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

• URL: http://arxiv.org/abs/2406.05340v2
• Date: Tue, 08 Oct 2024 06:01:43 GMT
• Title: Selecting the Number of Communities for Weighted Degree-Corrected Stochastic Block Models
• Authors: Yucheng Liu, Xiaodong Li,
• Abstract summary: We investigate how to select the number of communities for weighted networks without a full likelihood modeling. We propose a novel weighted degree-corrected block model (DCSBM), in which the mean adjacency matrix is modeled as the same as in standard DCSBM. Our method of selecting the number of communities is based on a sequential testing framework, and in each step the weighted DCSBM is fitted via some spectral clustering method.
• Score: 5.117940794592611
• License:
• 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), in which the mean adjacency matrix is modeled as the same as in 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, and in each step the weighted DCSBM is fitted via some spectral clustering method. A key step is to carry out matrix scaling on the estimated variance profile matrix. The resulting scaling factors can be used to normalize the adjacency matrix, from which the testing statistic is 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 also demonstrate the desirable empirical properties of our method.

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