Consensus Clustering

Synonyms

Clustering aggregation; Clustering ensembles

Definition

In Consensus Clustering we are given a set of n objects V, and a set of m clusterings {C₁, C₂, …, C _m } of the objects in V. The aim is to find a single clustering C that disagrees least with the input clusterings, that is, C minimizes

$$\displaystyle\begin{array}{rcl} D(C) =\sum _{C_{i}}d(C,C_{j}),& & {}\\ \end{array}$$

for some metric d on clusterings of V. Meilă (2003) proposed the principled variation of information metric on clusterings, but it has been difficult to analyze theoretically. The Mirkin metric is the most widely used, in which d(C, C′) is the number of pairs of objects (u, v) that are clustered together in C and apart in C′, or vice versa; it can be calculated in time O(mn).

We can interpret each of the clusterings C _i in Consensus Clustering as evidence that pairs ought be put together or separated. That is, w _uv ⁱ is the number of C _i in which C _i [u] = C _i [v] and w _uv ⁻ is the number of C_...