## 3 Methodology
### VGG16 Architectures in Federated Learning (Decentralized and Centralized)  
This section presents an in-depth analysis of the federated learning configurations implemented using the VGG16 architecture, evaluated under two paradigms: decentralized peer-to-peer coordination and centralized server-based orchestration. The purpose of this comparative exploration is to examine the impacts of communication topology and model  
Figure 4: Comparative illustration of federated training architectures using MobileNetV2 for fall detection. **(Left)** Decentralized training with clients collaboratively updating a shared model in a ring topology. Each client trains a local MobileNetV2 model with a custom classifier head and shares weights sequentially. **(Right)** Centralized training where clients send local model updates to a central server that coordinates aggregation. Both use the same architecture consisting of a frozen MobileNetV2 backbone, followed by GAP, BatchNorm, Dense(256), Dropout(0.3), and a final sigmoid layer for binary classification. aggregation strategy on binary fall-detection performance, while ensuring architectural consistency across experimental settings. The VGG16 convolutional neural network, known for its depth and hierarchical feature extraction capabilities, was employed as the core architecture for both training paradigms. To preserve the general-purpose visual features learned from large-scale datasets, the convolutional backbone of VGG16 pretrained on ImageNet was frozen during the training process. A custom classification head was then appended to adapt the model to the fall-detection task. The complete architecture is represented as follows:  
Model = VGG16 (frozen) \(\rightarrow\) Flatten \(\rightarrow\) BN \(\rightarrow\) Dense(512) \(\rightarrow\) Dropout(0.4) \(\rightarrow\) Dense(1, \(\sigma\))  
The Flatten layer converts high-dimensional spatial outputs from the convolutional stack into a one-dimensional vector suitable for fully connected layers. The Batch Normalization (BN) layer is incorporated to stabilize the learning process and accelerate convergence. The subsequent Dense layer consists of 512 ReLU-activated neurons designed to capture non-linear combinations of extracted features. To mitigate overfitting, a Dropout layer is applied with a rate of 0.4. The final classification layer is a single neuron activated by the sigmoid function \(\sigma\) and producing a probability value indicative of fall or non-fall status. In the decentralized federated learning setting, model training is performed collaboratively by a network of clients that operate in a ring-based topology. Each of the three clients (Client 1, Client 2, and Client 3) possesses its own private dataset and computational resources. At the beginning of the training cycle, all clients receive the initial global model parameters and proceed to perform local training independently. Following local training, model updates are propagated sequentially among the clients in a ring fashion, thereby avoiding any reliance on a central coordinator. After completing one round of updates through all clients, the updated weights are aggregated using Federated Averaging (FedAvg), defined as  
\[W_{global}=\frac{1}{N}{\sum_{i=1}^{N}W_{i}} \tag{3}\]  
where \(W_{i}\) is the local model weight from client i, and N = 3 is the total number of clients. Training is conducted over five global communication rounds, with each client executing 25 epochs of local training per round, using a batch size of 32. The ring-based communication protocol is depicted in the left panel of Figure 5, which visually conveys the flow of the global model through the three clients and back to a shared consensus. This decentralized architecture is particularly well suited for privacy-sensitive environments such as healthcare monitoring, in which raw data must remain on-device due to ethical or regulatory constraints. The collaborative nature of this setup ensures that each client contributes to the global model while preserving local autonomy.