ML_Graph/usps_norm_5NN

machine learning graph: usps_norm_5NN
Name usps_norm_5NN ML_Graph 2887 11,000 11,000 81,112 81,112 Undirected Weighted Graph Yes 2020 D. Pasadakis, C.L. Alappat, O. Schenk, G. Wellein O. Schenk
Structural Rank -1 0 100% 100% no no real
Download ML_Graph: adjacency matrices from machine learning datasets, Olaf Schenk. D. Pasadakis, C. L. Alappat, O. Schenk, and G. Wellein, "K-way p-spectral clustering on Grassmann manifolds," 2020. https://arxiv.org/abs/2008.13210 For $n$ data points, the connectivity matrix $G \in \mathbb{R}^{n\times n}$ is created from a k nearest neighbors routine, with k set such that the resulting graph is connected. The similarity matrix $S \in \mathbb{R}^{n\times n}$ between the data points is defined as $$s_{ij} = \max\{s_i(j), s_j(i)\} \;\; \text{with}\; s_i(j) = \exp (-4 \frac{\|x_i - x_j \|^2}{\sigma_i^2} )$$ with $\sigma_i$ standing for the Euclidean distance between the $i$th data point and its nearest k-nearest neighbor. The adjacency matrix $W$ is then created as $W = G \odot S$. Besides the adjacency matrices $W$, the node labels for each graph are part of the submission. If the graph has c classes, the node labels are integers in the range 0 to c-1. Graph: usps_norm_5NN Classes: 10