Nonmedoid

Nonmedoid is a term used in clustering, particularly in methods that select actual data points as cluster representatives, such as k-medoids. In this context, a medoid is a data point within a cluster whose average dissimilarity to all other points in the same cluster is minimal. A nonmedoid is any data point that is not chosen as a medoid for the current clustering solution.

In a k-medoids framework, the dataset is partitioned into k clusters, each represented by a medoid. The remaining data points in the dataset are nonmedoids. Nonmedoids do not serve as the cluster’s central representative, but they are used as candidates during the optimization process. For example, in the Partitioning Around Medoids (PAM) algorithm, the solution is iteratively improved by evaluating whether swapping a medoid with a nonmedoid reduces the total within-cluster dissimilarity.

The distinction between medoids and nonmedoids matters because medoids are actual data points that provide robust, interpretable cluster exemplars, while nonmedoids are the pool of potential representatives that can replace current medoids if a better partition is found. Distances from nonmedoids to the cluster’s medoid help evaluate cluster compactness, but nonmedoids themselves do not define the cluster center unless selected as a medoid.

Limitations and context: the concept is specific to discrete representatives in medoid-based clustering and relies on a chosen distance or dissimilarity measure. It contrasts with centroid-based clustering (like k-means), where centers may be non-data points. In practice, nonmedoids play a key role as candidates in iterative optimization and in interpreting cluster structure where medoids serve as tangible exemplars.