## 3 Materials and Methods
### Fall Detection Method
While numerous studies have demonstrated that analyzing variations in features allows for the creation of rule-based methods to detect falls and non-falls within a monitored environment, it is crucial to acknowledge that these rules necessitate a detailed examination of body and motion features, along with expert knowledge of biodynamics. Consequently, this study opted for a 1D causal convolutional neural network (CNN) with residual connections as the model of choice for learning and classification. One-dimensional CNNs were first used for sequence-to-sequence generation of audio data, as shown in [66]. Over time, various adaptations, including causal and dilated causal CNNs, were developed to cater to a broad spectrum of time-series and sequence datasets necessitating the maintenance of strict causal relationships during training and inference, as shown in [67; 68; 69; 70]. Notably, 1D convolutional networks have demonstrated significant efficacy in applications related to human motion modeling [71; 72; 73] and classification of complex patterns within 1D time-series datasets [74; 75; 76; 77]. This versatility and robust performance highlight the potential of 1D CNNs to capture intricate temporal dynamics, making them a compelling choice for studies focusing on sequence data regression and classification, eliminating the need for complex feature engineering. This study employs 1D dilated causal CNN layers with residual connections, as illustrated in Figure 7, to construct the classification model. Given that body motion features and bounding box attributes have been previously extracted and their temporal variations are used for training, the model architecture is intentionally simplified. It consists of three residual blocks followed by a fully connected layer with 32 neurons with sigmoid activation at the network's tail. The output node consists of a single neuron with sigmoid activation for the binary classification of fall and non-fall scenarios. Each residual block in the model starts with a dilated causal CNN layer, which uses a specific number of filters and a dilation parameter, followed by a Scaled Exponential Linear Unit (SELU) [78] activation layer. This setup allows for the initial expansion of the network's receptive field, enabling it to capture wider nonlinear temporal patterns and without a significant increase in computational complexity. After this, another causal CNN layer is applied, using the same number of filters but without dilation, and this is also followed by an SELU activation layer. To integrate learned features while preserving information from earlier layers, each block includes a skip connection that undergoes a 1 \(\times\) 1 convolution. This convolution is designed to match the number of filters to the block's final layer before adding it to the block's output. The model is structured with three residual blocks, each set to progressively increase the number of filters (16, 32, and 64) and dilation parameters (1, 2, and 3, respectively). This progressive design allows the network to hierarchically extract and refine features from simpler to more complex patterns. Incrementally expanding the number of filters and dilation rates ensures that the model can learn from different motion characteristics to distinguish between normal activities and fall incidents based on temporal patterns within the data. The proposed network is implemented using PyTorch version 2.1.0, a popular deep learning framework among machine learning researchers. During the training phase, the Adam [79] optimization algorithm is employed, chosen for its effective handling of sparse gradients and its adaptability in different scenarios. The initial learning rate is set to 0.001, a standard starting point that balances the speed and stability of the learning process. As training progresses, the Adam algorithm automatically adjusts this learning rate based on the training data's behavior, ensuring optimal convergence rates.