Statistical heterogeneity poses a significant challenge in federated learning. When client data distributions $P_k(x, y)$ vary widely, a single global model trained via standard FedAvg might perform poorly for many, if not all, clients. This approach represents a compromise that may not capture the specific patterns present in any particular client's data. While fully personalized models (which we'll discuss later) aim to create a unique model for each client, Clustered Federated Learning (CFL) offers an intermediate approach.

The core idea behind CFL is intuitive: if clients naturally fall into groups based on their data characteristics or model objectives, why not train a separate model for each group? Instead of forcing a single model onto diverse populations, CFL partitions the clients into clusters and trains a distinct model tailored to each cluster. Clients within the same cluster collaborate to train their shared cluster model, benefiting from more relevant updates than they might receive from a dissimilar client in a standard FL setup.

How Clustering Works in Federated Learning

Implementing CFL involves addressing two main questions: How do we measure similarity between clients? And how do we perform the clustering itself?

Measuring Client Similarity

Since the server doesn't have direct access to client data, similarity must be inferred indirectly. Common approaches include:

Model Update Similarity: The gradients or model weight updates computed by clients reflect their local data distributions. Clients with similar data are likely to produce similar updates. Metrics like cosine similarity between client update vectors can be used to gauge resemblance.
Model Performance: One can evaluate how well different models (potentially existing cluster models) perform on a client's local data. Clients for whom a particular model performs best can be grouped together. This often forms the basis for iterative clustering algorithms.
Loss Function Similarity: Related to model performance, the shape or value of the loss function can indicate similarity.
Data Representation Similarity (Less Common): Techniques might involve clients sharing highly abstracted, privacy-preserving representations of their data distributions, though this adds complexity and potential privacy risks if not done carefully.

Measuring similarity often requires additional communication rounds or computations compared to standard FedAvg.

Clustering Mechanisms

Once a similarity measure is defined, various clustering algorithms can be adapted for the federated setting. The process is typically iterative and managed by the central server:

Initialization: Start with an initial set of cluster models (e.g., randomly initialized, or derived from a global model).
Client Assignment: Clients determine their cluster affiliation. This might involve clients downloading candidate cluster models, evaluating them locally, and reporting back their preferred cluster based on the chosen similarity metric (often lowest loss). Alternatively, the server might compute similarities based on submitted updates and assign clients.
Intra-Cluster Training: Clients perform local training, typically starting from their assigned cluster's model.
Intra-Cluster Aggregation: The server aggregates updates only from clients within the same cluster to produce the next version of that cluster's model. Standard aggregation methods like FedAvg can be used within each cluster.
Iteration: Steps 2-4 are repeated. Client assignments might change in subsequent rounds as cluster models evolve and refine.

Overview of Clustered Federated Learning. Clients (A1-A3, B1-B2) with similar data distributions (P_A, P_B) are grouped. They interact primarily with their respective cluster models (Model A, Model B), managed by the server. The server also handles cluster assignments based on similarity.

Representative Clustering Algorithms

Several algorithms implement these ideas. A well-known example is the Iterative Federated Clustering Algorithm (IFCA), sometimes referred to as HypCluster. In IFCA, the server maintains multiple candidate models (one for each potential cluster). In each round:

The server sends all current cluster models to the participating clients.
Each client evaluates these models on its local data and identifies the model that yields the lowest loss. This determines the client's cluster assignment for that round.
Clients train locally using their assigned cluster model as the starting point.
Clients send their updates back to the server.
The server aggregates the updates for each cluster separately, updating the corresponding cluster model.

Other approaches might use hierarchical clustering methods to create nested groups or similarity graphs where edge weights represent client relatedness.

Advantages of Clustered Federated Learning

Improved Accuracy on Heterogeneous Data: By training specialized models for subgroups of clients, CFL can achieve higher accuracy compared to a single global model, particularly when distinct data patterns exist across clients.
Implicit Personalization: CFL provides a form of personalization, as clients benefit from a model trained on data similar to their own, without needing a fully unique model per client.
Better Convergence: Training within more homogeneous clusters can sometimes lead to faster and more stable convergence compared to averaging highly diverse updates in standard FL.

Challenges and Approaches

Despite its benefits, CFL introduces its own set of challenges:

Determining the Number of Clusters: Choosing the optimal number of clusters ( $k$ ) is often difficult and data-dependent. It might require prior knowledge or hyperparameter tuning.
Clustering Overhead: The process of measuring similarity, assigning clients, and potentially communicating multiple models can increase computational and communication costs compared to FedAvg.
Cluster Stability and Client Drift: Clients might oscillate between clusters, or the optimal clustering structure might change over time, requiring strong assignment mechanisms.
Cluster Imbalance: Clusters might end up with very different numbers of clients, affecting training dynamics and model quality.
Cold-Start Problem: Assigning a new client to the appropriate cluster requires an efficient mechanism without significant overhead.
Potential for Bias Reinforcement: If clusters strongly correlate with sensitive attributes, CFL could potentially reinforce biases present within those subgroups if not implemented carefully.

Clustered Federated Learning provides a valuable set of techniques for mitigating the negative impacts of statistical heterogeneity. It strikes a balance between the simplicity of a single global model and the complexity of full personalization, offering improved performance when clients can be meaningfully grouped based on their data or learning objectives. However, the practical implementation requires careful consideration of the clustering mechanism, associated overheads, and the optimal number of clusters for the specific application.

Clustered Federated Learning Approaches