How would you design a clustering algorithm that improves over K-Means?

You would add density awareness, robustness to outliers, and probabilistic assignment instead of hard centroids.

An improved algorithm would relax K-Means assumptions: replace means with medoids for robustness, introduce soft assignments like GMM for uncertainty, and incorporate density estimation to handle irregular shapes. This hybrid approach addresses K-Means’ main weaknesses: sensitivity, rigidity, and geometric bias.