Among the following statements about k-means clustering, which is true?

The statement that k-means clustering is sensitive to initial cluster configuration is true. This characteristic means that the results of the clustering can vary significantly depending on the initial positions of the centroids that are selected randomly at the start of the algorithm. Different initializations can lead to different final cluster assignments, which sometimes may result in suboptimal clustering if the algorithm converges to a local minimum rather than finding the most optimal solution.

In practice, this sensitivity is why multiple runs of the k-means algorithm are often performed with different initial centroid positions, and the best outcome can be chosen based on a criterion such as the lowest within-cluster variance. This variability in outcomes highlights the importance of the initial conditions in k-means clustering.

The other statements are not accurate in the context of k-means clustering. For instance, k-means is not suitable for categorical data as it relies on calculating distances (typically Euclidean) and mean calculations, which are not applicable to non-numeric categories. Clusters formed by k-means are generally spherical, which means it does not naturally accommodate arbitrary shapes without modifications, such as using kernel methods or clustering algorithms that specifically allow for varied geometries. Additionally, k-means does not guarantee a global optimum; it can