## 4 Results
### User Profiling  
#### 4.2.1 Theory and Calculation  
With the objective of building a method to determine how people use their mobile phones differently depending on their age, a model for the construction of a device interaction profile was developed. The proposed profiling method consists of counting how many cycles of each type each user has; therefore, this section explains how each cycle type is labeled. The focus of this process is to characterize a user by the way in which she or he interacts with the mobile device, and, as the interaction when the mobile device is locked is minimal, as a first step, locked cycles are discarded. As a next step, to increase the interpretability of the data, a subset of features that are more appropriate to characterize each type of cycle is selected. This subset is further reduced by totaling the type of interaction following the HuSBIT-10 taxonomy [9] and the physical activities' durations that are highly related between them. Once the data are simplified, the next step is to group the cycles according to their similarities, for which a clustering algorithm is an appropriate tool. The data have many samples, thus making the utilization of numerous clustering algorithms unfeasible because they require an excessive amount of time to be executed; thus, they are discarded. Moreover, these data present a distribution with varying density, and many samples are quite similar, which results in most of the clustering algorithms producing highly unbalanced groups. As a result, after testing a number of clustering algorithms, a self-organizing map (SOM) [30] is chosen. An SOM is an unsupervised artificial neural network that projects the data to a low-dimensional (usually 2D) network while maintaining their topological structure. The SOM algorithm starts by creating a neural network and initializes its weights, which can be random, decided beforehand, or set by prior calculation (for example, principal component analysis). Then, each sample of the dataset is associated with a neuron based on its weights, and these weights, along with the weights of neighboring neurons, are modified to be closer to the sample. After repeating this process several times but decreasing how much the weights are affected, the weights of the neurons will converge, and the network will be trained. One of the main hyperparameters of an SOM algorithm is the topology and its dimensions. The other two main hyperparameters are the initial learning rate, which affects how much the weights of each neuron are modified, and the sigma, which represents the radius by which nearby neurons affect each other. For this case, a hexagonal topology is used with dimensions of \(6\times 7\), a learning rate of 1.5, and a sigma of 1.3. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Total Calls** & **Outgoing** & **Lost** & **Incoming** \\ \hline Age & 0.256 & 0.189 & 0.071 & 0.339 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Correlation coefficients for calls vs. age. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Stationary** & **On the Move** \\ \hline Written elements vs. age & \(-0.697\) & \(-0.522\) \\ Elements removed vs. age & \(0.690\) & \(0.778\) \\ Total writing time vs. age & \(-0.446\) & \(-0.436\) \\ Writing frequency vs. age & \(-0.253\) & \(-0.660\) \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Correlation coefficients for typing and age. These specific values are established after performing a grid search. MiniSom ([[https://github.com/JustGlowing/minison](https://github.com/JustGlowing/minison)]([https://github.com/JustGlowing/minison](https://github.com/JustGlowing/minison)), accessed on 25 June 2023) is the implementation of the algorithm that is employed in this paper. Before applying the algorithm, the data are pre-processed in two ways. First, a logarithm is applied to the duration column, so that its distribution is similar to a Gaussian function, and its large scale has less impact on the clustering.