Phase-Consistent Magnetic Spectral Learning for Multi-View Clustering

2026-02-21

AI Summary

This work addresses the instability of shared structural signals in unsupervised multi-view clustering caused by inter-view directional conflicts and noise. To this end, it proposes a novel approach based on complex-valued magnetic affinity matrices, where cross-view directional consistency is modeled as phase components and non-negative magnitudes serve as the backbone. A Hermitian magnetic Laplacian is constructed to extract robust shared spectral signals, which in turn drive structured self-supervised multi-view representation learning. This study is the first to introduce phase consistency into multi-view clustering, effectively integrating directional and magnitude information. Extensive experiments demonstrate that the proposed method significantly outperforms strong existing baselines across multiple benchmark datasets, achieving notable gains in both clustering accuracy and stability.

Technology Category

• Machine Learning: Multi-instance/Multi-view Learning
• Computer Vision: Multi-modal Vision
• Data Mining & Knowledge Management: Mining of Visual, Multimedia & Multimodal Data

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Bridging structured and unstructured data
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

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.

Problem

• multi-view clustering
• view discrepancy
• spectral geometry
• unsupervised learning
• cross-view alignment

Innovation

• Phase Consistency
• Magnetic Laplacian
• Multi-View Clustering
• Complex-Valued Affinity
• Spectral Learning