A unifying theorem for spectral embedding and clustering

@inproceedings{Brand2003AUT,
  title={A unifying theorem for spectral embedding and clustering},
  author={Matthew Brand and Kun Huang},
  booktitle={AISTATS},
  year={2003}
}
Spectral methods use selected eigenvectors of a data affinity matrix to obtain a data representation that can be trivially clustered or embedded in a low-dimensional space. We present a theorem that explains, for broad classes of affinity matrices and eigenbases, why this works: For successively smaller eigenbases (i.e., using fewer and fewer of the affinity matrix ś dominant eigenvalues and eigenvectors), the angles between similar vectors in the new representation shrink while the angles… CONTINUE READING
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