Which statement is true concerning the optimal number of clusters in K-means?

The correct answer emphasizes minimizing the total within-cluster variation as the approach to determining the optimal number of clusters in K-means clustering. The core objective of K-means is to partition data into K clusters in a way that minimizes the variance within each cluster. This is quantified through the total within-cluster variation, which measures how close the data points in each cluster are to each other. By minimizing this variation, you achieve more cohesive clusters, indicating that the chosen value of K effectively represents the inherent structure of the data.

In practical application, various methods, such as the elbow method, silhouette analysis, or other statistical criteria, can help in evaluating different values of K based on the within-cluster variation. By analyzing the variance as K changes, you can identify the point where adding more clusters yields diminishing returns in variance reduction, helping you select a more optimal K.

The other options do not correctly represent the relationship between K and clustering effectiveness. Setting K equal to the total number of data points, for instance, would defeat the purpose of clustering by not grouping the data into meaningful categories. Asserting that the optimal K is universally defined ignores the context and characteristics of the specific dataset, as the optimal number of clusters can vary significantly based on the underlying