The research question raised in this study is which supervised machine learning method consistently provides the best multi-class classification results with large and highly imbalanced network datasets. To answer this question we chose the CIC-IDS2017, CSE-CIC-IDS2018 (Sharafaldin et al., 2018) and LITNET-2020 (Damasevicius et al., 2020) datasets as they are recent realistic software-generated traffic network datasets and meet the required criteria (Gharib et al., 2016) for a good network intrusion dataset. An answer to this question is that based on rankings of performance metrics and bias-variance decomposition the tree ensembles Adaboost, RandomForest Trees and Gradient Boosting Classifier performed best on the network intrusion datasets used in this research.

The novelty of this research is in a proposed methodology (see Section 4) and application of it for the recent and not yet in depth studied dataset LITNET-2020. A review of the LITNET-2020 dataset compliance to the criteria raised by Gharib et al. (2016) is first introduced in Section 2.2. A variant of random under-sampling (skewed ratio under-sampling, proposed by authors and discussed in Section 3.1) is used to reduce imbalance of classes in a nonlinear fashion. SMOTE up-sampling for numeric data and SMOTE-NC for categorical data (see Section 3.2) is executed to increase representation of rare classes. Further in this research, comparison of multi-class classification performance of the CIC-IDS2017 and CIC-IDS2018 datasets with the LITNET-2020 dataset is discussed in Section 5. Multi-class performance macro-averaged metrics are implemented in this research. Balanced accuracy (Formula (2)) and geometric mean of recall (Formula (4)) for the LITNET-2020 dataset are implemented for the first time (see results in Tables 16 and 17). Multi-criteria scoring is cross-validated with an approach of testing through data previously unseen for the models (see Section 4). For decision tree ensemble methods, instead of the weak CART base classifiers, parameters Tree depth and alpha were GirdSearched and validated using the method of maximum cost path analysis (Breiman et al., 1984), see Section 3.8. Additional ML model, Gradient Boosting Classifier, utilizing ensemble of Classification and regression trees (CART), was introduced for benchmark in this research via the use of XGBoost library (Chen and Guestrin, 2016) with GPU support (see Section 3.5.6). In our methodology, due to the highly imbalanced nature of the used data, cost sensitive method implementations were chosen. These choices lead to better results (see Table 20) compared to other reviewed studies. Furthermore, selection of models with better generalization capabilities in this research is achieved through decomposition of classification error into bias and variance (see results in Table 18).

There are many datasets that have been used by the researchers to evaluate the performance of their proposed intrusion detection and intrusion prevention approaches. Far from being complete, the list includes: DARPA 1998 (Lippmann et al., 1999) and 1999 traces by Lincoln Laboratory, USA, KDD’99 (Hettich and Bay, 1999), CAIDA (The Cooperative Association for Internet Data Analysis, 2010) datasets by University of California, USA, the Internet Traffic Archive and LBNL traces by Lawrence Berkeley National Laboratory, USA (Lawrence Berkeley National Laboratory, 2010), DEFCON by The Shmoo Group (2011), ISCX IDS 2012 (Shiravi et al., 2012), CIDDS-001 (Coburg Intrusion Detection Data Set) (Ring et al., 2017) and others. However, it has been widely acknowledged that machine learning research in an intrusion detection area needs to include new attack types and therefore researchers should consider more recent data sources.

In this research, three recent network data sets, compliant to the criteria described further (see Section 2.2) suggested by their authors for intrusion detection research, are explored. The datasets chosen are CIC-IDS2017, CSE-CIC-IDS2018 (Sharafaldin et al., 2018) by the University of Brunswick, Canada, and LITNET-2020 (Damasevicius et al., 2020). These datasets are of significant volume, contain anonymized real academic network traffic and are suited for multiple purposes of machine learning. LITNET-2020 is a new dataset that is given particular attention in this research, with discussion of compliance to the dataset suitability as devised by Gharib et al. (2016).

Criteria for building such datasets are discussed by Małowidzki et al. (2015), Buczak and Guven (2016), Maciá-Fernández et al. (2018), Ring et al. (2019), Damasevicius et al. (2020), and others.

