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Peer-reviewedCC BY 4.0Mathematics

Smooth Tensor Multi-View Clustering on Well Logs via Hypergraph Topology and Concurrent Group Sparsity

  • Shengjiang Xu1
  • Liwei Wang1
  • Long Tian1
  • Yinming Zhong1
  • Junshan Wang1
  • Wei Guo2
  • Haotian Zhang2
  1. 1Oil Production Technology Research Institute, Xinjiang Oilfield Company, China National Petroleum Corporation (CNPC), Karamay 834000, China
  2. 2School of Computer Science and Technology, Yibin University, Yibin 644000, China
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Abstract

Multi-view clustering has emerged as a powerful approach to geological facies characterization because it can integrate heterogeneous well-log sequences. However, real-world well-log data are susceptible to severe localized environmental disturbances, such as borehole collapse. Moreover, conventional pairwise graph methods fail to capture the inherent high-order semantic correlations in sequential petrophysical data, whereas standard tensor methods indiscriminately retain high-frequency structural noise. To address these limitations, we propose Smooth Tensor Multi-View Clustering on Well Logs via Hypergraph Topology and Concurrent Group Sparsity (HTCGS). First, HTCGS introduces a source-view hypergraph topology-injection mechanism that propagates high-order geological manifold structures across heterogeneous modalities, thereby enabling robust geometric prealignment. Second, it employs a cross-view concurrent joint-group-sparsity regularizer that uses an ℓ2,1-norm penalty to separate localized anomalies into an explicit cross-view error matrix, thereby preserving the latent subspace. Finally, HTCGS applies the Smooth Tensor Nuclear Norm (STNN) to the purified latent features, which acts as a low-pass tensor filter to extract global consensus information reflecting macroscopic geological continuity. The resulting unified objective is efficiently optimized using the Alternating Direction Method of Multipliers (ADMM). Extensive experiments on five benchmark datasets, comprising four well-log datasets and one seismic-facies dataset, show that HTCGS outperforms six recent representative multi-view clustering baselines.

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Cite

BibTeXRIS
BibTeX
@article{xu2026smooth,
  title = {{Smooth Tensor Multi-View Clustering on Well Logs via Hypergraph Topology and Concurrent Group Sparsity}},
  author = {Shengjiang Xu and Liwei Wang and Long Tian and Yinming Zhong and Junshan Wang and Wei Guo and Haotian Zhang},
  journal = {Mathematics},
  year = {2026},
  month = oct,
  doi = {10.3390/math14213848},
  url = {https://www.mdpi.com/2227-7390/14/21/3848},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Smooth Tensor Multi-View Clustering on Well Logs via Hypergraph Topology and Concurrent Group Sparsity
AU  - Shengjiang Xu
AU  - Liwei Wang
AU  - Long Tian
AU  - Yinming Zhong
AU  - Junshan Wang
AU  - Wei Guo
AU  - Haotian Zhang
PY  - 2026
DA  - 2026/10/22
JO  - Mathematics
DO  - 10.3390/math14213848
UR  - https://www.mdpi.com/2227-7390/14/21/3848
AB  - Multi-view clustering has emerged as a powerful approach to geological facies characterization because it can integrate heterogeneous well-log sequences. However, real-world well-log data are susceptible to severe localized environmental disturbances, such as borehole collapse. Moreover, conventional pairwise graph methods fail to capture the inherent high-order semantic correlations in sequential petrophysical data, whereas standard tensor methods indiscriminately retain high-frequency structural noise. To address these limitations, we propose Smooth Tensor Multi-View Clustering on Well Logs via Hypergraph Topology and Concurrent Group Sparsity (HTCGS). First, HTCGS introduces a source-view hypergraph topology-injection mechanism that propagates high-order geological manifold structures across heterogeneous modalities, thereby enabling robust geometric prealignment. Second, it employs a cross-view concurrent joint-group-sparsity regularizer that uses an ℓ2,1-norm penalty to separate localized anomalies into an explicit cross-view error matrix, thereby preserving the latent subspace. Finally, HTCGS applies the Smooth Tensor Nuclear Norm (STNN) to the purified latent features, which acts as a low-pass tensor filter to extract global consensus information reflecting macroscopic geological continuity. The resulting unified objective is efficiently optimized using the Alternating Direction Method of Multipliers (ADMM). Extensive experiments on five benchmark datasets, comprising four well-log datasets and one seismic-facies dataset, show that HTCGS outperforms six recent representative multi-view clustering baselines.
SN  - 2227-7390
ER  -