Using Low-Rank Approximation In Order To Improve the Efficiency of the Support Vector Machine and Applications

Support vector machine is one of the most powerful tools in the field of supervised machine learning to classify the existed data. In the data that the linear support vector machine does not have the required efficiency in their classification, using the kernel-based support vector machine which is based on the use of feature space instead of the original data is considered. As a result of this structure, nonlinear classification can be provided. One of the challenges in this approach is to increase the computational complexity and ultimately increase in the required time for classification. As such, it is not particularly useful for large datasets. This increase in computational time is mainly due to the appearance of the kernel in solving the quadratic optimization problem, which we will be able to overcome this problem using the presented low-rank approximation in this paper. In this technique, using a truncated Mercer series of the kernel, the quadratic optimization problem in the kernel-based support vector machine is replaced with a much simpler optimization problem. In the new presented approach, the required vector computations and matrix decompositions will be much faster such that these changes lead to faster resolution of the quadratic optimization problem and increase efficiency. Finally, the results of experiments show that using a low-rank kernel-based approximation of support vector machine, while keeping the classification performance in an acceptable range, the computational time has been significantly reduced.