Małowidzki et al. (2015) define the following features of a good dataset: it must contain recent data, be realistic, contain all typical attacks met in the wild, be labelled, be correct regarding operating cycles in enterprises (working hours), should be flow-based. Ring et al. (2019) contend that a good dataset should be comparable with real traffic and therefore have more normal than malicious traffic, since most of the traffic within a company is normal and only a small part is malicious. Detailed framework and analysis of criteria for such datasets is proposed by Canadian Institute for Cybersecurity (CIC) at the University of New Brunswik. Gharib et al. (2016) have proposed the eleven dataset selection criteria. These criteria are presented in Table 1. Following this publication of the criteria, CIC created a list of new datasets,1¹

See https://www.unb.ca/cic/datasets/index.html.

The LITNET-2020 dataset was selected for the current study as complying to most of the above mentioned requirements with some reservations regarding interaction completeness, heterogeneity and feature set completeness criteria.

These eleven criteria as applied to LITNET-2020 are discussed below. 1.

Complete network configuration: In order to investigate the real course of attacks, it is necessary to test the real network configuration. All of the network flows in this dataset are received or generated at the Network of Lithuanian academic institutions LITNET.

In datasets selected for the research, the benign class takes from 80 % up to 92 % of total records (see Table 2), and some small classes only have less than 0.001 % (see Table 4). The following Table 2 is a summary of the data set imbalance of benign versus malignant records:

The following Table 3 presents the split of malignant classes and is a summary of dataset imbalance shares in accordance with the taxonomy described by He and Ma (2013):

The following Table 4 represents a summary of extremely imbalanced (>1000 : 1) classes in the three selected datasets.

Various imbalance measures are discussed by Ortigosa-Hernández et al. (2017) in a study, dedicated to such measures. In Karatas et al. (2020), section III.E, authors review most practical to use imbalance ratios of several IDS datasets, including the CIC-IDS2017 and CSE-CIC-IDS2018.

Referring to Ortigosa-Hernández et al. (2017) and Karatas et al. (2020), the following Formula (1) can be used for the calculation of the imbalance ratio: (1) Imbalance Ratio = ρ = max { C i } min { C i } , where: C i shows the data size in the class i.

For example, historical NSL-KDD has an imbalance ratio of 648, CIC-IDS2017 has an imbalance ratio of 112 287 and CSE-CIC-IDS2018 has a slightly better imbalance ratio of 53 887. LITNET-2020 has an imbalance ratio of 70 769.

While imbalance ratios are an important part of the discussion, the absolute rarity is another concept introduced by He and Ma (2013) for the case when there is not enough records to learn the class. If there is not enough information within the feature-scape, determination of decision boundary cannot be made. There are no such classes in the LITNET-2020 datasets, and the data was sufficient for learning to all the machine learning algorithms used in our experiment. However, Infiltration, Heartbleed and Web Attack-Aql Injection classes in the CIC-IDS2017 dataset exhibit behaviour of such an absolute rarity and learning the decision boundaries for these classes is complicated and unspecific. In CSE-CIC-IDS2018 dataset, even though Infiltration class records are abundant, high overlap with benign class is observed.

The CIC-IDS-2017 dataset (Sharafaldin et al., 2018) is made available by Canadian Institute for Cyber Security Research at the University of New Brunswick2²

More information at https://www.unb.ca/cic/datasets/ids-2017.html.

The following Table 5 is a summary of class representation of this dataset.

Dataset features, all measures of duration or related aggregates, further used for this research belong to these categories:

The CSE-CIC-IDS2018 dataset (Sharafaldin et al., 2018) is made available by Canadian Institute for Cyber Security Research at the University of New Brunswick.4⁴

More information at https://www.unb.ca/cic/datasets/ids-2018.html.

The following Table 6 presents a summary of class representation of this dataset.

Same dataset features as described in Section 2.5 are used further in this research for selection of features.

LITNET-2020 is a new annotated network dataset for network intrusion detection, obtained from the real life Lithuanian academic network LITNET traffic by researchers from Kaunas Technology University (KTU). The environment of data collection, comparison of the dataset with other recently published network-intrusion datasets and description of attacks represented in the LITNET-2020 dataset is introduced by Damasevicius et al. (2020). The dataset contains benign traffic of the academic network and 12 attack types generated at KTU managed LITNET network from March 6, 2019 to January 31, 2020. Network traffic was captured using the open source nfcapd binary format, anonymised and processed into the CSV format, containing 39 603 674 time-stamped records. Nfsen, MeSequel, and Python script tools were used for extra feature generation and pre-processing, with data fields in CSV format named after fields, generated by Nfdump.6⁶

For a definition of features used in Nfdump 1.6 see https://github.com/phaag/nfdump/blob/master/bin/parse_csv.pl.

