Key Differences Between k-Means and GMM
Cluster Shape
- k-Means: Assumes clusters are spherical and equidistant from their centroids.
- GMM: Models clusters as Gaussian distributions, allowing for different shapes (e.g., ellipses) by incorporating mean and covariance matrices. GMM can model clusters of varying shapes and sizes by adjusting the Covariance Structures (e.g., full, diagonal, spherical).
Probability-Based Assignments
- k-Means: Assigns each point deterministically to the nearest cluster centroid.
- GMM: Provides a probability distribution for cluster membership, making it a soft clustering method.
- GMM handles overlapping clusters effectively by assigning probabilities to data points for each cluster, instead of enforcing hard boundaries like k-means.
Flexibility
- k-Means: Performs well when clusters are spherical and well-separated.
- GMM: Handles overlapping clusters and clusters with different shapes, leveraging its covariance modeling capability.