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This paper is devoted to the problem of class imbalance in machine learning, focusing on the intrusion detection of rare classes in computer networks. The problem of class imbalance occurs when one class heavily outnumbers examples from the other classes. In this paper, we are particularly interested in classifiers, as pattern recognition and anomaly detection could be solved as a classification problem. As still a major part of data network traffic of any organization network is benign, and malignant traffic is rare, researchers therefore have to deal with a class imbalance problem. Substantial research has been undertaken in order to identify these methods or data features that allow to accurately identify these attacks. But the usual tactic to deal with the imbalance class problem is to label all malignant traffic as one class and then solve the binary classification problem. In this paper, however, we choose not to group or to drop rare classes but instead investigate what could be done in order to achieve good multi-class classification efficiency. Rare class records were up-sampled using SMOTE method (Chawla et al., 2002) to a preset ratio targets. Experiments with the 3 network traffic datasets, namely CIC-IDS2017, CSE-CIC-IDS2018 (Sharafaldin et al., 2018) and LITNET-2020 (Damasevicius et al., 2020) were performed aiming to achieve reliable recognition of rare malignant classes available in these datasets. Popular machine learning algorithms were chosen for comparison of their readiness to support rare class detection. Related algorithm hyper parameters were tuned within a wide range of values, different data feature selection methods were used and tests were executed with and without over-sampling to test the multiple class problem classification performance of rare classes. Machine learning algorithms ranking based on Precision, Balanced Accuracy Score, G ¯ , and prediction error Bias and Variance decomposition, show that decision tree ensembles (Adaboost, Random Forest Trees and Gradient Boosting Classifier) performed best on the network intrusion datasets used in this research. [ABSTRACT FROM AUTHOR]

This paper features the study of global optimization problems and numerical methods of their solution. Such problems are computationally expensive since the objective function can be multi-extremal, nondifferentiable, and, as a rule, given in the form of a "black box". This study used a deterministic algorithm for finding the global extremum. This algorithm is based neither on the concept of multistart, nor nature-inspired algorithms. The article provides computational rules of the one-dimensional algorithm and the nested optimization scheme which could be applied for solving multidimensional problems. Please note that the solution complexity of global optimization problems essentially depends on the presence of multiple local extrema. In this paper, we apply machine learning methods to identify regions of attraction of local minima. The use of local optimization algorithms in the selected regions can significantly accelerate the convergence of global search as it could reduce the number of search trials in the vicinity of local minima. The results of computational experiments carried out on several hundred global optimization problems of different dimensionalities presented in the paper confirm the effect of accelerated convergence (in terms of the number of search trials required to solve a problem with a given accuracy). [ABSTRACT FROM AUTHOR]