What is the primary objective of k-means clustering?

The primary objective of k-means clustering is to separate dissimilar samples and group similar ones. This unsupervised learning algorithm works by assigning data points to clusters based on their features, effectively organizing the data into groups where the intra-cluster similarity is maximized, and inter-cluster similarity is minimized.

In k-means clustering, the algorithm iteratively refines the positions of the cluster centroids and the assignments of the data points to these centroids, ensuring that each point is grouped with those that are closest in terms of distance (usually Euclidean distance). The goal is to form clusters such that the points within each cluster are as similar as possible, while points in different clusters are as dissimilar as possible. This fulfills the core purpose of clustering, which is the identification of structures within data and the categorization of data points based on their attributes.

The other options either mischaracterize the k-means algorithm's objectives or do not align with its fundamental purpose. The intention to minimize the distance between all centroids and to aggregate all data points into a single cluster contradicts the core concept of distinguishing between different data points. Similarly, minimizing the total number of clusters can lead to oversimplification, making it harder to recover the underlying