%-------------------------------------------------------------------------------
% SuiteSparse Matrix Collection, Tim Davis
% https://sparse.tamu.edu/ML_Graph/Olivetti_norm_10NN
% name: ML_Graph/Olivetti_norm_10NN
% [machine learning graph: Olivetti_norm_10NN]
% id: 2879
% date: 2020
% author: D. Pasadakis, C.L. Alappat, O. Schenk, G. Wellein
% ed: O. Schenk
% fields: name title A id date author ed kind notes aux
% aux: label
% kind: undirected weighted graph
%-------------------------------------------------------------------------------
% notes:
% 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: Olivetti_norm_10NN Classes: 40                                  
%-------------------------------------------------------------------------------
