A key strength of twin studies arises from the fact that there are two types of twins, monozygotic and dizygotic, that share differing amounts of genetic information. Accurate differentiation of twin types allows efficient inference on genetic influences in a population. However, identification of zygosity is often prone to errors without genotying. In this study, we propose a novel pairwise feature representation to classify the zygosity of twin pairs of resting state functional magnetic resonance images (rs-fMRI). For this, we project an fMRI signal to a set of basis functions and use the projection coefficients as the compact and discriminative feature representation of noisy fMRI. We encode the relationship between twins as the correlation between the new feature representations across brain regions. We employ hill climbing variable selection to identify brain regions that are the most genetically affected. The proposed framework was applied to 208 twin pairs and achieved 94.19% classification accuracy in automatically identifying the zygosity of paired images.