29Oct
2016
Eugene / Learning, MIT Data Science: Data To Insights / 0 comment
Eigenvectors
To capture global connectivity structure, eigenvectors are really useful. Results will be spectral clustering.
Spectrum of matrix: set of eigenvalues
Matrix: Laplacian of graph
Adjacency matrix: $\left(\begin{array}{rrrrrr}
0 & 1 & 0 & 0 & 1 & 0\\
1 & 0 & 1 & 0 & 1 & 0\\
0 & 1 & 0 & 1 & 0 & 0\\
0 & 0 & 1 & 0 & 1 & 1\\
1 & 1 & 0 & 1 & 0 & 0\\
0 & 0 & 0 & 1 & 0 & 0\\
\end{array}\right)$
Laplacian matrix: $\left(\begin{array}{rrrrrr}
2 & -1 & 0 & 0 & -1 & 0\\
-1 & 3 & -1 & 0 & -1 & 0\\
0 & -1 & 2 & -1 & 0 & 0\\
0 & 0 & -1 & 3 & -1 & -1\\
-1 & -1 & 0 & -1 & 3 & 0\\
0 & 0 & 0 & -1 & 0 & 1\\
\end{array}\right)$