Selecting the Number of Communities for Weighted Degree-Corrected Stochastic Block Models

Yucheng Liu, Xiaodong Li
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:586-594, 2025.

Abstract

We investigate how to select the number of communities for weighted networks without a full likelihood modeling. First, we propose a novel weighted degree-corrected stochastic block model (DCSBM), where the mean adjacency matrix is modeled in the same way as in the standard DCSBM, while the variance profile matrix is assumed to be related to the mean adjacency matrix through a given variance function. Our method of selecting the number of communities is based on a sequential testing framework. In each step, the weighted DCSBM is fitted via some spectral clustering method. A key component of our method is matrix scaling on the estimated variance profile matrix. The resulting scaling factors can be used to normalize the adjacency matrix, from which the test statistic is then obtained. Under mild conditions on the weighted DCSBM, our proposed procedure is shown to be consistent in estimating the true number of communities. Numerical experiments on both simulated and real-world network data demonstrate the desirable empirical properties of our method.

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-liu25a, title = {Selecting the Number of Communities for Weighted Degree-Corrected Stochastic Block Models}, author = {Liu, Yucheng and Li, Xiaodong}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {586--594}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/liu25a/liu25a.pdf}, url = {https://proceedings.mlr.press/v258/liu25a.html}, abstract = {We investigate how to select the number of communities for weighted networks without a full likelihood modeling. First, we propose a novel weighted degree-corrected stochastic block model (DCSBM), where the mean adjacency matrix is modeled in the same way as in the standard DCSBM, while the variance profile matrix is assumed to be related to the mean adjacency matrix through a given variance function. Our method of selecting the number of communities is based on a sequential testing framework. In each step, the weighted DCSBM is fitted via some spectral clustering method. A key component of our method is matrix scaling on the estimated variance profile matrix. The resulting scaling factors can be used to normalize the adjacency matrix, from which the test statistic is then obtained. Under mild conditions on the weighted DCSBM, our proposed procedure is shown to be consistent in estimating the true number of communities. Numerical experiments on both simulated and real-world network data demonstrate the desirable empirical properties of our method.} }
Endnote
%0 Conference Paper %T Selecting the Number of Communities for Weighted Degree-Corrected Stochastic Block Models %A Yucheng Liu %A Xiaodong Li %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-liu25a %I PMLR %P 586--594 %U https://proceedings.mlr.press/v258/liu25a.html %V 258 %X We investigate how to select the number of communities for weighted networks without a full likelihood modeling. First, we propose a novel weighted degree-corrected stochastic block model (DCSBM), where the mean adjacency matrix is modeled in the same way as in the standard DCSBM, while the variance profile matrix is assumed to be related to the mean adjacency matrix through a given variance function. Our method of selecting the number of communities is based on a sequential testing framework. In each step, the weighted DCSBM is fitted via some spectral clustering method. A key component of our method is matrix scaling on the estimated variance profile matrix. The resulting scaling factors can be used to normalize the adjacency matrix, from which the test statistic is then obtained. Under mild conditions on the weighted DCSBM, our proposed procedure is shown to be consistent in estimating the true number of communities. Numerical experiments on both simulated and real-world network data demonstrate the desirable empirical properties of our method.
APA
Liu, Y. & Li, X.. (2025). Selecting the Number of Communities for Weighted Degree-Corrected Stochastic Block Models. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:586-594 Available from https://proceedings.mlr.press/v258/liu25a.html.

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