
| fraction                  | diagonal   | kappa   | rand   | crand   |       |
|---------------------------|------------|---------|--------|---------|-------|
| Tracemax RandomMatch      | 1.0%       | 1.00    | 1.00   | 1.000   | 1.00  |
| Tracemax NonRandomMatch   | 99.0%      | 0.98    | -0.01  | 0.960   | -0.01 |
| Tracemax Expected         | 100.0%     | 0.98    | 0.00   | 0.961   | 0.00  |
| Truematch Expected        | 100.0%     | 0.03    | 0.01   | 0.961   | 0.00  |
| Truematch NonRandomMatch1 | 49.5%      | 0.02    | 0.00   | 0.960   | -0.01 |
| Truematch NonRandomMatch2 | 49.5%      | 0.02    | 0.00   | 0.960   | -0.01 |
| Truematch RandomMatch     | 1.0%       | 1.00    | 1.00   | 1.000   | 1.00  |

Table 6: Agreement statistics

## 4. The Role Of Truematch In Truecluster

The truecluster concept (Oehlschl¨agel, 2007b) suggests a *cluster information criterion* (CIC)
that evaluates for each cluster model (for each number of clusters) a N x K matrix Pˆ that aggregates votes over many resamples. Pˆ is created by the *multiple match cluster count*
(*MMCC*) algorithm using the truematch algorithm as follows:
1. Create a N x K matrix C and initialize each cell Ci,k with zero

2. Take a resample (with replacement) of size N, use a *base cluster algorithm* to fit the K-cluster model c
∗to the resample. Then, use a suitable *prediction method* to determine cluster membership of the out-of-resample cases to get a complete cluster vector c 0with N elements c 0 i 3. For each row in C add one vote (add 1) to the column corresponding to the cluster membership in c 0 4. Repeat step 2 5. Estimate cluster memberships ˆc by row-wise majority count in C (breaking ties at random), use the truematch algorithm or *heuristic* to align c 0with cˆ, and rename the clusters in c 0like the corresponding clusters in cˆ
6. For each row in C add one vote (add 1) to the column corresponding to the cluster membership in c 0 7. Repeat from step 4 until some reasonable *convergence criterion* is reached 8. Divide each cell in C by its rowsum to get a matrix of estimated cluster membership probabilities Pˆ
Table 7 summarizes simulations with truecluster versus consensus clustering: 100 cases, 10,000 replications, for details see MMCCconcensus.r in R package truecluster (Oehlschl¨agel, 2007a), the table is sorted and grouped by the magnitude of CIC values). For random data without cluster structure, we would expect very 'fuzzy' Pˆ without clear preferences for any