cluster. Furthermore, we would expect CIC to increase for models with more true clusters and to decrease if models try to distinguish more clusters than justified by the data.

Table 7 shows that the MMCC algorithm using truematch delivers on this expectation:
CIC increases for justified clusters and declines for unjustified ones, even if unjustified clusters in the model are small. This works because once cluster decisions are unjustified, the trumatch algorithm starts distributing its votes randomly across undistinguishable columns of C and, thus, 'fuzzifies' Pˆ . Compare that to consensus clustering (Dimitriadou et al.,
2002) based on trace maximization obtained with R package clue (Hornik and Boehm, 2007; Hornik, 2005). Models with unjustified small clusters get CIC values as high as models without the unjustified cluster. This is a consequence of the trace maximization matching, adding inappropriate stability to the voting. Take, for example, the "random 99:1" model, which is as unjustified as the "random 50:50" model but receives a much higher CIC value. The stability induced by the trace maximization matching results in quite a crisp Pˆ2: for each row, we find high probability for one cluster and low probability for the other. If we assign cases to clusters based on the maximum probability per row in Pˆ , all cases are assigned to the same cluster. Such a degenerated Pˆ is not wrong but unfortunate. If we manually analyze Pˆ2, we might detect that Pˆ2 actually represents a onecluster (K=1) model. But if we are after automatic selection of models (number of clusters),
it is misleading that Pˆ2 does not represent K = 2 but K = 1. Analyzing a consensus cluster solution Pˆ K for degeneracies does not really help: the estimated probabilitites can be biased even before the matrix formally degenerates.