The self-consistent field iteration for p-spectral clustering

Abstract

The self-consistent field (SCF) iteration, combined with its variants, is one of the most widely used algorithms in quantum chemistry. We propose a procedure to adapt the SCF iteration for the p-Laplacian eigenproblem, which is an important problem in the field of unsupervised learning. We formulate the p-Laplacian eigenproblem as a type of nonlinear eigenproblem with one eigenvector nonlinearity , which then allows us to adapt the SCF iteration for its solution after the application of suitable regularization techniques. The results of our numerical experiments confirm the viability of our approach.

Please cite this paper as:

@article{upadhyaya2021self,
  title={The self-consistent field iteration for p-spectral clustering},
  author={Upadhyaya, Parikshit and Jarlbering, Elias and Tudisco, Francesco},
  journal={arXiv:2111.09750},
  year={2021}
}

Keywords: clustering spectral clustering nonlinear eigevenvalues graph Laplacian Cheeger inequality networks