spectral clustering

Data

subject:: Data Science Methods for Large Scale Graphs parent:: Graph Signals and Graph Signal Processing theme:: math notes

spectral clustering algorithm

1. Diagonalize $A=V\Lambda V^T$
2. Order the eigenvectors by decreasing eigenvalue magnitude This yields $V_c=\left[\begin{array}{cccc}{v}_1& v_2& \dots & v_c\end{array}\right],v_i\in {\mathbb{R}}^n=\left[\begin{array}{c}{u}_1\\ u_2\\ ⋮\\ u_n\end{array}\right],u_j\in {\mathbb{R}}^c$ we can see the rows $u_j$ as embeddings of the notes in ${\mathbb{R}}^c$ (community space)
3. yay we can cluster ($k$-means or whatever you want. can also use like gaussian mixture models)

This is the unsupervised version of spectral embedding.

See also graph fourier transform

Mentions

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