## 3 Methodology
### MobileNetV2 Architectures in Federated Learning  
In this experiment, both decentralized and centralized federated learning setups were implemented using the MobileNetV2 architecture for fall detection. The goal was to evaluate the performance and privacy implications under distinct coordination strategies while keeping the core model structure identical. The decentralized setup simulates a ring-based client environment, whereas the centralized configuration involves a server-client aggregation scheme. The dataset was first preprocessed to extract human-activity regions from annotated images using YOLO-format bounding boxes. Each image was resized to a fixed dimension of 128 \(\times\) 128 and normalized to the [0, 1] range. The multi-class labels were binarized such that  
\[Label=\left\{ \begin{array}{ll}0,&\quad\text{if $Fall$ Detected}\\ 1,&\quad\text{if $Walking$ or $Sitting}\end{array} \right.\]  
The full dataset comprised 463 labeled image-label pairs. These were separated using stratified sampling into training (80%), validation (10%), and testing (10%) groups to guarantee class balance:  
\[\text{Train}=370,\quad\text{Validation}=46,\quad\text{Test}=47\]  
The training set was further partitioned among N = 3 simulated clients for federated training:  
\[\text{Client}_{i}=(X_{i},y_{i}), \tag{1}\]  
where \(i\) = 1, 2, 3. Each client trained a local instance of MobileNetV2. Pretrained ImageNet weights were used to initialize it. The following layers made up the classifier head, while the base convolutional layers were frozen:  
\[\text{Model = MobileNetV2 (frozen)}\rightarrow\text{GAP}\rightarrow\text{BN} \rightarrow\text{Dense(256)}\rightarrow\text{Dropout(0.3)}\rightarrow\text{ Dense(1, $\sigma$)}\]  
This architecture's central model is MobileNetV2, a thin convolutional neural network that was pretrained using the ImageNet dataset. To avoid overfitting on the limited custom dataset and to preserve previously learned visual information, the pretrained convolutional layers are frozen during training. In order to improve generalization and reduce the number of parameters, the output of MobileNetV2 is routed through a Global Average Pooling (GAP) layer, which takes the place of conventional fully connected layers by averaging each feature map. After the GAP layer, the activations are normalized using Batch Normalization (BN), which helps to stabilize and accelerate the training. It also provides a slight regularization effect. A fully linked dense layer contains 256 neurons with ReLU activation to capture high-level abstract properties. During training, 30% of the neurons are randomly disabled by a Dropout layer with a rate of 0.3 to prevent overfitting. Binary classification with a single-node output layer is the last step. A sigmoid (\(\sigma\)) activation function provides a probability value between 0 and 1 that indicates the likelihood that the input image belongs to the \"fall\" class. This design leverages transfer learning to benefit from general-purpose features extracted by MobileNetV2 while tailoring the classification head to the specific task of fall detection. In the decentralized setup, the architecture is replicated across three independent clients, each responsible for local training using its own partition of the dataset. These clients operate in isolation and do not exchange raw data. Instead, after each training round, the clients share their model weight updates, which are later aggregated usingthe Federated Averaging (FedAvg) algorithm. This topology ensures data privacy while supporting collaborative model development in a peer-to-peer fashion. In contrast, the centralized configuration involves a central server coordinating the Federated Averaging process. All clients train the MobileNetV2 model locally for 25 epochs per round and send their updated weights to the central server.