Determining the number of communities in degree-corrected stochastic block models
We propose to estimate the number of communities in degree-corrected stochastic block models based on a pseudo likelihood ratio. For estimation, we consider a spectral clustering together with binary segmentation method. This approach guarantees an upper bound for the pseudo likelihood ratio statist...
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| Main Authors: | , , |
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| Format: | text |
| Language: | English |
| Published: |
Institutional Knowledge at Singapore Management University
2021
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| Subjects: | |
| Online Access: | https://ink.library.smu.edu.sg/soe_research/2485 https://ink.library.smu.edu.sg/context/soe_research/article/3484/viewcontent/20_037_pvoa.pdf |
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| Institution: | Singapore Management University |
| Language: | English |
| Summary: | We propose to estimate the number of communities in degree-corrected stochastic block models based on a pseudo likelihood ratio. For estimation, we consider a spectral clustering together with binary segmentation method. This approach guarantees an upper bound for the pseudo likelihood ratio statistic when the model is over-fitted. We also derive its limiting distribution when the model is under-fitted. Based on these properties, we establish the consistency of our estimator for the true number of communities. Developing these theoretical properties require a mild condition on the average degree: growing at a rate faster than log(n), where n is the number of nodes. Our proposed method is further illustrated by simulation studies and analysis of real-world networks. The numerical results show that our approach has satisfactory performance when the network is sparse and/or has unbalanced communities. |
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