Regarding the K-means clustering algorithm, which statement is true?

The statement about K-means clustering being correct is that it groups homogeneous observations. K-means clustering is designed to segment a dataset into distinct groups (or clusters) where the items within each group share similar characteristics. The algorithm works by minimizing the variance within each cluster, meaning that the observations in the same cluster are as close to each other as possible, thus creating homogeneity.

This approach relies on the algorithm’s objective to find centroids, which are the mean points of the clusters, and to assign observations to the nearest centroid based on a distance metric (commonly Euclidean distance). As a result, K-means effectively identifies clusters that are comprised of similar data points, which reinforces the principle of grouping homogeneous observations.

The other statements do not accurately reflect the core functionality of K-means. Standardization of observations, while beneficial for K-means and generally recommended to ensure each feature contributes equally to distance calculations, is not an inherent feature of the algorithm itself. K-means does not directly reduce dimensionality; it focuses on clustering data rather than simplifying it by reducing features. Finally, K-means does not rely on predefined categories; rather, it determines the cluster assignments based on the data itself and the defined number of clusters, which are