The FCM clustering algorithm was implemented separately for the milk and the fish KT-matrices [Tables 4(A, B) and Table 5, respectively] by using the Mat Lab function ‘fcm’. The algorithm needs three input parameters: c, m and ε, being respectively the number of fuzzy clusters, the exponent defining the nonlinearity of the function for assigning membership grades, and the error limit on the calculated objective function for stopping further iteration. In the whole analysis, the latter two parameters were fixed at m = 2 and ε = 0.01. The m = 2 implements a quadratic nonlinear membership grade function in terms the Euclidean distances between the data points and the clusters centers, Eq. (2), and ε = 0.01 is empirically assigned as a tolerance limit for iterations. The polymer having highest membership grade value in a cluster
was declared to be the cluster center. In order to reveal the data structure we increased the value of third parameter c systematically by 1 starting with c = 2. At each increment for c the output of the FCM algorithm (thatis,the subset of c polymers) was examined. What we expect is that the most distinct polymers would emerge as cluster centers first. The list would build up as more centers are added with increasing c. Finally, a smallest subset of polymers that is maximally diverse would appear, and reappear consistently if we seek still larger number of cluster centers. The FCM analysis with increasing c was pursued with this idea, and the results were