Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

CCFC++: Enhancing Federated Clustering through Feature Decorrelation

Jie Yan, Jing Liu, Yi-Zi Ning, Zhong-Yuan Zhang

TL;DR

This paper tackles data heterogeneity in federated clustering by analyzing how it induces dimensional collapse in CCFC representations. It proposes CCFC++, a decorrelation-regularized extension of CCFC, to reduce interdimensional correlations and mitigate collapse. The authors provide gradient-flow theory linking heterogeneity to low-rank encoder dynamics and validate the approach on MNIST, Fashion-MNIST, CIFAR-10, and STL-10, reporting up to 0.32 gains in $NMI$ and improved robustness to device failures. Overall, the work advances unsupervised federated learning by stabilizing representations under heterogeneity and enhancing clustering performance.

Abstract

In federated clustering, multiple data-holding clients collaboratively group data without exchanging raw data. This field has seen notable advancements through its marriage with contrastive learning, exemplified by Cluster-Contrastive Federated Clustering (CCFC). However, CCFC suffers from heterogeneous data across clients, leading to poor and unrobust performance. Our study conducts both empirical and theoretical analyses to understand the impact of heterogeneous data on CCFC. Findings indicate that increased data heterogeneity exacerbates dimensional collapse in CCFC, evidenced by increased correlations across multiple dimensions of the learned representations. To address this, we introduce a decorrelation regularizer to CCFC. Benefiting from the regularizer, the improved method effectively mitigates the detrimental effects of data heterogeneity, and achieves superior performance, as evidenced by a marked increase in NMI scores, with the gain reaching as high as 0.32 in the most pronounced case.

CCFC++: Enhancing Federated Clustering through Feature Decorrelation

TL;DR

This paper tackles data heterogeneity in federated clustering by analyzing how it induces dimensional collapse in CCFC representations. It proposes CCFC++, a decorrelation-regularized extension of CCFC, to reduce interdimensional correlations and mitigate collapse. The authors provide gradient-flow theory linking heterogeneity to low-rank encoder dynamics and validate the approach on MNIST, Fashion-MNIST, CIFAR-10, and STL-10, reporting up to 0.32 gains in and improved robustness to device failures. Overall, the work advances unsupervised federated learning by stabilizing representations under heterogeneity and enhancing clustering performance.

Abstract

In federated clustering, multiple data-holding clients collaboratively group data without exchanging raw data. This field has seen notable advancements through its marriage with contrastive learning, exemplified by Cluster-Contrastive Federated Clustering (CCFC). However, CCFC suffers from heterogeneous data across clients, leading to poor and unrobust performance. Our study conducts both empirical and theoretical analyses to understand the impact of heterogeneous data on CCFC. Findings indicate that increased data heterogeneity exacerbates dimensional collapse in CCFC, evidenced by increased correlations across multiple dimensions of the learned representations. To address this, we introduce a decorrelation regularizer to CCFC. Benefiting from the regularizer, the improved method effectively mitigates the detrimental effects of data heterogeneity, and achieves superior performance, as evidenced by a marked increase in NMI scores, with the gain reaching as high as 0.32 in the most pronounced case.
Paper Structure (19 sections, 4 theorems, 28 equations, 7 figures, 3 tables)

This paper contains 19 sections, 4 theorems, 28 equations, 7 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Background and related work
  3. CCFC++: unleashing CCFC's potential through feature decorrelation
  4. CCFC
  5. Overview of the CCFC Architecture
  6. The local training step
  7. Empirical observations on the global model
  8. Empirical observations on local models
  9. Theoretical analysis for dimensional collapse
  10. Setups and notations
  11. Analysis on gradient flow dynamics
  12. CCFC++
  13. Experiments
  14. Experimental setup
  15. Efficacy of the decorrelation regularizer
  16. ...and 4 more sections

Key Result

Theorem 3.4

Under assumptions ass1 and ass2, the gradient descent dynamics of the $\tau$-th largest singular value $\sigma_{\tau}^{\Pi}(t)$ of $\Pi(t)$ can be expressed as: where $u_{\tau}^{\Phi}(t)$ is the $\tau$-th left singular vector of $\Phi(t)$, $v_{{\tau}}^{\Pi}(t)$ is the $\tau$-th right singular vector of $\Pi(t)$, $C$ is a constant, the element $q_{ri}^{(c)}(t) \in \mathbb{R}$ located in the $r$-t

Figures (7)

  • Figure 1: CCFC architecture. In this work, we focus on the second step.
  • Figure 2: The learned representations of CCFC under different simulated federated scenarios on MNIST (best viewed in color). The first row displays the local data distributions of each client under different levels of data heterogeneity. The color bar denotes the number of samples, and $p$ denotes the imbalance in classes across different clients. A larger $p$ implies stronger data heterogeneity. The second row shows the covariance matrices of the learned representations by CCFC in the corresponding federated scenarios. The last row showcases the distribution of interdimensional correlations in the corresponding covariance matrices.
  • Figure 3: Dimensional collapse on the global model. There are a considerable number of singular values collapsing to zero for all scenarios, implying collapsed dimensions. And this problem exacerbates with the increase in data heterogeneity.
  • Figure 4: Dimensional collapse on the local model. There are a considerable number of singular values collapsing to zero for all scenarios, implying collapsed dimensions. And this problem exacerbates with the increase in data heterogeneity.
  • Figure 5: The efficacy of the decorrelation regularizer under different simulated federated scenarios on MNIST. The first row plots the singular values of the covariance matrix of the learned representations. The second row showcases the learned representations of the global model of CCFC and CCFC++. Each color corresponds to a true cluster. A larger $p$ implies stronger data heterogeneity.
  • ...and 2 more figures

Theorems & Definitions (6)

  • Remark 3.3
  • Theorem 3.4
  • Lemma 1
  • Lemma 2
  • Theorem 3
  • proof