When examining K-means clustering characteristics, which statement is accurate?

The statement regarding K-means clustering being susceptible to initial conditions is accurate. K-means is an iterative algorithm that requires the selection of initial centroids to start the clustering process. The final clustering outcome can vary significantly based on these initial positions. Different initializations can lead to different local minima, resulting in different clustering results upon completion of the algorithm. Because of this sensitivity to the choice of initial centroids, it is recommended to run the K-means algorithm multiple times with different initializations and select the best result based on a metric like the within-cluster sum of squares.

The other statements do not accurately reflect the characteristics of K-means clustering. For instance, preserving hierarchical relationships is a feature more commonly associated with hierarchical clustering methods, rather than K-means. K-means also requires prior knowledge of the number of clusters to be formed, as it necessitates defining the number of centroids at the start of the process. Finally, the results of K-means clustering are not invariant to sample size, as increasing the number of samples can lead to different clusters depending on the density and distribution of the data points.