A Soft Davies-Bouldin Separation Measure

We present a soft separation measure to validate fuzzy clustering results without defuzzyficaton. It is the generalization of Davies-Bouldin validation index (DB) for crisp clustering in the soft clustering domain; we named the measure Soft Davies-Bouldin index (SDB). We compared DB and SDB when applied to k-means and fuzzy c-means algorithms using eight datasets with ground-truth and two experimental fMRI datasets without ground-truth. We found that i) in more than half datasets, the optimal score of Soft Davies-Bouldin index was less than Davies-Bouldin index, ii) in half datasets that have ground-truth, the optimal score of Soft Davies-Bouldin index was less than Davies-Bouldin index in correspondence of the truth number of patterns, iii) the Soft Davies-Bouldin index outperformed the Davies-Bouldin index as central tendency of all datasets along the complete range of clusters considered.