By assigning a probability measure via the spectrum of the normalized Laplacian to each graph and using Lp Wasserstein distances between probability measures, we define the corresponding spectral distances dp on the set of all graphs. This approach can even be extended to measuring the distances betw...
The spectral distance σ(G1,G2) between n vertex graphs G1 and G2 is defined by σ(G1,G2)=∑i=1n|λi(G1)-λi(G2)|. Here we provide some initial results regarding this quantity. First, we give some general results concerning the spectral distances between arbitrary graphs, and ...
05 On vertex-transitive graphs with a unique hamiltonian circle 51:10 Learning Tasks in the Wasserstein Space 55:54 Influence of the endothelial surface layer on the motion of red blood cells 51:22 Effect of Dependence on the Convergence of Empirical Wasserstein Distance 59:08 AI for Science; ...
This work presents a novel procedure for computing (1) distances between nodes of a weighted, undirected, graph, called the Euclidean Commute Time Distance (ECTD), and (2) a subspace projection of the nodes of the graph that preserves as much variance as possible, in terms of the ECTD – ...
(practically constant) dimensions Based on approximate matrix decompositions [DKM06] ) / ) (log( 2 n O Pick a column C from matrix of distances C T C i L Suppose C is a basis for L… Now Choose C-transpose We can now show i i C L i i C T T C C L T 1 C T 1 C C ...
Second, increasing the thickness of the dispersion element simultaneously increases the lateral and axial distances between the imaging results of the different spectral channels. While the former benefits spectral encoding, the latter can lead to defocusing of the image. In addition, internal dispersion...
defplot_vgcn_embed(graph,node_num,emb,label):node,distances,questions=vgcn.node_level_embedding(graph,node_num,emb)vg_df=pd.DataFrame()vg_df['Premise']=[node]*len(distances)vg_df['Hypothesis']=questionsvg_df['Chebyshev_Distance']=distancesvg_g=nx.from_pandas_edgelist(vg_df,source='Hypoth...
L p -Gromov-Hausdorff distances for Shape Comparison The Gromov–Hausdorff distance between metric spaces appears to be a useful tool for modeling some object matching procedures. Since its conception it has ... F Mémoli 被引量: 0发表: 0年 ...
We assume all the graphs under consideration are simple and connected. Further, |V(G)|=n is the order and |E(G)|=m is the size of G. The degree of v, denoted by dG(v) (we simply write dv) is the number of edges incident on the vertex v. For other standard definitions, we ...
Using this new notion of distances, we show that any black box algorithm for constructing a spanner can be used to construct a spectral sparsifier. We show that given an undirected weighted graph G, simply taking the union of spanners of a few (polylogarithmically many) random subgraphs of ...