## 1 Introduction  
The personalization of the virtual learning environment (VLE) reflects the ways in which learning processes may be controlled so that each environment is optimally attractive to the learner. This includes personalized navigation, a personalized recommendation engine, personal instructors, personalized learning paths, fragment sorting and content adaptation as a means to customize learning objects for constrained environments, and student knowledge diagnosis as a task in realizing personalized education, among others [1; 2; 3; 4; 5; 6; 7; 8; 9]. VLE constraints may be dictated by both personal preferences and the learning style of the learner [10]. In general, \"learning styles\" refer to a range of theories that aim to account for differences in individual learning methods. Many theories share the proposition that humans can be classified according to their \"style\" of learning but differ in how the proposed styles should be defined, categorized, and assessed [11]. The learning style of the learner can be automatically determined by the learner's activities in a virtual learning environment [12]. Automatic identification of the learning style of the learner(s) employs user modeling, which may be divided into static or dynamic modeling, via stereotypes and highly adaptive user models [13]. In our previous papers, we investigated the exemplar-based methods that are sometimes applied to automatic learning-style diagnostics [14; 15]. For example, the Bayesian case model (BCM) is a generative format that uses unsupervised learning methods and may predict the proportions of learning-style clusters for each student. Probabilistic models, in general, try to use the Bayes formula or mixture models in a multi-label scenario [16]. In addition, BCM offers explanations for each learning-style cluster, using prototypes and important features. In unsupervised learning, only input data is provided to the model. Conversely, in supervised learning, input data is provided to the model, along with the output data. The goal of supervised learning is to train the model so that it can predict the output when it is given new data. The supervised user (learner) model classifies students into their particular classes according to their learning style (for example, visual, kinesthetic, aural, social, solitary, verbal, or logical) and/or assigns multiple learning-style labels to the learner. Multi-label classification allows the model to classify data sets with more than one target variable [17]. When making predictions, a given input may belong to more than one label. The task of determining the learning style of a student (or a group of students) may be treated as a multi-label classification task. Formally, multi-label classification is the problem of finding a model that maps input \(\mathbf{x}\) to binary vector \(\mathbf{y}\) (assigning a value of 0 or 1 for each element (label) in \(\mathbf{y}\)). In the case of students' learning styles, prediction labels might be taken from the widely adopted Felder-Silverman model [10], wherein learning styles are a balance between pairs of extremes, such as Active/Reflective, Sensing/Intuitive, Verbal/Visual, and Sequential/Global. Each student or a group of students may be assigned a set of these labels by the model, and some of the labels are more typical for a particular student (or group of students) than others. Therefore, for each label, the model should predict the probability that the student (or group of students) is characterized by the label(s). The model might be trained on the data set, manually labeled by experts, that stores students' activities in the VLE. The values of the data features primarily store the number of times that a particular learning activity was selected by a student or for how long it was used by the student in question. Therefore, the aim of this research is to identify multi-label classification methods that are suitable for students' learning-style detection, as well as the interpretation methods that can explain the classification results.