## 2 Materials and Methods
### Modelling
#### 2.2.1 Mental Heart Rate Calculation  
The total HR was measured by the wristbands. The basal HR component was estimated before the start of the experiment, by a continuous measurement of the individuals, and was also updated during the experiment. Lastly, the physical component was estimated by a linear autoregressive (AR) SISO model, in which step count data, assessed with an accelerometer, were used as an input, and the physical HR as the model output.  
\[HR_{\textit{Mental}}\ =\ HR_{\textit{Total}}-HR_{\textit{Basal}}-HR_{\textit{Physical}}- HR_{\textit{Thermal}} \tag{1}\]  
The wearable measures heart rate and activity (steps) which are used as inputs to the data-based-mechanistic (DBM) model as used by [PERSON] [24]. Most of the metabolic energy for most people during their life is produced in an aerobic way. This means that HR, pumping the oxygen to the cell level via de lungs, indicates how much aerobic metabolic energy can be produced. The total HR can be decomposed into a basal component, a physical component and a mental component. The basal one is the amount of HR required to keep the body functioning. The physical one is the part of the total HR to perform a  
Figure 1: Mindstretch menu for labelling emotions. The time interval in which the emotion was experienced can be adjusted. Below, the experienced emotion is designated.  
specific physical activity such as running, walking, writing, etc. The mental component is considered as the total HR minus the basal one and the physical one. These different components can be estimated in real time (Figure 2). When the wearable measures activity and HR, the algorithm can detect the minimal HR or basal component for the individual subject by monitoring 24/7. As soon as the subject leaves the bed, the wearable measures the physical activity in time and the response of the HR to this physical performance. From the dynamics of those two signals, the physical component of the total HR can be calculated. The same happens when the outside temperature is varying, and the HR is responding to this by controlling body temperature. From the dynamics, the thermal component is calculated. It has been shown that the mental component of HR correlates with the blood hormone noradrenaline [27; 28; 37].  
Next, this data-based mechanistic (DBM) model was identified for every labelled emotion event of every participant, describing the dynamic mental HR response to an emotion. In this approach, abstract model parameters were estimated based on the mental HR data, which were given a physical or biological meaning afterwards [38; 39]. More concretely, single-input single-output (SISO) discrete-time transfer function (TF) models were applied to characterise the relationship between the (step) input, which is a binary input, differentiating between the period right before and after the onset of the emotion, and the output, the mental HR response, associated to it (Figure 3). The model parameters were considered to be time-invariant because the emotion processing of an individual in a single instance was not supposed to change over the course of the experience of that emotion, which is typically very short in duration. Afterwards, the estimated model orders and parameters of the SISO TF were used as features in a support vector machine (SVM) ML classifier, to classify the different emotions. There are several advantages of using DBM models for the current emotion recognition. First, the estimated model parameters can be given a biological meaning and can be interpreted in a meaningful way [39; 40]. Second, DBM models can be used for small datasets, while purely ML-based classifiers often need a lot of features and large datasets [39]. Therefore, DBM is a faster method than purely ML-based or deep learning methods for real-time applications in daily life.  
Figure 2: Total heart rate decomposed in the basal, the physical, the thermal and the mental component.