Phase-Consistent Magnetic Spectral Learning for Multi-View Clustering

TL;DR

Phase-Consistent Magnetic Spectral Learning for MVC is proposed, which explicitly model cross-view directional agreement as a phase term and combine it with a nonnegative magnitude backbone to form a complex-valued magnetic affinity, extract a stable shared spectral signal via a Hermitian magnetic Laplacian, and use it as structured self-supervision to guide unsupervised multi-view representation learning and clustering.

Abstract

Unsupervised multi-view clustering (MVC) aims to partition data into meaningful groups by leveraging complementary information from multiple views without labels, yet a central challenge is to obtain a reliable shared structural signal to guide representation learning and cross-view alignment under view discrepancy and noise. Existing approaches often rely on magnitude-only affinities or early pseudo targets, which can be unstable when different views induce relations with comparable strengths but contradictory directional tendencies, thereby distorting the global spectral geometry and degrading clustering. In this paper, we propose \emph{Phase-Consistent Magnetic Spectral Learning} for MVC: we explicitly model cross-view directional agreement as a phase term and combine it with a nonnegative magnitude backbone to form a complex-valued magnetic affinity, extract a stable shared spectral signal via a Hermitian magnetic Laplacian, and use it as structured self-supervision to guide unsupervised multi-view representation learning and clustering. To obtain robust inputs for spectral extraction at scale, we construct a compact shared structure with anchor-based high-order consensus modeling and apply a lightweight refinement to suppress noisy or inconsistent relations. Extensive experiments on multiple public multi-view benchmarks demonstrate that our method consistently outperforms strong baselines.

Figures (9)

• Figure 1: Phase effects beyond affinity magnitude. With identical affinity magnitudes, consistent directions yield a coherent flow and a stable global structure, whereas conflicting directions cancel out and induce a different spectrum.
• Figure 2: Overall framework of Phase-Consistent Magnetic Spectral Learning for MVC. Each view is encoded into latent features with reconstruction learning. View-wise latent anchors induce sparse sample--anchor relations, which are aggregated into a multi-view anchor hypergraph to form a compact shared magnitude backbone. We stabilize the backbone by refining hyperedge weights via curvature/Ricci-flow reweighting, then encode cross-view directional agreement as a magnetic (phase) term and extract a shared spectral signal using a Hermitian magnetic Laplacian. The resulting signal defines a global target distribution $P$ to supervise per-view predictions $Q^{(v)}$ via KL alignment, while label contrastive consistency further reduces cross-view mismatch for robust clustering.
• Figure 3: t-SNE visualizations before vs. after training. Left/right panels show embeddings before/after training, respectively.
• Figure : (a) 100Leaves
• Figure : (a) 100Leaves