ML_Graph/k49_norm_10NN

machine learning graph: k49_norm_10NN
Name k49_norm_10NN
Group ML_Graph
Matrix ID 2874
Num Rows 38,547
Num Cols 38,547
Nonzeros 618,158
Pattern Entries 618,158
Kind Undirected Weighted Graph
Symmetric Yes
Date 2020
Author D. Pasadakis, C.L. Alappat, O. Schenk, G. Wellein
Editor O. Schenk
Structural Rank
Structural Rank Full
Num Dmperm Blocks
Strongly Connect Components -1
Num Explicit Zeros 0
Pattern Symmetry 100%
Numeric Symmetry 100%
Cholesky Candidate no
Positive Definite no
Type real
Download MATLAB Rutherford Boeing Matrix Market
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: k49_norm_10NN Classes: 49