The Impact of Normalization on K-means Clustering: A Comparative Analysis

Figure1: The differences between K-means clustering results with and without normalization

K-means clustering is a popular method for grouping data into clusters based on their similarities. Here, we explore the effects of applying K-means in two different scenarios: first, without any preprocessing, and second, after normalizing the dataset by mapping all features to the range [0, 1]. This article investigates whether the results of these two methods are identical and explains the reasons behind any differences.

Method 1: K-means Without Normalization

In the first approach, K-means is applied directly to the raw dataset without any preprocessing. Each feature may have different ranges and scales, which can influence the calculation of distances between data points. Since K-means minimizes the sum of squared distances between data points and their assigned cluster centers, features with larger ranges will have a greater impact on the clustering process.

Example: If one feature represents age (ranging from 0 to 100) and another feature represents income (ranging from 0 to 100,000), the clustering will prioritize income differences over age due to the larger scale of income.

Method 2: K-means with Normalization

In the second approach, we normalize the dataset by scaling each feature to the [0, 1] range. This ensures that all features contribute equally to the calculation of distances. Normalization helps in removing any bias towards features with larger ranges, making the clustering process more balanced. After normalization, K-means is performed again, and the results are saved for comparison.

Normalization Formula:

Where Xis the feature value, Xmin⁡ is the minimum value of the feature, and Xmax⁡ is the maximum value.

Are the Results Identical? Why or Why Not?

The results of the two methods are not identical. The primary reason is the influence of feature scales on the distance calculation used in K-means.

1. Impact of Feature Scale on Clustering: In the first approach, features with larger ranges dominate the calculation of distances between data points. This can result in clusters that reflect variations in those features more strongly, while smaller-scale features have little impact.
2. Balanced Contribution After Normalization: In the second approach, normalization scales all features to a common range, ensuring that each feature contributes equally to the clustering process. This can lead to different cluster centers and, consequently, different cluster assignments compared to the unnormalized data.
3. Distance Calculation Differences: K-means relies on Euclidean distance, which is sensitive to the scale of features. Normalization alters the scale, thus changing the distance relationships between points. As a result, the clustering boundaries and cluster centers can shift after normalization.

Conclusion

In summary, the results of K-means clustering on raw and normalized data differ due to the impact of feature scales on distance calculations. Normalization ensures that all features contribute equally, leading to clusters that better reflect the overall structure of the data. This makes normalization a crucial preprocessing step when features have varying scales, ensuring more meaningful and interpretable clustering results.