Asymptotic Theory of Eigenvectors for Latent Embeddings with Generalized Laplacian Matrices
广义拉普拉斯矩阵潜在嵌入的特征向量渐近理论
Laplacian matrices are commonly employed in many real applications, encoding the underlying latent structural information such as graphs and manifolds. The use of the normalization terms naturally gives rise to random matrices with dependency. It is well-known that dependency is a major bottleneck of new random matrix theory (RMT) developments. To this end, in this paper, we formally introduce a class of generalized (and regularized) Laplacian matrices, which contains the…