The following Table 7 presents a summary of class representation of this dataset.

The benign class in our datasets constitutes up to 90 % of total records. Fixed ratio random under-sampling, utilizing uniform distribution for record selection, of benign and over-represented malignant class records was implemented on data load for all datasets. Under-sampling refers to the process of reducing the number of samples in a dataset. Fixed ratio random under-sampling method aims to balance class distribution through the random-uniform elimination of majority class examples. It is worth noting that random under-sampling can discard potentially useful data that could be important for the machine learning process. Under-sampling methods can be categorized into two groups: (i) fixed ratio under-sampling and (ii) cleaning under-sampling (Lemaitre et al., 2016). Fixed ratio under-sampling is based on a statistically random selection, which targets the provided absolute record numbers of a given class or a ratio, constituting a proportion of the total number of labels. Cleaning under-sampling is based on either (i) clustering, (ii) the nearest neighbour analysis, or (iii) classification accuracy (based on instance hardness threshold, Smith et al., 2014).

Cleaning under-sampling approaches do not target a specific ratio, but rather clean the feature space based on some empirical criteria (Lemaitre et al., 2016). According to Lemaitre et al. (2016), these criteria are derived from the nearest neighbour rule, namely: (i) condensed nearest neighbours (Hart, 1968), (ii) edited nearest neighbours (Wilson, 1972), (iii) one-sided selection (Kubat and Matwin, 1997), (iv) neighbourhood cleaning rule (Laurikkala, 2001), and (v) Tomek links (Tomek, 1976).

Cleaning under-sampling methods such as Edited Nearest Neighbours, TomekLinks, Condensed Nearest Neighbours were tested, however, due to the size of sub-sampled data and the large computational overhead they require, these methods were not further explored. The fixed random under-sampling was implemented in two steps as follows: 1.

Major class records were first randomly under-sampled to a target number of records, such as to provide sufficient learning for all models. Target numbers were obtained after analysis of learning curves. Sufficient learning is defined here as the objective to have learning and testing curves to converge within a margin less than 1 %, which for all models in this experiment occurs after approximately 0.6 million records.

In this paper, to balance minority classes, we investigate random and SMOTE (Synthetic Minority Over-sampling Technique) (Chawla et al., 2002) over-sampling methods. Random over-sampling is a base method that aims to balance class distribution through the random replication of minority class examples. Unfortunately, this can increase the likelihood of classifier overfitting (Batista et al., 2004). Therefore, we removed all duplicates in training data.

A more advanced method, capable of increasing minority class size without duplication, is SMOTE. SMOTE forms new minority class examples by linearly interpolating between minority class examples that are close. Thus, the overfitting problem risk is mitigated as the decision boundaries of the classifier for the minority class are moved further away from the minority class space. SMOTE works in feature space, not in data space, therefore, before the procedure to over-sample is executed, the first step is to select numeric features to over-sample, as it is not necessary to over-sample in all dimensions. SMOTE over-sampling is achieved by following these steps: a) take k nearest neighbours from minority class for some minority class vector in the feature space, b) randomly choose the vector from those k neighbours, c) take a difference between the vector and its neighbour, and multiply the difference vector by a random number which lies between 0, and 1, d) repeat previous step until the target number of synthetic points is reached. After this, new records can be added to the current data (see Chawla et al., 2002, for a complete algorithm). SMOTE method can be combined with some under-sampling methods to remove examples of all classes that tend to be misclassified. For example, in SMOTE with the Edited Nearest Neighbours (ENN) algorithm (Batista et al., 2004), after SMOTE is used to over-sample a number of records in defined minority classes, ENN is used to remove samples from both classes such that any sample that is misclassified by its given number of nearest neighbours is removed from the training set. Batista et al. (2004) have demonstrated the best results on imbalanced datasets with minority classes containing under 100 records. However, due to the complexity of the edited neighbours procedures (Witten et al., 2005) being O ( n k l ), where n is a number of samples, d – a number of dimensions (features) and k – a number of nearest neighbours, this solution is resource intensive.

