Where does cluster collide?

A grouping of objects that an algorithm assigns so that objects within a group are more similar to each other than to those outside it. MacQueen introduced the k-means procedure in Some Methods for Classification and Analysis of Multivariate Observations (1967), which partitions a set of points into k groups by moving each point to the nearest group centre and recomputing the centres until the assignment settles. The referent is a subset of data points in a feature space, and the unit is a group produced by an optimisation rule, not anything that exists in the world before the analysis runs. What marks this meaning is that the grouping is constructed by a method the analyst chooses, and a different method, or a different k, yields different clusters from the same data.[1]

Unit

A group of data points assigned by an algorithm

Recovery means

Not applicable

Measured by

Assignment of observations to groups that minimises within-group distance in a feature space

A geographic concentration of interconnected companies, specialised suppliers, service providers, and associated institutions in a particular field. Porter set out this meaning in Location, Competition, and Economic Development (2000), where a cluster is a real spatial and economic entity that raises productivity through proximity, shared labour, and the flow of knowledge between firms. The referent is a place and the firms rooted in it, and the unit is a regional agglomeration that competitors, suppliers, and universities inhabit together. This differs from the statistical meaning because the grouping is not imposed by an analyst; it forms from the decisions of firms about where to locate, and it is defined by economic linkage and shared geography rather than by distance in a feature space.[2]

Unit

A geographic concentration of related firms and institutions

Recovery means

Not applicable

Measured by

Geographic co-location and linkage of firms, suppliers, and institutions within a region and field

A group of stars held together by their mutual gravity, formed from the same cloud and moving through the galaxy as one system. Harris catalogued the globular clusters of the Milky Way in A Catalog of Parameters for Globular Clusters in the Milky Way (1996), recording for each one its position, distance, and structure as a physical object with measurable size and membership. The referent is a bound stellar system, open or globular, and the unit is a real astronomical body, not a grouping an analyst chooses to draw. This meaning differs from the others because gravity does the binding: the cluster exists whether or not anyone measures it, and its members belong to it as a matter of physics rather than of similarity or shared address.[3]

Unit

A gravitationally bound group of stars

Recovery means

Not applicable

Measured by

Position, distance, size, and membership of stars bound together by mutual gravity

An aggregation of cases of a disease that is greater than would be expected in a given area and period by chance. Besag and Newell set out a test for this idea in The Detection of Clusters in Rare Diseases (1991), which compares the observed count of cases around each case to what a baseline rate predicts and flags where the excess is unlikely to be random. The referent is a set of people who fell ill close together in place and time, and the unit is a local excess of incidence over an expected rate. This differs from the astronomical meaning because nothing binds the cases physically, and from the statistical meaning because the grouping is judged against an external baseline of expected occurrence, not assembled to minimise within-group distance.[4]

Unit

An unusual aggregation of disease cases in place and time

Recovery means

Not applicable

Measured by

Statistical excess of observed cases over the count expected within an area and period