Today, the number of cyber-attacks has increased and become more complex with an increase in the size of high-dimensional data, which includes noisy and irrelevant features. In such cases, the removal of irrelevant and noisy features, by Feature Selection (FS) and Dimensions Reduction (DR) methods, can be very effective in increasing the performance of intrusion detection systems (IDS). This paper compares some FS and DR methods for detecting cyber-attacks with the best accuracy using implementation on KDDCUP99 dataset. A Deep Neural Network (DNN) is used for training and simulating them. The results show the filter methods are faster than wrapper methods but less accurate. Whereas the Wrapper methods have more accuracy but are computationally costlier. Embedded methods have the best output and maximum values, which is 99% for all the metrics, comparing to it the DR methods have shown a good performance and speed, among them Linear Discriminant Analysis (LDA) method even better than embedded method.