As our datasets have not only continuous but also nominal features, we used a modification of SMOTE – Synthetic Minority Over-sampling Technique-Nominal Continuous (SMOTE-NC), from imbalanced-learn library (Lemaître et al., 2017) in the research. We used a recommended number of neighbours equal to k = 5, and separated categorical and numeric features before over-sampling.

Based on the ideas of research and practical implementation recommendations made by Sharafaldin et al. (2018) and Shetye (2019), a selection of features was tested with 3 classes of methods: (a) filtering – correlation and related heat map analysis (b) univariate – recursive feature elimination and (c) iterative – regularization methods. In this research, features were selected with SelectKBest from Scikit-learn library (Pedregosa et al., 2011). The SelectKBest method takes as a parameter a score function, such as χ 2 or Anova F-value, or information gain function and retains the first k features with the highest scores.

If the Anova F-value function is used, a test result is considered statistically significant if it is unlikely to have occurred by chance, assuming the truth of the null hypothesis. If χ 2 is used as a score function, SelectKBest will compute the χ 2 statistic between each feature of X and y (assumed to be class labels). A small value will mean the feature is independent of y. A large value will mean the feature is non-randomly related to y, and so likely to provide important information. Only k features will be retained. Mutual information (information gain) between two random variables is a non-negative value, which measures the dependency between the variables. It is equal to zero if and only if two random variables are independent, whereas higher values mean higher dependency. Mutual information methods can capture any kind of statistical dependency, but being non-parametric (Ross, 2014), it requires more samples for accurate estimation and is computationally more expensive, therefore, as a result of a better time performance in this research, Anova F-value was selected.

Embedded methods penalize a feature based on a coefficient threshold. On each iteration of the model training process those features which contribute the most to the training for a particular iteration are selected.

Further on in this paper, two methods, the filtering and SelectKBest from Scikit-Learn were used to select features.

When performing feature selection, SelectKBest is focusing on the largest classes, therefore a possible improvement would be to do feature selection in a pipeline, by firstly selecting the most important features for the rarest class and then adding features needed for every class.

Generating additional synthetic features was not attempted in this research, as all chosen datasets contain a significant number of such.

Cost-sensitive learning is a subfield of machine learning that takes the costs of prediction errors (and potentially other costs) into account when training a machine learning model (Brownlee, 2020).

If not configured, machine learning algorithms assume that all misclassification errors made by a model are equal. In case of an intrusion detection problem, missing a positive or minority class case is worse than incorrectly classifying an example from the negative or majority class.

The simplest and most popular approach to implementing cost-sensitive learning is to penalize the model less for training errors made on examples from the minority class by adjusting weights. The decision tree algorithm can be modified to weight model error by class weight when selecting splits. The Heuristic rule, also confirmed with intuition from decision trees (Brownlee, 2020), is to invert the ratio of the class distribution in the training dataset.

In this research, weights adjustment for decision trees was implemented using Scikit-learn library model parameters class_weight, setting it to ‘balanced’, which does the above mentioned inversion of class weights. Prior statistics were used for Quadratic discriminant analysis model.

For a performance comparison of machine learning methods on network intrusion detection data with imbalanced classes, we selected the most popular machine learning algorithms from surveys and review papers, related to intrusion detection (Buczak and Guven, 2016; Sharafaldin et al., 2018; Damasevicius et al., 2020).

Standard performance metrics for classifiers are presented in Section 3.6.1, and Bias and Variance decomposition metric (see Section 3.7) was used to evaluate ML algorithm tendencies to overfit or underfit.

The decomposition of the loss into bias and variance helps to improve understanding of generalization capacities of compared learning algorithms, such as overfitting and underfitting. Various methods of decomposition are reviewed in Domingos (2000). It has been demonstrated that high variance correlates to overfitting, and high bias correlates to underfitting. In practical terms, when comparing the performance of learning algorithms, models with lower bias and variance over the same test data would be preferred. It is worth noting that models with a higher degree of parameter freedom tend to demonstrate lower bias and higher variance, and models with a low degree of freedom demonstrate high bias and lower variance.

