## 2 Materials and Methods
### The Datasets  
There are at least two approaches that might be considered for obtaining new mappings between emotion representation models. The first one is to use a set of heuristics based on expert (psychological) knowledge, and that approach was the basis for creation of the state-of-the-art matrix. The second approach is to find a dataset that is annotated with both emotion representation models and to use statistical or machine learning techniques to find a mathematical model for the mapping. The latter approach was chosen for this study. The datasets were obtained by pairing lexicons of affect-annotated words. The evaluation sets were retrieved from affect-annotated lexicons that use PAD and/or a dimensional adaptation of [PERSON]'s six basic emotions model. The available lexicons might be created by manual, automatic or semi-automatic annotation [27]. As we wanted to use the data retrieved from the lexicons as the \"ground truth\", only the lexicons with manual annotations were taken into account. The following lexicons were used in this study (historical order):  
1. **The Mehrabian and Russel lexicon**. This lexicon is a relatively old one, as it was developed and published in 1977 by [PERSON] and [PERSON] [28]. It was developed by manual annotation of English words and contains 151 words. The annotators used a PAD model for representation of emotions for the first time and the PAD model has been a reference model ever since then. The annotated sets include mean and standard deviations of evaluations per dimension provided for all participants. Sample words with annotations are presented in Table 1.  
There are at least two observations derived from studying the lexicon: firstly, some words are more ambiguous than others; and, secondly, some dimensions are more ambiguous than others (distribution of standard deviations differs). 2. **The ANEW Lexicon**. The ANEW lexicon was initially developed for English [29], but has many national adaptations. The lexicon contains the most frequently used words (1040). Annotation is based on a PAD model, and mean as well as standard deviations per dimension are provided. Sample words with annotations are presented in Table 2. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Word** & **Valence Mean (SD)** & **Arousal Mean (SD)** & **Dominance Mean (SD)** \\ \hline strong & 0.58 (0.24) & 0.48 (0.3) & 0.62 (0.3) \\ lonely & \(-\)0.66 (0.35) & \(-\)0.43 (0.36) & \(-\)0.32 (0.3) \\ happy & 0.81 (0.21) & 0.51 (0.26) & 0.46 (0.38) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Sample annotations of words from [PERSON] and [PERSON] lexicon. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Word** & **Valence Mean (SD)** & **Arousal Mean (SD)** & **Dominance Mean (SD)** \\ \hline strong & 7.11 (1.48) & 5.92 (2.28) & 6.92 (2.43) \\ lonely & 2.17 (1.76) & 4.51 (2.68) & 2.95 (2.12) \\ happy & 8.21 (1.82) & 6.49 (2.77) & 6.63 (2.43) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Sample annotations of words from ANEW lexicon. Please note the difference in scaling the dimensions for [PERSON] and [PERSON]'s and ANEW lexicons. Re-scaling is required for comparisons. 3. **The Synseketch lexicon**. [PERSON] [30] contains 5123 English words annotated manually with overall emotion intensity and [PERSON]'s six basic emotions (anger, joy, surprise, sadness, disgust and fear). The Synseketch lexicon was found partially invalid from the viewpoint of this study--some words had no annotations in any of the dimensions of the basic six emotion set. The all-zeros vector might be interpreted in two ways: a case of neutral annotation or an error. An additional feature provided within the lexicon (overall emotion intensity) was used to differentiate the two cases. If overall emotion intensity was assigned a non-zero value and the other dimensions were not, the vector was considered invalid and excluded from further analysis. Sample words with annotations are presented in Table 3.
4. **The NAWL lexicon**.