Unsupervised learning analyzes data that contain only input features \( X = \{ \textbf{x}_1, \ldots , \textbf{x}_n \} \) . No labels are provided. The goal is to detect hidden patterns or structures. Clustering methods, such as k-means, group points into clusters based on feature similarity. Points in the same cluster are more similar to each other than to points in other clusters. Dimensionality reduction techniques map high-dimensional data into a lower-dimensional space while keeping essential structure. Because no predefined outputs exist, unsupervised learning is useful for exploratory analysis, anomaly detection, and feature extraction. The k-means algorithm [21] is an unsupervised method that partitions data into \( k \) clusters. The dataset contains points \( \textbf{x}_1, \textbf{x}_2, \dots , \textbf{x}_n \) with \( \textbf{x}_j \in \mathbb {R}^d \) . The algorithm proceeds in an iterative loop: Initialize \( k \) centroids \( \textbf{c}_1, \dots , \textbf{c}_k \) at random.