doi:10.1093/IMAIAI/IAV001Noureddine El KarouiHau-tieng WuOxford University PressN. E. Karoui and H. tieng Wu, Graph connection laplacian and random matrices with random blocks, Information and Inference, 4 (1) (2015), pp. 1-44.
SIAM Journal on Matrix Analysis and ApplicationsA.S. Bandeira, A. Singer, D.A. Spielman, A Cheeger inequality for the graph connection Laplacian, arXiv:1204.3873A.S. Bandeira, A. Singer, and D.A. Spielman. A Cheeger Inequality for the Graph Connection Laplacian. Arxiv preprint arXiv:...
Given a graph G̃ (with Laplacian L̃ with eigenvalues 0 = \widetilde{\lambda}_{1} \leq \cdots \leq \widetilde{\lambda}_{n} and corresponding eigenvectors \widetilde{\mathbf{u}}_{1},\ldots ,\widetilde{\mathbf{u}}_{n}), let \mathscr{G} be the set of all q-cuts of G̃...
Courant theorem provides an upper bound for the number of nodal domains ofeigenfunctions of a wide class of Laplacian-type operators. In particular, itholds for generic eigenfunctions of quantum graph. The theorem stipulates that,after ordering the eigenvalues as a non decreasing sequence, the ...
In order to reflect the local structures, there are three major categories: graph Laplacian regularization, avoiding cannot-links, and tangent space approximation. In fact, the root of these approaches comes from the single manifold learning algorithms based on preserving locality relationships among ...
DGCNN [7] proposes an edge convolution approach by the Laplacian matrix to construct graph convolution. The graph structures provide stronger spatial location relationships and are more conducive to network learning than points alone. However, the relative positions of different vertices in the graph ...
graph connection LaplacianO(d) synchronizationvector diffusion mapsThe O(d) synchronization problem consists of estimating a set of n unknown orthogonal d × d matrices O¹,...,On from noisy measurements of a subset of the pairwise ratios OiOj-1. We formulate and prove a Cheeger-type ...
Connection LaplacianSpectral convergenceDiscretizationWe consider a convolution-type operator on vector bundles over metric-measure spaces. This operator extends the analogous convolution Laplacian on functions in our earlier work to vector bundles, and is a natural extension of the graph connection ...
Laplacian spectrumeigenvalue (of graph)Laplacian eigenvalue (of graph)Let G be a bipartite graph with n vertices and m edges. Let S(G) be the subdivision of G, obtained by inserting a new vertex on each edge of G. The ordinary characteristic polynomial of S(G) and the Laplacian ...
We show that, similar to the undelayed case, the\nsynchronization of the network depends on the connection topology,\ncharacterized by the spectrum of the graph Laplacian. Consequently, scale-free\nand random networks are capable of synchronizing despite the delayed flow of\ninformation, whereas ...