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 C o m b i n e d M c 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.

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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.