## 2 Materials and Methods
### Analysis  
The SOM algorithm was programmed using the open-source application Jupyter Notebook, the Python programming language (version 3.8) and the os, numpy, pandas, sompy, matplotlib.pyplot, BmuHitsView, HitMapView, sklearn.metrics, classification_report libaries, and View2D for file manipulation, data mining, SOM calculation, specific statistical metrics and graphical plotting, respectively. These procedures provided a set of topological maps whose visual representation demonstrates the spatial arrangement of the processing units distributed along two-dimensional matrices with a spatial resolution of 5 \(\times\) 8 neurons (height \(\times\) width), totaling 40 neurons.  
Models were developed using the SOM algorithm and combinations of chosen outcomes to select the one that best preserved the implemented input data and obtained valid values in evaluating the algorithm's performance concerning the generated grouping.  
First, two metrics within the SOM algorithm quantify the degree of similarity between the original data set and the obtained clustering. Topographic error quantifies the discrepancy (or preservation of similarity) between the spatial organization of neurons (processing units) and the topological relationships in the original data. A smaller model's value indicates that the spatial organization of neurons in the topological map adequately preserves the existing structure in the input (original) data [35].  
The quantization error measures the distance between each data sample and its winning neuron (BMU--Best Matching Unit) in the SOM; then, the average of these distances is calculated for all samples. It is a measurement that denotes the map's resolution. A smaller quantization error indicates that the SOM neurons are being more precisely tuned to represent the patterns in the original data [35].  
The Adjusted Rand Index (ARI) was used to evaluate the quality of the clusters generated by the SOM. Values close to 0 indicate that the clusters are independent, and negative values suggest a disagreement between the clusters [36; 37]. The degree of similarity among the assigned groupings was graded by Adjusted Mutual Information (AMI), which varies from 0 to 1, in which 1 indicates a perfect match and 0 indicates a random match [36].  
Accuracy represents the SOM's ability to correctly group data into clusters that correspond to the actual class of the data (true data labels) or the negative class.  
The F1-score provides a way to balance accuracy and sensitivity by considering both false positives and negatives, which is useful when a significant imbalance exists between classes. High values indicate a good balance between precision and recall. In contrast, a low F1-score suggests that there are problems with data clustering. Precision, recall, and F1-score can provide a more complete view of the quality of the classification [37].  
Descriptive statistical analyses and univariate inferences of the demographic, anthropometric, and functional variables of the falling and non-falling older adult groups were performed using the \(t\)-test (variables with parametric distribution) and the Mann-Whitney U test (non-parametric variables). The Kruskal-Wallis test for independent samples was used to initially compare the four age groups. All statistical analyses were performed in the Statistical Package for Social Sciences (IBM SPSS, version 22; IBM Corp, Armok, NY, USA), adopting a significance level of 5%.