The loss function of a learning algorithm can be decomposed into three terms: a variance, a bias, and a noise term, which will be ignored further for simplicity (Raschka, 2018). Loss function depends on the machine learning algorithm. For decision trees (CART), training proceeds through a greedy search, each step based on information gain. For the random forest classifier, loss function is the Gini impurity. Cross-entropy is the default loss function to use for multi-class classification problems with MLP.

The prediction bias is calculated as the difference between the expected prediction accuracy of a model and the true prediction accuracy (equation (7)). In formal notation the B i a s of an estimator β ˆ is the difference between its expected value E [ β ˆ ] and the true value of a parameter β being estimated (Raschka, 2018): (7) Bias = E [ β ˆ ] − β .

The variance (equation (8)) is a measure of the variability of model’s predictions if the learning process is repeated multiple times with random fluctuations in the training set. (8) Variance = E [ ( β ˆ − E [ β ˆ ] ) 2 ] . Variance is obtained by repeating prediction on a model trained on stratified shuffle-split training data. The more sensitive the model-building process is towards fluctuations of the training data, the higher the variance (Raschka, 2018).

Finding the values where training and testing learning curves converge allows for creation of better generalizing decision trees, decrease of overfitting and underfitting. The Tree depth (implemented in Scikit-learn library through parameter max _ depth) and α (implemented in Scikit-learn library through parameter ccp _ alpha) were obtained using the method of maximum cost path analysis (Breiman et al., 1984), implemented in Scikit-learn library cost-complexity-pruning-path function and searching for a minimum of Bias and Variance. In this algorithm the cost-complexity measure R α ( T ) of a given tree T is defined in formula (9) as follows: (9) R α ( T ) = R ( T ) + α | T ˜ | , where | T ˜ | is the number of terminal nodes in T, R ( T ) is defined as the total mis-classification cost of the terminal nodes for the complexity parameter α (⩾0). As α increases, more descendent nodes are pruned.

Many variables in the datasets CIC-IDS2017 and CSE-CIC-IDS2018 appear to be correlated with each other, which increases bias while using Quadratic Discriminate Analysis. A statistical measure known as VIF (Variance Inflation Factor) was proposed by Lin et al. (2011) to support elimination of cross-correlation of features and is implemented in this research from statsmodels library (Seabold and Perktold, 2010).

The number of estimators was obtained using the Scikit-learn’s GridSearch (LaValle et al., 2004) method. See Sections 4.4–4.5 and Table 15 for implementation details in this research.

The following procedures were implemented to condition the dataset for better learning of under-represented attack classes: a) removal of unused features and related record duplicates, b) random under-sampling of benign class records, such as to represent no more than a number of records, providing sufficient learning for the worst performing model, obtained after analysis of learning curves and c) over-sampling using SMOTE for the training sub-sample of extremely rare records (see Table 4) up until the minimum number of examples of classes with high imbalance.

Duplicate rows were removed (leaving the first one), see Table 8.

The following 8 features ‘Bwd PSH Flags’, ‘Bwd URG Flags’, ‘Fwd Avg Bytes/Bulk’, ‘Fwd Avg Packets/Bulk’, ‘Fwd Avg Bulk Rate’, ‘Bwd Avg Bytes/Bulk’, ‘Bwd Avg Packets/Bulk’, ‘Bwd Avg Bulk Rate’, containing no information ( Std = 0 ) in all loaded files and duplicate feature ‘Fwd Header Length.1’ ( corr = 1 ) with ‘Fwd Header Length’ were removed.

After dropping the duplicates, the 2 522 362 remaining records were investigated for missing values and infinities.

As a result, 1 358 missing values containing records were removed with drop duplicates. The remaining 353 rows with missing values were found to be split between ‘Benign’ (350) and ‘DoS Hulk’ (3) classes and missing values were replaced with −1.

Further, 1 211 records with infinities in two features Flow ‘Bytes/s’ and ‘Flow Packets/s’ were found and replaced by maximums of values per class, see Table 9.

This processing step is made under an assumption that such a replacement for lost values would be possible to implement after learning the values during the initial training of a real life intrusion detection system.

