Spectral Embeddings of Degree-$α$ Laplacians in Random Dot Product Graphs
Spectral clustering methods for network data are commonly based on a few matrix representations, such as the adjacency matrix and the symmetric Laplacian. We study a continuum of degree-normalized spectral embeddings that includes these commonly used choices as special cases. Under a random dot product graph model, we establish a row-wise central limit theorem for this family of embeddings. The result provides an explicit description of how degree normalization affects both population geometry and the local uncertainty of embedded nodes. We use the limiting distributions to compare different normalizations in two-community stochastic block models through a projected-Gaussian Bayes-error d...
| Authors | John Park, Ning Hao |
|---|---|
| Primary category | stat.ML |
| Published | 11 August 2026 |
| Last updated at source | 11 August 2026 |
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