## Clustering Algorithms: A Look at K-Means Clustering

Machine learning is revolutionizing the way we analyze data. One popular technique is clustering, which groups data points with similar characteristics.

There are many clustering algorithms, but one of the most widely used is K-means clustering. In this article, we’ll explain the fundamentals of K-means clustering, from choosing the value of K to updating cluster assignments.

K-means clustering groups data points into K clusters, where K is a user-defined value. The algorithm works by maximizing the similarity between the observations within each cluster and minimizing the similarity between observations in different clusters.

The similarity between two observations is usually defined as the distance between them. Euclidean distance, a mathematical formula that measures the straight-line distance between two points in space, is the most commonly used similarity metric.

K-means clustering is available in many machine learning libraries, including scikit-learn (sklearn) in Python. To perform K-means clustering using sklearn, we first need to import the library:

`import sklearn.cluster`

### Choosing the Value of K

The most important parameter in K-means clustering is the number of clusters (K). Choosing the right number of clusters can be challenging.

If K is too small, large clusters will form that contain dissimilar observations. On the other hand, if K is too large, small, insignificant clusters will form, which may not be useful for data analysis.

One way to choose the value of K is to test different values and compare their results. The performance of K-means clustering can be measured by two metrics: Inertia and Silhouette Score.

Inertia is the sum of squared distances between each observation and its closest cluster centroid. The lower the Inertia, the better the clustering.

Silhouette Score is a measure of how well each observation lies within its assigned cluster. The higher the Silhouette Score, the better the clustering.

By testing different values of K and comparing their Inertia and Silhouette Score metrics, we can choose the optimal number of clusters that best separates the data into meaningful groups.

### Assigning Observations to Initial Clusters

Once we’ve chosen the value of K, the next step is to assign each observation to an initial cluster randomly. We do this by allocating each observation to any of the K clusters.

For larger datasets, this can be computationally expensive, so we can also randomly select a subset of the data to assign to initial clusters.

### Iteratively Updating Cluster Assignments

After the initial assignments, we iteratively update the cluster assignments until they converge. The convergence criterion is either when the observations no longer change clusters or when the maximum number of iterations is reached.

To update cluster assignments, we first calculate the mean of each feature for each cluster. We call this mean the cluster centroid.

We then assign each observation to the cluster whose centroid is closest to the observation. This procedure is repeated until the centroids no longer move or the maximum number of iterations is reached.

In summary, K-means clustering is a widely used algorithm for grouping data points with similar characteristics. It maximizes the similarity between observations within each cluster and minimizes the similarity between observations in different clusters.

The most important parameter in K-means clustering is the number of clusters (K). We can choose the optimal value of K by testing different values and comparing their performance metrics.

After choosing K, we assign each observation to an initial cluster randomly. Finally, we iteratively update the cluster assignments until they converge by calculating the mean of each feature for each cluster and assigning each observation to the closest cluster centroid.

In conclusion, K-means clustering is a powerful algorithm for grouping data points with similar characteristics, and it can be a valuable tool for data analysis. By applying K-means clustering to a dataset, we can gain insights into the data that may not be evident by just looking at it.

## Example in Python: K-Means Clustering Applied to Basketball Player Metrics

In this article, we’ve explored the fundamental concepts behind K-means clustering. In this section, we’ll apply K-means clustering to a real-world dataset to show how the algorithm works in practice.

Specifically, we’ll look at basketball player metrics and cluster them based on their performance in specific categories such as points, assists, and rebounds. We’ll also cover the steps required to prepare and clean the data and find the optimal number of clusters.

### Importing Required Modules

We’ll be using several Python modules in this example, including pandas for data manipulation, numpy for numerical computations, matplotlib for visualization, sklearn for machine learning, and preprocessing for scaling the data. We import these modules as follows:

```
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from sklearn.cluster import KMeans
from sklearn.preprocessing import StandardScaler
```

### Creating the DataFrame

We’ll create a DataFrame containing basketball player metrics using the following code:

```
df = pd.DataFrame({
'points': [10, 12, 8, 15, 9, 11, 13, 14, 7, 16],
'assists': [2, 3, 1, 4, 2, 3, 3, 4, 1, 5],
'rebounds': [4, 5, 3, 6, 4, 5, 6, 7, 2, 8]
})
```

This DataFrame contains ten basketball players and their performance statistics for points, assists, and rebounds.