Further numbers of records for Benign and second largest class Dos Hulk were transformed with a skewed fixed ratio under-sampling. Remaining data is split into test and train sub-samples. The training sub-set is then over-sampled with SMOTE (thus training record count values of 4 999 and 2 999 in Table 10). This procedure keeps all extremely imbalanced class records (Table 4) intact and adds new records for the training, resulting in record counts for the training and testing samples presented in Table 10.

After this, the values of numeric columns were scaled to a range of [ 0 ; 1 ] with Scikit-learn (Pedregosa et al., 2011) QuantileTransform. This transformation assigns each feature into a quantile individually and scales such that it is in the given range on the training set, by default between zero and one.

Further in this research, the 40 best features were selected using the SelectKBest procedure from the Scikit-learn library (Pedregosa et al., 2011) and followed by Variance inflation factor analysis with a target threshold value equal to 40, to eliminate variables with high collinearity.

The same pre-processing procedure from Section 4.1 was applied to dataset CIC-IDS2018.

The timestamp column and related record duplicates were removed, as no time series dependent machine learning methods were chosen in this research.

Afterwards, 8 features ‘Bwd URG Flags’, ‘Bwd Pkts/b Avg’, ‘Bwd PSH Flags’, ‘Bwd Blk Rate Avg’, ‘Fwd Byts/b Avg’, ‘Fwd Pkts/b Avg’, ‘Fwd Blk Rate Avg’, ‘Bwd Byts/b Avg’ containing no information (eq. Std = 0) were removed.

The following sampling procedures were executed in order to achieve a better balance between major classes and extremely rare classes:

It should be noted that 7 373 records with infinities in two features ‘Flow Bytes/s’ and ‘Flow Packets/s’ were found and replaced by maximums of values per class, see Table 12.

Presence of such values could indicate that related flows were not terminated on recording.

After the data cleaning, the dataset was normalized with QuantileTransform. The 40 best features from SelectKBest were passed through the Variance Inflation Factor procedure with a threshold of 40 which was selected to eliminate collinearity of features.

Due to the choice of supervised machine learning models and problem definition in this study, the LITNET-2020 dataset timestamp feature was not used. Features related to the source and destination address, such as source and destination issuing authorities, are highly supportive in discovering not only the attacker but also the attack class, therefore, in order to support generalization of training, they were eliminated.

After removing timestamp and address related features, related duplicate records were also removed, see Table 13.

The resulting dataset is even more imbalanced. The target number of records of the Benign and the Code Red type was set after learning curves that indicate the number of records required by the worst performing model for sufficient learning. Sufficient learning is defined here as the objective of getting the learning and testing curves to converge within a margin of less than 1 %, which for all models under experiment occurs after approximately 0.5 million records.The dataset was further split by half into testing and validation.

As a final step, a Synthetic Minority Over-sampling Technique for Nominal and Continuous features for datasets with categorical features, SMOTE-NC, introduced by Chawla et al. (2002) was implemented, see Table 14.

After the data cleaning, the dataset was normalized with QuantileTransform. The 40 best features from SelectKBest were obtained and further checked for feature collinearity. Collinear features were reduced using the Variance Inflation Factor procedure (see Section 3.9) with a threshold value of 40.

All code for models was realized in the Python 3.7 environment on Anaconda 3 using Scikit-learn7⁷

https://scikit-learn.org/stable/.

Model parameters were searched with the GridSearch method. Tree depth and alpha were further validated using the method of maximum cost path analysis (Breiman et al., 1984), implemented in Scikit-learn by the cost-complexity-pruning-path function (see Section 3.8).

The following parameter ranges were selected for the grid search:

The parameters used in this study are presented in the Table 15.

Tables 16, 17 and 18 represent the results of ML methods rankings using a Standard Ranking approach (Adomavicius and Kwon, 2011), where equal items get the same ranking number, and a gap is left in between the smaller and bigger result, where the bigger result means a worse result.

In Table 16, the results of scoring by Balanced Accuracy are in favour of trees or their ensembles, Adaboost being the strongest, closely followed by Random Forest Classifier and K-Nearest Neighbours.

