The security of networked systems has become a critical universal issue that influences individuals, enterprises and governments. The rate of attacks against networked systems has increased dramatically, and the tactics used by the attackers are continuing to evolve. Intrusion detection is one of the solutions against these attacks. A common and effective approach for designing Intrusion Detection Systems (IDS) is Machine Learning. The performance of an IDS is significantly improved when the features are more discriminative and representative. This study uses two feature dimensionality reduction approaches: (i) Auto-Encoder (AE): an instance of deep learning, for dimensionality reduction, and (ii) Principle Component Analysis (PCA). The resulting low-dimensional features from both techniques are then used to build various classifiers such as Random Forest (RF), Bayesian Network, Linear Discriminant Analysis (LDA) and Quadratic Discriminant Analysis (QDA) for designing an IDS. The experimental findings with low-dimensional features in binary and multi-class classification show better performance in terms of Detection Rate (DR), F-Measure, False Alarm Rate (FAR), and Accuracy. This research effort is able to reduce the CICIDS2017 dataset’s feature dimensions from 81 to 10, while maintaining a high accuracy of 99.6% in multi-class and binary classification. Furthermore, in this paper, we propose a Multi-Class Combined performance metric $Combine{d}_{Mc}$ with respect to class distribution to compare various multi-class and binary classification systems through incorporating FAR, DR, Accuracy, and class distribution parameters. In addition, we developed a uniform distribution based balancing approach to handle the imbalanced distribution of the minority class instances in the CICIDS2017 network intrusion dataset.

Despite the successful contributions in the field of network intrusion detection using machine learning algorithms and deep networks to learn the boundaries between normal traffic and network attacks, it is still challenging to detect various attacks with high performance. In this paper, we propose a novel mathematical model for further development of robust, reliable, and efficient software for practical intrusion detection applications. In this present work, we are concerned with optimal hyperparameters tuned for high performance sparse autoencoders for optimizing features and classifying normal and abnormal traffic patterns. The proposed framework allows the parameters of the back-propagation learning algorithm to be tuned with respect to the performance and architecture of the sparse autoencoder through a sequence of trigonometric simplex designs. These hyperparameters include the number of nodes in the hidden layer, learning rate of the hidden layer, and learning rate of the output layer. It is expected to achieve better results in extracting features and adapting to various levels of learning hierarchy as different layers of the autoencoder are characterized by different learning rates in the proposed framework. The idea is viewed such that every learning rate of a hidden layer is a dimension in a multidimensional space. Hence, a vector of the adaptive learning rates is implemented for the multiple layers of the network to accelerate the processing time that is required for the network to learn the mapping towards a combination of enhanced features and the optimal synaptic weights in the multiple layers for a given problem. The suggested framework is tested on CICIDS2017, a reliable intrusion detection dataset that covers all the common, updated intrusions and cyber-attacks. Experimental results demonstrate that the proposed architecture for intrusion detection yields superior performance compared to recently published algorithms in terms of classification accuracy and F-measure results.

We propose a free selective simplex for the downhill Nelder Mead simplex algorithm (1965), rather than the determinant simplex that forces its elements to perform a single operation, such as reflection. Unlike the Nelder-Mead algorithm, the elements of the proposed simplex select various operations of the algorithm to form the next simplex. In this way, we allow non-isometric reflections similar to that of the Nelder Mead, triangle simplex, but with rotation through an angle, permitting the proposed algorithm to have more control over the simplex, to change its size and direction for better performance. As a consequence, the solution that comes from the proposed simplex is always dynamic adaptive in size and orientation to different landscapes of mathematical functions. The proposed algorithm is examined in a large collection of different structures and classes of optimization problems. Additionally, comparisons are made with two enhanced, up-to-date versions of the Nelder-Mead algorithm. The numerical results show that Hassan Nelder Mead is stable due to non-dependence on the number of parameters processed. It also performs a higher accuracy for high dimensions compared with the other algorithms and a faster convergence rate toward global minima with respect to the number of simplex gradient estimates.

This article provides a new tool for examining the efficiency and robustness of derivative-free optimization algorithms based on high-dimensional normalized data profiles that test a variety of performance metrics. Unlike the traditional data profiles that examine a single dimension, the proposed data profiles require several dimensions in order to analyze the relative performance of different optimization solutions. To design a use case, we utilize five sequences (solvers) of trigonometric simplex designs that extract different features of non-isometric reflections, as an example to show how various metrics (dimensions) are essential to provide a comprehensive evaluation about a particular solver relative to others. In addition, each designed sequence can rotate the starting simplex through an angle to designate the direction of the simplex. This type of features extraction is applied to each sequence of the triangular simplexes to determine a global minimum for a mathematical problem. To allocate an optimal sequence of trigonometric simplex designs, a linear model is used with the proposed data profiles to examine the convergence rate of the five simplexes. Furthermore, we compare the proposed five simplexes to an optimized version of the Nelder–Mead algorithm known as the Genetic Nelder–Mead algorithm. The experimental results demonstrate that the proposed data profiles lead to a better examination of the reliability and robustness for the considered solvers from a more comprehensive perspective than the existing data profiles. Finally, the high-dimensional data profiles reveal that the proposed solvers outperform the genetic solvers for all accuracy tests.

This paper proposes a novel mathematical theory of adaptation to convexity of loss functions based on the definition of the condense-discrete convexity (CDC) method. The developed theory is considered to be of immense value to stochastic settings and is used for developing the well-known stochastic gradient-descent (SGD) method. The successful contribution of change of the convexity definition impacts the exploration of the learning-rate scheduler used in the SGD method and therefore impacts the convergence rate of the solution that is used for measuring the effectiveness of deep networks. In our development of methodology, the convexity method CDC and learning rate are directly related to each other through the difference operator. In addition, we have incorporated the developed theory of adaptation with trigonometric simplex (TS) designs to explore different learning rate schedules for the weight and bias parameters within the network. Experiments confirm that by using the new definition of convexity to explore learning rate schedules, the optimization is more effective in practice and has a strong effect on the training of the deep neural network.