Implement K-Means Clustering

K-Means clustering is an iterative algorithm that partitions data into 'k' distinct clusters. The process involves:

1. Initialization: Randomly select 'k' initial centroids from the data points or generate them randomly.
2. Assignment: Assign each data point to the nearest centroid based on a distance metric (commonly Euclidean distance).
3. Update: Recalculate the position of each centroid by taking the mean of all data points assigned to that cluster.
4. Iteration: Repeat steps 2 and 3 until the centroids no longer move significantly or a maximum number of iterations is reached.

Key considerations include choosing an appropriate value for 'k' (often using the elbow method or silhouette analysis) and handling the sensitivity to initial centroid placement, which can be mitigated by running the algorithm multiple times with different initializations.