Results of this research support notion that Balanced Accuracy metric (see Table 16) should be used for measuring accuracy in case of highly and extremely imbalanced data sets. Error Rate for all models is below 0.1, while Balanced Accuracy manifests some insufficient learning. Accuracy of Extremely rare (malicious) classes in this research is dominated by majority (benign) class, representing over 80% of the whole data (see Tables 2 and 3) and therefore Error Rate is overly optimistic, under-representing the prediction error of Extremely rare classes (see Table 4), important to this research.

The ranking results in Table 17 were obtained based on the minimum of the sum of rankings for Presicion and G ¯. The results of scoring by Precision and G ¯ are in favour of the same tree ensembles.

The rankings of bias and variance decomposition in Table 18 are obtained on a basis of the minimum of the sum of bias and variance (equal to the model mean squared error, when not accounted for the noise component). The bias and variance are calculated according to formulas (7) and (8). To calculate bias, we have to estimate β and β ˆ. β is equal to true class labels vector of test dataset. To estimate β ˆ, the bootstrap with replacement of training dataset is taken 5 times, each time the model is trained and its prediction for each training dataset is stored as a separate vector β ˆ value. Then Bias 2 is estimated as squared length of the difference of average prediction vector ( E [ β ˆ ]) and test dataset true label vector (β) and divided by the number of test records. The variance (Var) is then calculated by formula (8), e.g. it estimates the variance in β ˆ calculated for each bootstrap sample with replacement from the training dataset.

The QDA values that are much higher than average compared to other algorithm errors from the same data in Table 18 are a characteristic property of models with low number of hyper-parameters as noted in Brownlee (2020). Values obtained in this experiment could be local optima, but authors were not able to find other parameter values that would result in lower difference of values for this model between datasets. However, bias and variance of this model was noticed to be sensitive to changes in a list of features selected before the parameter search process. The list of features chosen for model training is individual for each dataset.

Comparison of results of research in different implementations for CIC-IDS2017 and CSE-CIC-IDS2018 datasets is presented in Table 19. Performance metrics are not directly comparable to our research (further in Table 19 – this research), as validation results in our experiment were obtained using multiple class optimization and 50% of dataset as a hold-out data, versus standard k-fold cross-validation, known to be prone to knowledge leak. In our methodology, cost sensitive model implementations provided classification for multiple class measures. However, for comparison, traditional measures suitable only for balanced datasets are presented with other reviewed studies (see Table 19). It is important to note that optimization in this experiment was done on Balanced Accuracy Score, therefore, other measures are sub-optimal.

In Sharafaldin et al. (2018) authors had an objective to introduce the CIC-IDS-2017 dataset, and default parameter model results of machine learning are presented for purely benchmark purposes of future research. Feature selection was performed using the random forest regression feature selection algorithm. The results of Precision, Recall and F 1 were obtained in their studies in a form of weighted average of each evaluation metrics and are represented in Table 19. Iterative Dichotomiser 3, decision tree learner with an early stopping, as implemented in Weka (Witten and Frank, 2002), is used in their research. In our research the results were obtained using macro average for the above mentioned and other performed metrics. Macro averages of metrics are more sensitive to the imbalance of classes.

In Sharafaldin et al. (2019) authors improve results on RFT through proposing super-feature creation versus random feature regression algorithm for feature selection used in previous research (Sharafaldin et al., 2018). In our research the feature selection was obtained through fast Kbest procedure with Anova F-value optimization function, however, algorithm has been chosen after testing three classes of feature selection methods.

In Yulianto et al. (2019) strategy, SMOTE is utilized with CIC-IDS-2017. However, only benign and DDos class data of CIC-IDS-2017 dataset is taken, calculating binary classification problems, therefore, produces results that are incomparable to our research results. Features in their research are also selected differently, first utilizing Primary Components Analysis (PCA), then the Ensemble Feature Selection (EFS), using EFS Package in R Studio and ensemble methods gbm, glm, lasso, ridge and treebag from the fscaret library. The AdaBoost classification with default weak decision tree classifiers was used during the training. Meanwhile, in our research a choice was made to strengthen the base classifier via pruning. The results of Precision, Recall and F 1 obtained are represented in Table 19.

