Clustering and the K-Means Algorithm

What Is Clustering?

Clustering is an unsupervised learning technique that groups data points based on their similarity. Points within a cluster should be more similar to one another under the chosen distance measure than to points in other clusters.

Common applications include:

• Customer segmentation
• Grouping news articles by topic
• Organizing images
• Exploring patterns in user behavior

Understanding K-Means

K-Means is a popular clustering algorithm that divides data into a specified number of clusters, represented by the value K.

The algorithm generally follows these steps:

1. Select the number of clusters, K.
2. Initialize K cluster centers, called centroids.
3. Assign each data point to its nearest centroid.
4. Recalculate each centroid using the points assigned to it.
5. Repeat the assignment and recalculation steps until the clusters stabilize or a stopping condition is reached.

K-Means attempts to minimize the sum of squared distances between data points and their assigned cluster centers.

Implementing K-Means in Python

Install the required libraries if they are not already available:

pip install numpy matplotlib scikit-learn

Use the following example to group customers based on two illustrative features: annual spending and purchase frequency.

import matplotlib.pyplot as plt
from sklearn.cluster import KMeans
from sklearn.preprocessing import StandardScaler
# Illustrative customer data:
# Annual spending and purchase frequency
X = [
[20, 2],
[25, 3],
[22, 2],
[80, 8],
[85, 9],
[78, 7],
[45, 5],
[50, 4],
[48, 5]
]
# Scale the features
scaler = StandardScaler()
X_scaled = scaler.fit_transform(X)
# Create and train the model
model = KMeans(
n_clusters=3,
random_state=42,
n_init=10
)
labels = model.fit_predict(X_scaled)
print("Cluster assignments:", labels)
# Visualize the clusters
plt.scatter(
[row[0] for row in X],
[row[1] for row in X],
c=labels
)
plt.xlabel("Annual Spending")
plt.ylabel("Purchase Frequency")
plt.title("Customer Segmentation Using K-Means")
plt.show()

Understanding the Output

The model assigns each customer a cluster label, such as 0, 1, or 2. These labels identify groups; they do not indicate a ranking or business category automatically.

You must inspect the characteristics of each group before assigning interpretations such as frequent buyers or low-spending customers.

Advantages and Limitations

Advantages:

• Relatively simple to understand and implement.
• Efficient for many datasets.
• Useful when the number of clusters can be estimated.

Limitations:

• Requires choosing the number of clusters in advance.
• Can be affected by outliers and feature scaling.
• Works best when clusters are reasonably compact and separated.
• Different initial centroids can produce different results.