clustersnot

Clustersnot is a term that has appeared in discussions of cluster analysis but does not have a single, widely accepted definition. In some treatments, it is described as a negation of cluster membership: a predicate that indicates that a given data point is not assigned to a specified cluster under a particular labeling. More broadly, other researchers use clustersnot to refer to instability or inconsistency of cluster assignments under perturbations, measuring how often points fail to stay in the same cluster when data are perturbed or when different clustering algorithms are applied.

In practical use, the clustersnot concept can function as a diagnostic tool. A clustersnot rate, for example, might quantify the proportion of data points that do not meet a clustering criterion, such as mismatching a reference partition or failing to persist in a cluster under perturbation. This framing makes clustersnot a potential complement to traditional cluster validity measures, highlighting points that resist stable assignment.

Computation of a clustersnot-based metric generally requires a clustering result and a reference or criterion. One common approach is to mark a point as clustersnot if its assigned cluster differs from the reference cluster under a chosen mapping, or if its assignment changes under a small perturbation of the data. Because there is no standardized definition, the term is used inconsistently across sources; some see it as a shorthand for outliers or noise, while others treat it as a formal component of a robustness assessment.

See also: clustering, cluster validity, outliers, stability in clustering.