## 1 Introduction
One of the extended models found some applications in affective computing, for example, the PAD (pleasure-arousal-dominance) model [15; 16]. Furthermore, [PERSON]'s six emotions model has been adapted as a dimensional model with each emotion forming one dimension (sometimes a dimension for neutral state is also added). The dimensional models are frequently used by the emotion recognition algorithms and off-the-shelf solutions. Dimensional adaptation of [PERSON]'s six basic emotions is used for solutions based on facial expressions, and Facial Action Coding Scheme (FACS) is the most widely implemented technique [17]. Sentiment analysis of textual inputs (used in opinion mining) mainly explores the valence dimension of the Circumplex/PAD model [18]. Emotion elicitation techniques based on physiology mostly report only on the arousal dimension [19], as positive and negative experiences might cause a similar activation of the nervous system. Componential models use several factors that constitute or influence the resulting emotional state. The OCC model proposed by [PERSON], [PERSON] and [PERSON] defines a hierarchy of 22 emotion types representing all possible states which might be experienced [20]. In contrast to discrete or dimensional models of emotions, the OCC model takes into account the process of generating emotions. However, several papers outline that the 22 emotional categories need to be mapped to a (possibly) lower number of different emotional expressions [21; 22]. The analysis of the emotion recognition solutions reveals that there is no one commonly accepted standard model for emotion representation. Dimensional adaptation of [PERSON]'s six basic emotionsand the Circumplex/PAD model are the ones widely adopted in emotion recognition solutions. The problem of mapping is multifaceted, including mapping between dimensional and discrete representations, as well as mapping among different dimensional models. There are several solutions to the first issue: using weights, representing discrete labels as points in dimensional spaces and so on. However, the paper concentrates on the latter issue of mapping between dimensional representations. Appreciating label-based and componential models, a further part of this study focuses on mapping between dimensional models only. (2) There are few studies on mapping between emotion representation models. The papers provide mapping techniques that enable conversions among a personality model, an OCC model and a PAD model of emotion. The mappings have a significant explanatory value of how personality characteristics, moods and emotions are interrelated [16; 23]. However, as the personality model is not used in emotion recognition, they are not directly applicable in this study. Exploration of the literature provides one model of mapping between [PERSON]'s five basic emotions and the PAD model [24]. The mapping technique reported in [23; 24] provides a linear mapping based on a matrix of coefficients provided in Equation (1). \[ \begin{split}\text{PAD}[\mathit{Anger},\ \mathit{Disgust},\ \mathit{Fear},\ \mathit{Happiness},\ \mathit{Sadness}]\\ =\left[\begin{array}{cccc}-0.51&-0.40&-0.64&0.40&-0.40\\ 0.59&0.20&0.60&0.20&-0.20\\ 0.25&0.10&-0.43&0.15&-0.50\end{array}\right]\end{split}  \tag{1}\]  
The mapping has been used in several further studies [25; 26] and remains the most popular one. The existing matrix was not trained on any dataset, instead it was derived from an OCC model. The existing matrix might be considered rather as a theoretical model than a model based on evidence. Nevertheless, this is the only known mapping matrix; therefore, we use it as a reference, as there is no other one to compare our solution to. One might notice, that out of six emotions in [PERSON]'s basic set, the mapping utilizes only five, excluding surprise. An analysis of late fusion studies reveals that two approaches are applied: all emotion recognition algorithms use the common representation model as an output [1], or all representations are mapped into a Circumplex/PAD model of emotions.