# A Continuous Music Recommendation Method Considering Emotional Change
## 6 Experiments and Evaluation
### Experimental Results and Evaluation
#### 6.3.2 Evaluation of User Emotion Prediction Results Considering Emotional Changes  
To demonstrate the effectiveness of the proposed method, a comparative experiment was conducted between the emotion prediction results using the mental model proposed in a previously reported study [26] and the emotion prediction results by applying the PMM proposed in this paper. In this comparison, the mental model from the previous study was adapted by mapping its emotions to four categories. This modified mental model is referred to as the MMM. Equation (23) is the emotional state transition matrix of the MMM based on four emotions. \[P= \begin{array}{cccc}&Happy&Angry&Sad&Peaceful\\ &Angry&\\ Sad&\\ Peaceful&\\ \end{array} \left[ \begin{array}{cccc}0.34&0.16&0.14&0.36\\ 0.17&0.35&0.34&0.14\\ 0.15&0.29&0.41&0.15\\ 0.35&0.13&0.13&0.39\end{array} \right] \tag{23}\]  
In order to predict user emotions considering emotional changes, we first extracted user data to be used in the experiment. Table 10 shows an example of a user's emotional vector by time, and \(t_{0}\) means the current time. For example, for a prediction experiment, we want to predict the emotions of the user at time \(t_{0}+1\) and \(t_{0}+2\) based on the history data up to time \(t_{0}\) based on the current time. Equation (24) is the emotion vector of the user at the current time, and Equation (25) is the emotion state transition matrix generated based on the history data up to the current time. \[ \begin{array}{cccc}\overset{\rightarrow}{V_{u}^{t_{0}}}=(1.0,0.0,0.0,0.0) \\ &Happy&Angry&Sad&Peaceful\\ &Happy&Angry&Sad&Peaceful\\ &Angry&\\ Sad&Peaceful&\\ \end{array}  \tag{24}\]  
\[P= \begin{array}{cccc}Happy&Happy&Sad&Peaceful\\ &Angry&\\ Sad&\\ Peaceful&\\ \end{array} \left[ \begin{array}{cccc}0.65&0.05&0.00&0.29\\ 1.00&0.00&0.00&0.00\\ 0.00&0.00&0.00&0.00\\ 0.67&0.04&0.00&0.29\end{array} \right] \tag{25}\]  
Figure 9 shows the mental model through the emotional state transition matrix of the user. \begin{table}
\begin{tabular}{c c c c c} \hline
**Time** & **Happy** & **Angry** & **Sad** & **Peaceful** \\ \hline \(t_{0}-5\) & 0.80 & 0.00 & 0.00 & 0.20 \\ \(t_{0}-4\) & 0.67 & 0.00 & 0.00 & 0.33 \\ \(t_{0}-3\) & 0.50 & 0.00 & 0.00 & 0.50 \\ \(t_{0}-2\) & 0.71 & 0.00 & 0.00 & 0.29 \\ \(t_{0}-1\) & 0.50 & 0.25 & 0.00 & 0.25 \\ \(t_{0}\) & 1.00 & 0.00 & 0.00 & 0.00 \\ \(t_{0}+1\) & 0.67 & 0.00 & 0.00 & 0.33 \\ \(t_{0}+2\) & 0.60 & 0.00 & 0.00 & 0.40 \\ \hline \end{tabular}
\end{table} 
Table 10: Example of a user’s emotional vector for each time. To predict the emotional state at times \(t_{0}+1\) and \(t_{0}+2\), the emotional state transition matrix using the emotional vector at the current time and PMM is calculated as in Equation (26). \[ \begin{split} P(E_{1})=[1.0,\ 0.0,\ 0.0,\ 0.0]\begin{bmatrix}0.65 & 0.06 & 0.00 & 0.29\\ 1.00& 0.00 & 0.00 & 0.00\\ 0.00& 0.00 & 0.00 & 0.00\\ 0.67& 0.04 & 0.00 & 0.29\end{bmatrix}^{1}\\ P(E_{2})=[1.0,\ 0.0,\ 0.0,\ 0.0]\begin{bmatrix}0.65 & 0.06 & 0.00 & 0.29\\ 1.00 & 0.00 & 0.00 & 0.00\\ 0.00 & 0.00 & 0.00 & 0.00\\ 0.67& 0.04 & 0.00 & 0.29\end{bmatrix}^{2}\\ \end{split}  \tag{26}\]  
As a result of the calculation, the result of predicting the emotional state of the user at times \(t_{0}+1\) and \(t_{0}+2\) is as shown in Equation (27). \[ \begin{split} V_{u}^{t_{0}+1}&=(0.65,0.06,0.00,0.29)\\ V_{u}^{t_{0}+2}&=(0.68,0.05,0.00,0.27)\end{split}  \tag{27}\]  
In addition, to predict the emotional state at times \(t_{0}+1\) and \(t_{0}+2\), the emotional state transition matrix using the emotional vector of the current time and MMM is calculated as in Equation (28). \[ \begin{split} P(E_{1})=[1.0,\ 0.0,\ 0.0,\ 0.0]\begin{bmatrix}0.34 & 0.16& 0.14& 0.36\\ 0.17& 0.35& 0.34& 0.14\\ 0.15& 0.29& 0.41& 0.15\\ 0.35& 0.13& 0.13& 0.39\end{bmatrix}^{1}\\ P(E_{2})=[1.0,\ 0.0,\ 0.0,\ 0.0]\begin{bmatrix}0.34 & 0.16& 0.14& 0.36\\ 0.17& 0.35& 0.34& 0.14\\ 0.15& 0.29& 0.41& 0.15\\ 0.35& 0.13& 0.13& 0.39\end{bmatrix}^{2}\\ \end{split}