Drug Repositioning plays a vital role in discovering new targets for existing drugs. Drug discovery and drug repositioning plays an important role in biomedical development. Considering the importance of identification of drug-target interactions, the experimental methods prove to be very expensive, time-consuming and demanding. Hence, developing extensive computational techniques and models for prediction of drug-target interactions is of great significance to help in shortening the development period and save money. In this work, we propose an extensive computational approach involving k-medoid graph regularized matrix factorization, namely KGRMF. The dataset is converted into adjacency matrices. There are three matrices constructed per dataset, namely Drug similarity matrix, Compound similarity matrix, Drug-Target Interaction matrix. Various computations are performed including Laplacian and sparsification of the drug-drug and target-target similarity matrices. Convergence is obtained by minimizing the function.