Wasserstein-Aligned Hyperbolic Multi-View Clustering

TL;DR

WAH-MVC introduces a unified framework that leverages hyperbolic geometry to preserve hierarchical structure while aligning cross-view semantics via Wasserstein-based distribution matching on the Lorentz manifold. It combines view-specific Lorentz embeddings, an efficient hyperbolic SWD-based alignment (HHSW), and a Lorentz-aware contrastive clustering mechanism (LorentzMLR with target distributions) to encourage shared semantics across views. The approach achieves state-of-the-art clustering performance on multiple benchmarks and demonstrates robustness to backbone choices, while ablation studies quantify the contribution of each component and the benefits of hyperbolic geometry and distribution-level alignment. By integrating OT-style distribution alignment with hyperbolic embeddings, WAH-MVC provides a scalable, geometry-aware solution for complex multi-view clustering tasks with hierarchical structure and view gaps.

Abstract

Multi-view clustering (MVC) aims to uncover the latent structure of multi-view data by learning view-common and view-specific information. Although recent studies have explored hyperbolic representations for better tackling the representation gap between different views, they focus primarily on instance-level alignment and neglect global semantic consistency, rendering them vulnerable to view-specific information (\textit{e.g.}, noise and cross-view discrepancies). To this end, this paper proposes a novel Wasserstein-Aligned Hyperbolic (WAH) framework for multi-view clustering. Specifically, our method exploits a view-specific hyperbolic encoder for each view to embed features into the Lorentz manifold for hierarchical semantic modeling. Whereafter, a global semantic loss based on the hyperbolic sliced-Wasserstein distance is introduced to align manifold distributions across views. This is followed by soft cluster assignments to encourage cross-view semantic consistency. Extensive experiments on multiple benchmarking datasets show that our method can achieve SOTA clustering performance.

Figures (7)

• Figure 1: Real-world scene categories often form latent hierarchies. Here, fine-grained labels (e.g., Home, Work, Natural, Urban) are grouped into higher-level concepts like Indoor and Outdoor. Hyperbolic space has shown success in modeling hierarchical structure.
• Figure 2: Comparison of traditional instance-level alignment and the proposed hyperbolic distribution-level alignment. Instance-level alignment maximizes pairwise similarity but poorly captures global semantics, whereas our method aligns holistic view-wise distributions via sliced-Wasserstein distance (SWD) on the Lorentz manifold.
• Figure 3: The framework of WAH-MVC. It consists of three main components: (1) Lorentz Feature Embedding, which maps view-specific features into a curvature-aware Lorentz manifold for improved representation learning; (2) Wasserstein-Alignment for Feature Distribution ($\mathcal{L}_{\text{HHSW}}$), which aligns distributions of different views in hyperbolic space using a sliced Wasserstein distance; (3) Contrastive Cluster Enhancement ($\mathcal{L}_{\text{sem}} + \mathcal{L}_{\text{reg}}$), which enhances cluster discriminability by enforcing semantic consistency across views through contrastive learning.
• Figure 4: Effect of $\tau$ on ACC and NMI for all datasets.
• Figure 5: Convergence analysis of WAH-MVC on Amazon (left) and Scene-15 (right).