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: optdigits_10NN Classes: 10