Appendix: City Block Distance and Rough-Fuzzy Clustering for Iden- tification of Co-Expressed microRNAs†

In this section, the performance of the proposed roughfuzzy clustering algorithm1 is compared with that of hard c-means (HCM)2, fuzzy c-means (FCM)3, rough-fuzzy cmeans (RFCM)4, cluster identification via connectivity kernels (CLICK)5, and self organizing map (SOM)6 with respect to gene ontology. The performance of the normalized rangenormalized city block distance (NRNCBD) over Pearson distance (PD) and Euclidean distance (ED) is also presented. The genes that are targeted by at least 75% miRNAs in a cluster are analyzed and the results are reported in Fig. 1. The final annotation ratios generated by all the algorithms at their optimum values of λ and ω for molecular functions (MF), biological processes (BP), and cellular components (CC) ontologies on four miRNA microarray data sets are shown in this figure. All the results reported here confirm that the proposed clustering algorithm provides higher or comparable final annotation ratios than that obtained using several existing clustering algorithms in most of the cases. The upper portion of Fig. 1 presents the comparative results of the RFCM and proposed clustering algorithm, in terms of final annotation ratio or cluster frequency, for the MF, BP, and CC ontologies on four miRNA expression data sets. All the results reported here confirm that the proposed method provides higher or comparable final annotation ratios than that obtained using the RFCM algorithm in most of the cases. Out of 12 cases, the proposed method provides higher final annotation ratio in 7 cases. On the other hand, the RFCM with the NRNCBD generates better results in 1, 2, and 2 cases for MF, BP, and CC ontologies, respectively. The middle portion of Fig. 1 reports the comparative final annotation ratio of the HCM, FCM, and the proposed algorithm on four data sets. From the results reported in this portion, it is seen that out of total 12 comparisons, the proposed algorithm attains higher final annotation ratio than that ob-