Center-Wise Intra-Inter Silhouettes

Fuzzy C-Means Based Liver CT Image Segmentation with Optimum Number of Clusters

“…On the other hand, choosing a too small cluster number causes the grouping of dissimilar points into the same cluster. The partitions of interest are those composed of compact and well separated clusters that best meet our expectations [12].…”

“…However, it is possible for different fuzzy partitions on the same dataset to evaluate to the same silhouette values, provided that they are converted to the same crisp partition by means of defuzzification. Such fuzzy partitions can be obtained on one dataset by slightly changing the fuzzifier m when performing FCM clustering [12].…”

“…Since compactness is determined by the set of intra-distances, while separation is determined by inter-distances, it is desirable to have small intra-distances and large inter-distances. Evaluating fuzzy logical connectives on point (pixel) membership values computes the intra-and inter-scores, either crisp or fuzzy, as shown in the definition below [12]:…”

“…Values around zero either emerge from mis-clustering or the point being in overlapping regions. The average generalized silhouette gSil computed using Eq.10 over all the data set X having n points, is a measure of the dataset clustering quality [12].…”

“…The compactness distance a j and the separation distance b j of each data point x j are defined as weighted means of the associated pairwise distances using the following form [12]:…”