### Cleaning and Preparing the DataFrame

Before we can apply K-means clustering to our DataFrame, we need to prepare and clean the data. We’ll first remove any rows containing missing values using the `dropna()`

method:

`df.dropna(inplace=True)`

Next, we’ll perform scaling on our DataFrame using the `StandardScaler()`

method.

Scaling standardizes the data so that features with larger values do not dominate the results:

```
scaler = StandardScaler()
df_scaled = pd.DataFrame(scaler.fit_transform(df), columns=df.columns)
```

### Finding the Optimal Number of Clusters

To find the optimal number of clusters, we’ll use the elbow method. We loop through a range of K values and compute the SSE (Sum of Squared Errors) for each value of K.

SSE is defined as the sum of the squared distances between each data point and its assigned cluster centroid. We then plot the SSE values against the corresponding K values.

The optimal number of clusters is where the SSE value starts to flatten out. We can usually find this point by looking for an elbow shape in the plot.

```
sse = []
for k in range(1, 10):
kmeans = KMeans(n_clusters=k, max_iter=1000)
kmeans.fit(df_scaled)
sse.append(kmeans.inertia_)
plt.plot(range(1, 10), sse)
plt.title('Elbow Method')
plt.xlabel('Number of Clusters')
plt.ylabel('SSE')
plt.show()
```

The elbow plot suggests that the optimal number of clusters is three since that’s where the SSE value starts to flatten out.

### Performing K-Means Clustering with Optimal K

We’ll now perform K-means clustering with the optimal number of clusters (three) using the `KMeans()`

method:

```
kmeans = KMeans(n_clusters=3)
kmeans.fit(df_scaled)
```

We can retrieve the cluster assignments for each player using the `labels_`

attribute:

`df['cluster'] = kmeans.labels_`

Finally, we can display the updated DataFrame, which contains the original player metrics and the assigned cluster:

`print(df)`

#### Output:

```
points assists rebounds cluster
0 10 2 4 1
1 12 3 5 2
2 8 1 3 0
3 15 4 6 2
4 9 2 4 1
5 11 3 5 2
6 13 3 6 2
7 14 4 7 2
8 7 1 2 0
9 16 5 8 2
```

The updated DataFrame shows that players 2 and 8 belong to cluster 0, players 0 and 4 belong to cluster 1, and the remaining players belong to cluster 2.

### Additional Resources

If you’re interested in learning more about K-means clustering or machine learning in general, there are many resources available online. Some recommended resources for further reading include:

- “Hands-On Machine Learning with Scikit-Learn, Keras, and TensorFlow” by Aurlien Gron
- “Python Machine Learning” by Sebastian Raschka and Vahid Mirjalili
- “Introduction to Machine Learning with Python” by Andreas MÃ¼ller and Sarah Guido
- The scikit-learn documentation

Additionally, domain expertise in specific fields is a valuable resource for machine learning applications.

Experts in the domain can provide insights into which variables to include in the analysis, what kind of data is useful, and how to interpret the results. In conclusion, K-means clustering is a powerful algorithm for grouping data points with similar characteristics, and it can be a valuable tool for data analysis.

The most important parameter in K-means clustering is the number of clusters, and we can choose the optimal value of K by testing different values and comparing their performance metrics. The steps to perform K-means clustering include importing required modules, creating a DataFrame, cleaning and preparing the DataFrame, finding the optimal number of clusters using the elbow method, and performing K-means clustering with the optimal number of clusters.

By applying K-means clustering to a dataset, we can gain insights into the data that may not be evident by just looking at it. Further reading and domain expertise can help extend our understanding of K-means clustering and machine learning.

Overall, K-means clustering is an essential tool in the field of data analytics and is valuable for identifying groups of similar data points that can lead to better decision-making and insights.