Phase-Consistent Magnetic Spectral Learning for Multi-View Clustering

Mingdong Lu; Zhikui Chen; Meng Liu; Shubin Ma; Zhengyang Tang

cs.LGFeb 21, 2026

Phase-Consistent Magnetic Spectral Learning for Multi-View Clustering

Authors: Mingdong Lu, Zhikui Chen, Meng Liu, Shubin Ma, Zhengyang Tang

Organizations: School of Software, Dalian University of Technology

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 Phase-Consistent Magnetic Spectral Learning for MVC: we derive a confidence-directed cross-view flow from anchor assignments, encode it 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. Experiments on ten public benchmarks show that our method achieves the best result on 22 of 30 dataset-metric combinations and ranks among the top two on 27 combinations, demonstrating strong and broadly consistent performance against classical and recent MVC baselines.

Figures & tables

Panel of Figure 1 — 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.

Symbol	Meaning
$V,\,n,\,K$	#views, #samples, #clusters
$X^{(v)},\,Z^{(v)}$	input data and latent codes of view $v$
$d$	latent dimension
$m_{a},\,m$	anchors per view; total anchors $m=Vm_{a}$
$A^{(v)}$	latent anchor centers of view $v$
$C^{(v)}$	sample–anchor coefficients of view $v$

Table 1: Notation for the main geometric and spectral components.

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-inspired flow reweighting, then encode confidence-directed cross-view flow 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.

Dataset	$V$	$n$	$K$
100Leaves (Cope et al. 2013 )	3	1600	100
Caltech-5V (Xu et al. 2022 )	5	1400	7
Digit-Product (Cui et al. 2024 )	2	30000	10
ALOI (Geusebroek et al. 2005 )	4	10800	100
BDGP (Cai et al. 2012 )	2	2500	5
Fashion-MV (Xiao et al. 2017 )	3	10000	10

Table 2: Dataset statistics.

V

n

, and

K

denote the numbers of views, samples, and clusters, respectively.

Method	Caltech-5V			CUB			UCI-3V			Fashion-MV			Multi-COIL-20
	ACC	NMI	ARI	ACC	NMI	ARI	ACC	NMI	ARI	ACC	NMI	ARI	ACC	NMI	ARI
Kmeans	78.51	68.31	61.71	75.83	75.01	61.15	90.05	83.66	80.71	77.84	75.47	68.03	65.48	83.81	63.26
DEC’16	88.64	81.12	81.16	72.67	69.13	53.81	86.65	84.83	80.06	77.85	81.63	71.11	75.01	85.31	70.45
DMCAG’23	83.64	75.41	66.95	67.42	63.64	50.16	85.85	82.26	76.09	84.01	90.12	82.13	99.71	99.68	99.16
AEMVC’25	75.21	66.43	58.32	77.46	76.51	62.72	93.23	91.42	89.71	67.81	55.82	49.21	91.53	94.15	91.31
hubREP’25	68.79	61.31	54.37	67.01	72.45	56.78	83.81	86.56	80.02	73.12	73.61	62.16	68.33	80.32	65.34

Table 3: Overall clustering performance (%). Rows correspond to methods, and column groups correspond to datasets. Best results are shown in bold , and second-best results are underlined. The symbol “–” indicates that the method failed to yield stable results on the corresponding dataset.

Panel of Figure 3 — Figure 3: t-SNE visualizations before vs. after training. Left/right panels show embeddings before/after training, respectively.

Panel of Figure 4 — Figure 4: Affinity heatmaps on two datasets. Ground-truth labels are used only to reorder samples for visualization. Clearer diagonal blocks indicate stronger within-cluster connectivity, while suppressed off-diagonal entries indicate reduced cross-cluster leakage.

Fashion-MV
Dataset / Variant	ACC	NMI	ARI	$\Delta_{K}\uparrow$	Sub $\downarrow$	Iner $\downarrow$
Real-Spec ( $q{=}0$ )	95.91	92.72	93.14	0.089	0.46	1.72
Mag-Spec (Ours)	97.78	94.89	95.21	0.125	0.31	1.34
Shuffled-Phase	92.83	88.12	88.91	0.061	0.62	2.15
Random-Phase	92.39	87.52	88.11	0.058	0.66	2.22
BDGP

Table 4: Controlled phase ablation under fixed

S^{\prime}

on three datasets.

\Delta_{K}

denotes the eigengap, Sub denotes the subspace distance, and Iner denotes the

k

-means inertia.

Panel of Figure 5 — Figure 5: Stage-I weight sensitivity. ARI and ACC surfaces over $(\lambda_{1},\lambda_{2})$ on (a) 100Leaves and (b) Fashion-MV, respectively (axes in log scale).

Multi-View Clustering

Multi-view clustering groups data by combining complementary representations while accounting for their shared structure, differences, and missing or noisy observations.

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May 15, 2026J/K move · Enter open · S save

Learning Disentangled Representations for Generalized Multi-view Clustering

Xin Zou, Ruimeng Liu, Chang Tang, Zhenglai Li+3

School of Computing and Information Technology, University of Wollongong, NSW, 2500, Australia · School of Software Engineering, Huazhong University of Science and Technology, Wuhan 430074, China

Disentangled Representation Learning Multi-View Learning Multi-View Clustering

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Multi-View Clustering (MVC) has gained significant attention for its ability to leverage complementary information across diverse views. However, existing deep MVC methods often struggle with view-distribution entanglement during cross-view fusion, which hampers the quality of the shared latent space and leads to suboptimal Figures. To address this issue, we propose the Generalized Multi-view Auto-Encoder (GMAE), a framework designed to preserve cross-view complementarity through disentangled representation learning. Specifically, GMAE employs dual-path autoencoders to decouple source features into view-specific and view-common embeddings, facilitating the discovery of clearer clustering structures. We further construct cross-view adversarial discriminators to guide view-specific encoders in capturing more discriminative features. By strategically modulating mutual information, GMAE effectively aligns distributions and prevents representation collapse, ensuring the generation of robust, non-trivial embeddings. Comprehensive experiments on 13 benchmark datasets demonstrate that GMAE consistently outperforms state-of-the-art methods in both complete and incomplete MVC tasks. Our code implementation is available at the repository: https://github.com/obananas/GMAE.

Abstract

Multi-View Clustering

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