Intrusion Detection Systems (IDS) are implemented to identify deviations from normal behavior and detect new disruptions. Several intrusion detection systems utilize a single classification method to categorize network data as usual or unusual. Based on the extensive growth in data, there is a slowdown in this detection system process, leading to unsatisfactory classification and influencing the classification accuracy. Therefore, this research methodology considered dimensionality reduction methods to process the higher dimensional data samples into low-dimensional data through conserving structural information and significant characteristics of the original information through sparse computation. The computation achieves sparsity in the similarity matrix, which is deprived of the ability to evaluate the complete matrix initially. The idea is to build a multi-class SVM from the reduced dataset to increase attack classification accuracy rapidly. In this paper, to simplify a reasonable and balanced evaluation against remaining up-to-date detection methodologies, the KDD cup dataset is employed to estimate the efficiency of this intrusion detection system and the accuracies of different attacks in the dataset. The empirical results for the proposed sparse computation-empowered Multi-class SVM (SC-MSVM) approach are compared with the existing IDS techniques and show that it performs better than the existing approaches.