ML_Graph/mnist_test_norm_10NN
machine learning graph: mnist_test_norm_10NN
Name |
mnist_test_norm_10NN |
Group |
ML_Graph |
Matrix ID |
2878 |
Num Rows
|
10,000 |
Num Cols
|
10,000 |
Nonzeros
|
145,600 |
Pattern Entries
|
145,600 |
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: mnist_test_norm_10NN Classes: 10
|