Personalized Feature Extraction through Factor Analysis: A Federated Learning Approach

FedFac is a method for optimizing the objective function in deep neural networks (DNNs) by decomposing the weights into client-shared and client-specific parts. This decomposition is achieved using factor analysis, a statistical technique that identies inter-dependence structures among a large set of variables. In FedFac, the hidden layers of the DNN are treated as higher-level representations of raw data, and factor analysis is applied to split the hidden elements into client-shared and client-specific groups. The goal is to optimize the objective function by decompose the weights into client-shared ones that can be shared among clients, and client-specific ones that capture the unique characteristics of each client.
By applying factor analysis to the hidden layers of the DNN, FedFac identifies the inter-dependence structure among the hidden elements within each layer. The hidden elements are then split into client-shared and client-specific groups based on their relationships with other hidden elements. The client-shared group contains hidden elements that have similar characteristics across clients, while the client-specific group contains hidden elements that are unique to each client.
Once the weights are decomposed into client-shared and client-specific parts, the optimization process can be performed separately for each group. This allows FedFac to find the optimal values of the hyperparameters that result in the best performance for each client. The method is particularly useful in scenarios where the data is heterogeneous and complex, making it difficult to perform decomposition directly on the neurons.
In summary, FedFac is a powerful tool for optimizing the objective function in deep neural networks by decomposing the weights into client-shared and client-specific parts using factor analysis. By identifying the inter-dependence structure among the hidden elements within each layer, FedFac can find the optimal values of the hyperparameters that result in the best performance for each client, making it particularly useful in scenarios where the data is heterogeneous and complex.