On fast computation of directed graph Laplacian pseudo-inverse

Incremental Computation of Pseudo-Inverse of Laplacian

A divide-and-conquer based approach for computing the Moore-Penrose pseudo-inverse of the combinatorial Laplacian matrix (L) of a simple, undirected graph is proposed. The nature of the underlying sub-problems is studied in detail by means of an elegant interplay between L and the effective resistance distance (Ω). Closed forms are provided for a novel two-stage process that helps compute the p...

Incremental Computation of Pseudo-Inverse of Laplacian: Theory and Applications

A divide-and-conquer based approach for computing the Moore-Penrose pseudo-inverse of the combinatorial Laplacian matrix (L) of a simple, undirected graph is proposed. The nature of the underlying sub-problems is studied in detail by means of an elegant interplay between L and the effective resistance distance (Ω). Closed forms are provided for a novel two-stage process that helps compute the p...

On the pseudo-inverse of the Laplacian of a bipartite graph

We provide an efficient method to calculate the pseudo-inverse of the Laplacian of a bipartite graph, which is based on the pseudo-inverse of the normalized Laplacian.

Recursive computation of pseudo-inverse of matrices

Fast Computation of Graph Kernels

Using extensions of linear algebra concepts to Reproducing Kernel Hilbert Spaces (RKHS), we define a unifying framework for random walk kernels on graphs. Reduction to a Sylvester equation allows us to compute many of these kernels in O(n) worst-case time. This includes kernels whose previous worst-case time complexity was O(n), such as the geometric kernels of Gärtner et al. [1] and the margin...