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It is essential to get the regular check-up of our eye so that the earlier detection of diabetic retinopathy (DR) can be made possible. DR is the disease because of retinal damage due to prolonged diabetic mellitus. The detection of DR using eye fundus images has been a current research topic in the area of medical image processing. Several methods have been developed to automate the process of DR detection. Researchers have made use of different classifiers to efficiently detect the presence of diabetes. SVMs contribute to the latest modelling of DR detection. Although, it proved to be an efficient technique but time consuming, especially when the dataset is large. Also, there is noticeable decrease in the performance of SVM when the dataset is corrupted by noise and outliers. This paper presents the idea of making use of twin support vector machines (TWSVMs) and its robust variants for DR detection. We give the detail of feature extraction from the digital fundus images which are fed to the TWSVMs and its robust variants. The comparison with the previous works of SVM illustrates the superiority of our model. It should be noted that the choice of TWSVM classifier not only solved the problem of time consumption but also made the DR detection robust.