Group ML_Graph

Group Description
ML_Graph: adjacency matrices from machine learning datasets, Olaf Schenk.

The following adjacency matrices were used in the numerical experiments in:
 
D.  Pasadakis,  C.  L.  Alappat,  O.  Schenk,  and  G.  Wellein,  "K-way
p-spectral clustering on Grassmann manifolds," 2020.  [Online]. Available:
https://arxiv.org/abs/2008.13210

-------------------------------------------------------------------------------
Graph Creation
-------------------------------------------------------------------------------

For all the graphs in the folder, 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

\begin{equation}
    W = G \odot S.
\end{equation}

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.

-------------------------------------------------------------------------------
Description of matrices
-------------------------------------------------------------------------------

For a more detailed description of the datasets, and references of the sources
the datasets were obtained from, see the paper cited in the beginning of this
description.

    Graphs from various machine learning datasets

    Name             Neighbours            Nodes      Edges     Classes
har_10NN                  10               10299      75868          6  
indianpines_10NN          10                9144      62328          8  
JapaneseVowels_10NN       10                9961      65572          9  
worms20_10NN              10               20055     120413         20  
optdigits_10NN            10                5620      39825         10  
Vehicle_10NN              10                 846       5447          4  
mfeatkarhunen_10NN        10                2000      13834         10  
mfeatfactors_10NN         10                2000      13721         10  
mfeatmorphological_10NN   10                2000      11416         10  
mfeatpixel_10NN           10                2000      13966         10  
mfeatzernike_10NN         10                2000      13707         10  
semeion_10NN              10                1593      11113         10  
mice_10NN                 10                1077       6742          8  
yeast_30NN                30                1484      31175         12  
cnae9_10NN                10                1080       9139          9  
dermatology_5NN            5                 366       1220          6  
iris_30NN                 30                 150       2759          3  
Ecoli_10NN                10                 336       2280          8  
Binaryalphadigs_10NN      10                1404       9696         36  
Glass_10NN                10                 214       1493          6  
collins_15NN              15                1000       8246         30  
micromass_10NN            10                 571       4834         20  
breasttissue_10NN         10                 106        706          6  
Plants_10NN               10                1600      10965        100  
plantsmargin_12NN         12                1600      12741        100  
plantstexture_10NN        10                1599      10602        100  
Spectro_10NN              10                 531       3711         48  

    Graphs from image classification problems. The RGB values are normalised 
    in the interval [0,1].

    Name             Neighbours            Nodes      Edges     Classes
usps_norm_5NN             5                11000      40556         10 
Fashion_MNIST_norm_10NN  10                10000      79152         10 
kmnist_norm_10NN         10                10000      78466         10 
k49_norm_10NN            10                38547     309079         49 
mnist_test_norm_10NN     10                10000      72800         10 
YaleB_10NN               10                 2414       8568         10 
umistfacesnorm_10NN      10                  575       3495         20 
YaleA_10NN               10                  165       1134         10 
Olivetti_norm_10NN       10                  400       2828         40
Displaying collection matrices 1 - 20 of 36 in total
Id Name Group Rows Cols Nonzeros Kind Date Download File
2857 Binaryalphadigs_10NN ML_Graph 1,404 1,404 19,392 Undirected Weighted Graph 2020 MATLAB Rutherford Boeing Matrix Market
2881 Plants_10NN ML_Graph 1,600 1,600 21,930 Undirected Weighted Graph 2020 MATLAB Rutherford Boeing Matrix Market
2859 cnae9_10NN ML_Graph 1,080 1,080 18,278 Undirected Weighted Graph 2020 MATLAB Rutherford Boeing Matrix Market
2858 breasttissue_10NN ML_Graph 106 106 1,412 Undirected Weighted Graph 2020 MATLAB Rutherford Boeing Matrix Market
2867 Ecoli_10NN ML_Graph 336 336 4,560 Undirected Weighted Graph 2020 MATLAB Rutherford Boeing Matrix Market
2868 Fashion_MNIST_norm_10NN ML_Graph 10,000 10,000 158,304 Undirected Weighted Graph 2020 MATLAB Rutherford Boeing Matrix Market
2869 Glass_10NN ML_Graph 214 214 2,986 Undirected Weighted Graph 2020 MATLAB Rutherford Boeing Matrix Market
2873 JapaneseVowelsSmall_10NN ML_Graph 9,961 9,961 131,144 Undirected Weighted Graph 2020 MATLAB Rutherford Boeing Matrix Market
2879 Olivetti_norm_10NN ML_Graph 400 400 5,656 Undirected Weighted Graph 2020 MATLAB Rutherford Boeing Matrix Market
2885 Spectro_10NN ML_Graph 531 531 7,422 Undirected Weighted Graph 2020 MATLAB Rutherford Boeing Matrix Market
2888 Vehicle_10NN ML_Graph 846 846 10,894 Undirected Weighted Graph 2020 MATLAB Rutherford Boeing Matrix Market
2890 YaleA_10NN ML_Graph 165 165 2,268 Undirected Weighted Graph 2020 MATLAB Rutherford Boeing Matrix Market
2891 YaleB_10NN ML_Graph 2,414 2,414 34,808 Undirected Weighted Graph 2020 MATLAB Rutherford Boeing Matrix Market
2860 collins_15NN ML_Graph 1,000 1,000 16,492 Undirected Weighted Graph 2020 MATLAB Rutherford Boeing Matrix Market
2861 dataset12mfeatfactors_10NN ML_Graph 2,000 2,000 27,442 Undirected Weighted Graph 2020 MATLAB Rutherford Boeing Matrix Market
2862 dataset16mfeatkarhunen_10NN ML_Graph 2,000 2,000 27,668 Undirected Weighted Graph 2020 MATLAB Rutherford Boeing Matrix Market
2863 dataset18mfeatmorphological_10NN ML_Graph 2,000 2,000 22,832 Undirected Weighted Graph 2020 MATLAB Rutherford Boeing Matrix Market
2864 dataset20mfeatpixel_10NN ML_Graph 2,000 2,000 27,932 Undirected Weighted Graph 2020 MATLAB Rutherford Boeing Matrix Market
2865 dataset22mfeatzernike_10NN ML_Graph 2,000 2,000 27,414 Undirected Weighted Graph 2020 MATLAB Rutherford Boeing Matrix Market
2866 dermatology_5NN ML_Graph 366 366 2,440 Undirected Weighted Graph 2020 MATLAB Rutherford Boeing Matrix Market