The self-consistent field iteration for p-spectral clustering

TL;DR

This paper adapts the self-consistent field iteration, a quantum chemistry algorithm, to solve the p-Laplacian eigenproblem in unsupervised learning, demonstrating its effectiveness through numerical experiments.

Contribution

It introduces a novel adaptation of the SCF iteration for the nonlinear p-Laplacian eigenproblem in machine learning.

Findings

Numerical experiments confirm the viability of the adapted SCF method.

The approach effectively solves the p-Laplacian eigenproblem in unsupervised learning.

The method demonstrates promising results in convergence and accuracy.

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 viablity of our approach.