K-Means Clustering is a concept that falls under *Unsupervised* Learning. This algorithm can be used to find groups within *unlabeled* data.

Topics to be covered:

- Creating a DataFrame for a two-dimensional dataset
- Finding the centroids of 3 clusters, and then of 4 clusters

## Example of K-Means Clustering in Python

To start, here is an example of a two-dimensional dataset:

import pandas as pd

data = {

"x": [25, 34, 22, 27, 33, 33, 31, 22, 35, 34, 67, 54, 57, 43, 50, 57, 59, 52, 65, 47, 49, 48, 35, 33, 44, 45, 38,

43, 51, 46],

"y": [79, 51, 53, 78, 59, 74, 73, 57, 69, 75, 51, 32, 40, 47, 53, 36, 35, 58, 59, 50, 25, 20, 14, 12, 20, 5, 29, 27,

8, 7]

}

df = pd.DataFrame(data)

print(df)

Run the code in Python, and you’ll get the following DataFrame:

```
x y
0 25 79
1 34 51
2 22 53
3 27 78
4 33 59
5 33 74
6 31 73
7 22 57
8 35 69
9 34 75
10 67 51
11 54 32
12 57 40
13 43 47
14 50 53
15 57 36
16 59 35
17 52 58
18 65 59
19 47 50
20 49 25
21 48 20
22 35 14
23 33 12
24 44 20
25 45 5
26 38 29
27 43 27
28 51 8
29 46 7
```

### Find the Centroids of 3 Clusters

First, install the Matplotlib package. This package will be used to create the chart in Python.

pip install matplotlib

Then install the sklearn package. This package will be used to apply the K-Means Clustering in Python.

pip install scikit-learn

You can then specify the number of clusters. For example, assign 3 clusters as follows:

`KMeans(n_clusters=3)`

The complete code to find the centroids of 3 clusters:

import pandas as pd

import matplotlib.pyplot as plt

from sklearn.cluster import KMeans

data = {

"x": [25, 34, 22, 27, 33, 33, 31, 22, 35, 34, 67, 54, 57, 43, 50, 57, 59, 52, 65, 47, 49, 48, 35, 33, 44, 45, 38,

43, 51, 46],

"y": [79, 51, 53, 78, 59, 74, 73, 57, 69, 75, 51, 32, 40, 47, 53, 36, 35, 58, 59, 50, 25, 20, 14, 12, 20, 5, 29, 27,

8, 7]

}

df = pd.DataFrame(data)

kmeans = KMeans(n_clusters=3)

kmeans.fit(df)

centroids = kmeans.cluster_centers_

print(centroids)

plt.scatter(df["x"], df["y"], c=kmeans.labels_.astype(float), s=50, alpha=0.5)

plt.scatter(centroids[:, 0], centroids[:, 1], c="red", s=50)

plt.show()

Run the code in Python, and you’ll see 3 clusters with 3 distinct centroids:

```
[[29.6 66.8]
[43.2 16.7]
[55.1 46.1]]
```

Note that the center of each cluster represents the mean of all the observations that belong to that cluster.

Additionally, the observations that belong to a given cluster are closer to the center of that cluster, in comparison to the centers of other clusters.

### Find the Centroids of 4 Clusters

In this case, change the *n_clusters* from 3 to 4:

`KMeans(n_clusters=4)`

The full Python code for 4 clusters:

import pandas as pd

import matplotlib.pyplot as plt

from sklearn.cluster import KMeans

data = {

"x": [25, 34, 22, 27, 33, 33, 31, 22, 35, 34, 67, 54, 57, 43, 50, 57, 59, 52, 65, 47, 49, 48, 35, 33, 44, 45, 38,

43, 51, 46],

"y": [79, 51, 53, 78, 59, 74, 73, 57, 69, 75, 51, 32, 40, 47, 53, 36, 35, 58, 59, 50, 25, 20, 14, 12, 20, 5, 29, 27,

8, 7]

}

df = pd.DataFrame(data)

kmeans = KMeans(n_clusters=4)

kmeans.fit(df)

centroids = kmeans.cluster_centers_

print(centroids)

plt.scatter(df["x"], df["y"], c=kmeans.labels_.astype(float), s=50, alpha=0.5)

plt.scatter(centroids[:, 0], centroids[:, 1], c="red", s=50)

plt.show()

Run the code, and you’ll now see 4 clusters with 4 distinct centroids:

```
[[27.75 55. ]
[43.2 16.7 ]
[55.1 46.1 ]
[30.83333333 74.66666667]]
```

That’s it. You can learn more about the application of K-Means Clusters in Python by visiting the sklearn documentation.