The permutations of the random spanning tree needed to calculate cluster membership probabilities takes time and memory which can be improved by increasing the number of cores used in the Parallel Processing environment setting.
The Permutations to Calculate Membership Probabilities parameter uses permutations and evidence accumulation to calculate the probability of cluster membership for each feature. A high probability tells you that you can be confident the feature belongs in the cluster it was assigned. A low probability may indicate the feature is very different than the cluster it was assigned or that the feature could be included in a different cluster if the Analysis Fields, Cluster Size Constraints, or Spatial Constraints were changed in some way.
Calculating these probabilities uses permutations of random spanning trees and evidence accumulation. This can take significant time to run for larger datasets. It is recommended that you iterate and find the optimal number of clusters for your analysis first and then calculate probabilities for your analysis in a subsequent run. You can also divide and perform operations across multiple processes by increasing the number of cores used in the Parallel Processing Factor environment setting.