ML_Graph/dataset16mfeatkarhunen_10NN

machine learning graph: dataset16mfeatkarhunen_10NN
Name dataset16mfeatkarhunen_10NN ML_Graph 2862 2,000 2,000 27,668 27,668 Undirected Weighted Graph Yes 2020 D. Pasadakis, C.L. Alappat, O. Schenk, G. Wellein O. Schenk
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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 \begin{equation} 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} ) \end{equation} 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: dataset16mfeatkarhunen_10NN Classes: 10