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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2603.22838 |
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| _version_ | 1866911541074329600 |
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| author | Shen, Tao Wang, Wanjie |
| author_facet | Shen, Tao Wang, Wanjie |
| contents | We study layer-specific community detection in an $L$-layer network $\{A^{(l)}\}_{l\in[L]}$ on a common set of $n$ nodes. Because modern networks are constructed from multi-modal data or with different contexts, the community labels $π^{(l)}\in[K]^n$ are layer-dependent and the degree heterogeneity parameters $θ_i^{(l)}$ vary widely across nodes and layers. The inhomogeneity and extreme sparsity raise a challenge for classical community detection methods.
We propose a multilayer-assisted regularized spectral method (MARS-CD) to address this challenge. For layer $l$, MARS-CD first constructs $X^{(l)}$ from the remaining layers, so that the problem is transformed into a network-with-covariates clustering problem on $(A^{(l)}, X^{(l)})$. Then we recover $π^{(l)}$ by NAC in Hu and Wang (2024) that allows misalignment. The key component is to construct $X^{(l)}$, where we stack regularized embeddings. Building upon this, we establish the first theoretical guarantees for the quality of $X^{(l)}$ under multilayer networks with extreme sparsity. These further lead to weak and strong consistency for recovering $π^{(l)}$. We further develop an optional label alignment step to interpret the shared community structure across layers.
Simulations demonstrate the superior performance of our MARS-CD method. Applying MARS-CD to international food trading networks provides an interpretable product-specific community structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_22838 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Community Detection on Inhomogeneous Multilayer Networks with Extreme Sparsity Shen, Tao Wang, Wanjie Methodology We study layer-specific community detection in an $L$-layer network $\{A^{(l)}\}_{l\in[L]}$ on a common set of $n$ nodes. Because modern networks are constructed from multi-modal data or with different contexts, the community labels $π^{(l)}\in[K]^n$ are layer-dependent and the degree heterogeneity parameters $θ_i^{(l)}$ vary widely across nodes and layers. The inhomogeneity and extreme sparsity raise a challenge for classical community detection methods. We propose a multilayer-assisted regularized spectral method (MARS-CD) to address this challenge. For layer $l$, MARS-CD first constructs $X^{(l)}$ from the remaining layers, so that the problem is transformed into a network-with-covariates clustering problem on $(A^{(l)}, X^{(l)})$. Then we recover $π^{(l)}$ by NAC in Hu and Wang (2024) that allows misalignment. The key component is to construct $X^{(l)}$, where we stack regularized embeddings. Building upon this, we establish the first theoretical guarantees for the quality of $X^{(l)}$ under multilayer networks with extreme sparsity. These further lead to weak and strong consistency for recovering $π^{(l)}$. We further develop an optional label alignment step to interpret the shared community structure across layers. Simulations demonstrate the superior performance of our MARS-CD method. Applying MARS-CD to international food trading networks provides an interpretable product-specific community structure. |
| title | Community Detection on Inhomogeneous Multilayer Networks with Extreme Sparsity |
| topic | Methodology |
| url | https://arxiv.org/abs/2603.22838 |