## 3 Results
### Experimental Evaluation and Comparative Analysis of Multi-Label Classifiers
As the data set is small, each _OneVsRestClassifier_ that uses another estimator as a parameter was evaluated using the hold-out method: the data set was split up into a \"train\" and \"test\" set. The training set is the data on which the model is trained, and the test set is used to see how well that model performs on unseen data. The evaluation results are presented in Figures 2-8, below. According to the results, _MultinomialNB_ and _GradientBoostingClassifier_ should be preferred for the classification of learning styles as their F1 scores are the highest and their Hamming losses are the lowest. As we know from the theory, the Hamming loss is a better metric than accuracy for multi-label classification as, in the latter case, a misclassification is no longer a definite wrong or right answer [40; 41]. Besides this, the Hamming loss is also used to measure the performance of imbalanced data set approaches [42]. Figure 4: Recall values according to the labels of the OneVsRestClassifier, which uses another estimator as a parameter. Figure 3: Precision values according to the labels of the OneVsRestClassifier, which uses another estimator as a parameter. Figure 2: Hamming losses and Hamming scores of the OneVsRestClassifier, which uses another estimator as a parameter. Figure 5: F1 score values according to the labels of the OneVsRestClassifier, which uses another estimator as a parameter. Figure 6: Precision averages of the OneVsRestClassifier, which uses another estimator as a parameter. Figure 7: Recall averages of the OneVsRestClassifier, which uses another estimator as a parameter. Due to the large number of multi-label classification methods, for our algorithm adaptation methods, we relied on the evaluation results presented in [16]: RFPT and BPNN are the best-performing methods. In order to experimentally test the application of neural networks for student learning-style detection, we constructed a fully connected neural network of 4 layers using a _sigmoid_ activation function in the output layer and a _relu_ activation function in the other layers. The _sigmoid_ activation function was chosen because it most often showed a return value in the range of 0 to 1, and our task was to assign to each sample a set of probabilities for target labels corresponding to the student's learning style (intuitive, sensing, verbal, active, global, sequential, reflective, or visual). The number of neurons in each layer was equal to the number of learning activities (this was 12). The batch size was 30. The He_uniform variance scaling initializer was used to set the initial random weights. The neural network was trained on the data of the same training data set that was used for applying the OneVsRest strategy. The data set has no missing values. The Binary_crossentropy loss function and adaptive moment estimation (Adam) learning method (optimizer = tf.keras.optimizers.Adam (lr = 0.0001)) was used, which computes adaptive learning rates for each parameter. With Adam, the learning rate may at first increase in the early layers; thus, helping to improve the efficiency of the deep neural network. The network converged after 30 epochs. In the NN, the correlation is taken into account since the hidden layers are summing all the input signals together via a fully connected layer. The neural network will learn about the co-occurrence of labels, finding some deterministic rules for generating the best output. The predictions of the model are presented in the form of \"[0.991552591 0.599381804 0.772709548 0.0182502270 0.00593709946 0.112661839 0.981987536 0.987546802]\" for every data sample, indicating the probability values for each learning-style class. The model was evaluated on the validation data set, using the repeated k-fold cross validator, which was repeated 5 times. The average model accuracy obtained was quite small--2.66. The reasons for that may be the small training data set, imperfect data labeling by the experts, insufficient feature engineering, and/or the imbalance of data.