## 1 Introduction  
This paper concerns one of the challenges in automatic multimodal affect recognition, i.e., mapping between emotion representation models. There are numerous emotion recognition algorithms that differ on input information channels, output labels, and representation models and classification methods. The most frequently used emotion recognition techniques that might be considered when designing an emotion monitoring solution include: facial expression analysis, audio (voice) signal analysis in terms of modulation, textual input analysis, physiological signals and behavioral patterns analysis. As literature on emotion recognition methods is very broad and has already been summarized several times, for an extensive bibliography, one may refer to [PERSON] and [PERSON] [1] or [PERSON] et al. [2]. [PERSON] et al. claim that multimodal fusion improves robustness and accuracy of human emotion analysis. They observed that current solutions mostly use one input channel only and integration methods are regarded as ad-hoc [3]. Late fusion combines the classification results provided by separate classifiers for every input channel; however, this requires some mapping between emotion representation models used as classifier outputs [3]. Differences in emotion representation models used by emotion recognition solutions are among the key challenges in fusing affect from the input channels. This paper concentrates on the challenge of mapping between emotion representation models. The purpose of the paper is to propose a method (including a set of metrics) for an evaluation of the mapping accuracy, as well as to propose a new mapping. The main research question addressed in this study is as follows: How to compare results from multiple emotion recognition algorithms, especially when they are provided in different affect representation models? The studies related to this research fall into two categories: (1) emotion representation models, which are used as an output of affect recognition solutions; and (2) research on mapping algorithms between the models. (1) There are three major model types of emotional state representation: discrete, dimensional and componential [4]. Discrete models distinguish a set of basic emotions (word labels) and describe each affective state as belonging to a certain emotion from the predefined set. A significant group of emotion recognition algorithms uses emotion representation based on labels only, e.g., distinguishing stress from a no-stress condition [5]. The label-based representation causes serious integration problems, when the label sets are different. Fuzziness of linking concepts with words and a problem of semantic disambiguation are the key issues causing the difficulty. One of the best known and extensively adapted discrete representation model is [PERSON]'s six basic emotions model, which includes joy, anger, disgust, surprise, sadness and fear [6]. Although the model was not initially proposed for emotion recognition, it is the one used most frequently, for example in e-learning affect-aware solutions [7]. Simple affective applications, such as games, frequently use very simple models of two or three labels [8; 9]. Furthermore, some more sophisticated solutions, applied in e-learning, incorporating affect recognition, use their own discrete label set [10; 11; 12]. Dimensional models represent an emotional state as a point in a multi-dimensional space. The circumplex model of affect, one of the most popular dimensional models, was proposed by [PERSON] [13]. In this model, any emotion might be represented as a point in a space of two continuous dimensions of valence and arousal. The valence (pleasure) dimension differentiates positive from negative emotions, while the dimension of arousal (activation) enables a differentiation between active and passive emotional states. Both dimensions are continuous with neutral affective states represented in the middle of the scale [14]. The model was repeatedly extended with new dimensions, such as dominance and imageability.