkage function. Save the result within the dist variable.
Build a dendrogram visualizing the dist. Do not set any additional parameters.

Перейдіть на комп'ютер для реальної практикиПродовжуйте з того місця, де ви зупинились, використовуючи один з наведених нижче варіантів

Все було зрозуміло?

Секція 3. Розділ 2

Dendrograms


              1234567891011121314
            
# Import the libraries
import pandas as pd
import matplotlib.pyplot as plt
from scipy.cluster.hierarchy import linkage, dendrogram

# Read the data
data = pd.read_csv('https://codefinity-content-media.s3.eu-west-1.amazonaws.com/138ab9ad-aa37-4310-873f-0f62abafb038/train_data1.csv')

# Compute the distances
dist = linkage(data)

# Build the dendrogram
dendrogram(dist)
plt.show()

Завдання

Given the 2-D set of points data (training dataset). The scatter plot is shown below.

[object Object]

Build the dendrogram for this data. Follow the next steps:

Import dendrogram and linkage from scipy.cluster.hierarchy.
Compute the distances of data points using the linkage function. Save the result within the dist variable.
Build a dendrogram visualizing the dist. Do not set any additional parameters.

Завдання

Given the 2-D set of points data (training dataset). The scatter plot is shown below.

[object Object]

Build the dendrogram for this data. Follow the next steps:

Import dendrogram and linkage from scipy.cluster.hierarchy.
Compute the distances of data points using the linkage function. Save the result within the dist variable.
Build a dendrogram visualizing the dist. Do not set any additional parameters.

Все було зрозуміло?

Секція 3. Розділ 2

Dendrograms


              1234567891011121314
            
# Import the libraries
import pandas as pd
import matplotlib.pyplot as plt
from scipy.cluster.hierarchy import linkage, dendrogram

# Read the data
data = pd.read_csv('https://codefinity-content-media.s3.eu-west-1.amazonaws.com/138ab9ad-aa37-4310-873f-0f62abafb038/train_data1.csv')

# Compute the distances
dist = linkage(data)

# Build the dendrogram
dendrogram(dist)
plt.show()

Завдання

Given the 2-D set of points data (training dataset). The scatter plot is shown below.

[object Object]

Build the dendrogram for this data. Follow the next steps:

Import dendrogram and linkage from scipy.cluster.hierarchy.
Compute the distances of data points using the linkage function. Save the result within the dist variable.
Build a dendrogram visualizing the dist. Do not set any additional parameters.

Завдання

Given the 2-D set of points data (training dataset). The scatter plot is shown below.

[object Object]

Build the dendrogram for this data. Follow the next steps:

Import dendrogram and linkage from scipy.cluster.hierarchy.
Compute the distances of data points using the linkage function. Save the result within the dist variable.
Build a dendrogram visualizing the dist. Do not set any additional parameters.

Все було зрозуміло?


              1234567891011121314
            
# Import the libraries
import pandas as pd
import matplotlib.pyplot as plt
from scipy.cluster.hierarchy import linkage, dendrogram

# Read the data
data = pd.read_csv('https://codefinity-content-media.s3.eu-west-1.amazonaws.com/138ab9ad-aa37-4310-873f-0f62abafb038/train_data1.csv')

# Compute the distances
dist = linkage(data)

# Build the dendrogram
dendrogram(dist)
plt.show()

Завдання

Given the 2-D set of points data (training dataset). The scatter plot is shown below.

[object Object]

Build the dendrogram for this data. Follow the next steps:

Import dendrogram and linkage from scipy.cluster.hierarchy.
Compute the distances of data points using the linkage function. Save the result within the dist variable.
Build a dendrogram visualizing the dist. Do not set any additional parameters.

Секція 3. Розділ 2