Kanimozhi and Jacob (2019a, 2019b) classified the CSE-CIC-IDS2018 data set using ADA, RF, kNN, SVM, NB and ANN (Artificial neural network) machine learning methods. For an ANN authors used MLP with two layers, lbfgs solver, grid searched alpha parameter (for L2 regularization) and Hidden layer sizes. In their research, authors used 0–1 classification. Either “Benign” or “Malicious” labels were used for training, making the results directly incomparable with our multi-class approach. Results of the accuracy, precision, recall, F 1 and AUC were obtained. The results of Precision, Recall and F 1 are represented in Table 19.

In the study Karatas et al. (2020) classified the CSE-CIC-IDS2018 dataset using KNN, RFT, GBC, ADA, DT (Decision tree), and LDA (Linear discriminant analysis with singular value decomposition solver) algorithms. Parameters that were selected for all the implemented algorithms are described in Karatas et al. (2020) Table 8. Number of classes was determined to be six (one for non-attack type, and 5 for attack types), making the results directly incomparable with our multi-class approach. Cross-validation with 80%/20% split of training and test data was used. Results of the accuracy, precision, recall and F 1 were obtained. The results of Precision, Recall and F 1 are represented in Table 19.

In their study Kilincer et al. (2021) classified the CSE-CIC-IDS2018 dataset using KNN, DT, and SVM algorithms. Options of Matlab for KNN with KNN Fine algorithm, DT with Fine tree and SVM Quadratic algorithm gave the best results in this research. Results on a limited amount of records (up to 1584 records per class, see Kilincer et al. (2021) Table 3) were used in this research for CSE-CIC-IDS2018 dataset classes. Authors focus on UNSW-NB15 dataset with no discussion on pre-processing for CSE-CIC-IDS2018, parameter search or tree pruning or overfitting. Results of the accuracy, precision, recall, F 1 and g-mean were obtained. The results of Precision, Recall and F 1 are represented in Table 19.

In Dutta et al. (2020) authors used SMOTE and ENN to balance the LITNET-2020 dataset. Classes are reduced to two, normal and malignant, therefore, results are directly incomparable with ours. The approach also differs in that authors reduce dimensionality with Deep sparse autoencoder (Zhang et al., 2018), selecting 15 features. Then authors stack LSTM with adam optimizer and DNN with four layers, back-propagation and stochastic gradient descent as the optimizer and early stopping on Keras with TF back-end and Scikit-learn. 5-fold validation was used in that research. Results of the precision, recall, false positive rate, and MCC were obtained. The results of Precision, Recall and F 1 are represented in Table 19.

Regarding the limitations of the approach taken in this research, it is important to note that new categories of malicious traffic in reality are introduced daily. Therefore, models tuned using this method will not detect zero day threats.

Another know limitation is that in absolute rarity case, or when data has not been obtained and labelled sufficiently, models will predict with high Error rate. A possible known solution to this problem is an anomaly detection for the unseen data.

Moreover, datasets CIC-IDS2017 and IDS-2018 lack some categorical flag data, which is possible to obtain, like it has been demonstrated in LITNET-2020 case.

Even though LITNET-2020 lacks temporal features, introduced in CIC-IDS datasets, this, however, can be resolved by running the CICFlowMeter on the original PCAP files.

Temporal average approach of flags does not help some classes like Infiltration, however, flag features could be added to CIC-IDS datasets in the future.

While SMOTE was helpful for some rare classes, the method did not help much where sub-classes overlap due to lack of host data or feature latency.

Some features can be extracted and supplemented, which might be used in future research, however, extraction requires high degree of previous network traffic logging, whereas authors are aware that organizations lack resources to collect data on such a level of detail.

Details of comparison of each class and dataset before and after SMOTE up-sampling is not represented here due to substantial amount of tables. However, it is important to note that some rare classes in these datasets learn very well even with a small numbers of records, which is confirmed by testing using dedicated unseen data. Some classes learn significantly better after adding synthetic data, which is further supported with tests on model performance and classification reports executed before (prefixed with n as n P r and n G ¯ for no-SMOTE) and after enriching data using SMOTE procedure in Table 20 prefixed with s as sPr and s G ¯.

As demonstrated in Table 20, random data under-sampling and SMOTE over-sampling techniques are supportive in ensuring that extremely under-represented classes (see Table 4) can learn with non-zero precision and G ¯, or provide better results.