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The prediction of protein-protein interactions (PPIs) is essential to understand the cellular processes from a medical perspective. Among the various machine learning techniques, kernel-based Support Vector Machine (SVM) has been commonly employed to discriminate between interacting and non-interacting protein pairs. The main drawback of employing the kernel-based SVM to datasets with many features, such as the primary sequence-based protein-protein dataset, is the significant increase in computational time of training stage. This increase in computational time is mainly due to the presence of the kernel in solving the quadratic optimisation problem (QOP) involved in nonlinear SVM. In order to fix this issue, we propose a novel and efficient computational algorithm by approximating the kernel-based SVM using a low-rank truncated Mercer series as well as desired. As a result, the QOP for the approximated kernel-based SVM will be very tractable in the sense that there is a significant reduction in computational time of training and validating stages. We illustrate the novelty of the proposed method by predicting the PPIs of “S. Cerevisiae” where the protein features extracted using the multiscale local descriptor (MLD), and then we compare the predictive performance of the proposed low-rank approximation with the existing methods. Finally, the new method results in significant reduction in computational time for predicting PPIs with almost as accuracy as kernel-based SVM.