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4132. A Variational Model for graph p-Laplacian eigenfunctions under p-orthogonality constraints
Invited abstract in session TA-32: Nonsmooth optimization and applications, Part I, stream Advances in large scale nonlinear optimization.
Tuesday, 8:30-10:00Room: 41 (building: 303A)
Authors (first author is the speaker)
| 1. | Giuseppe Antonio Recupero
|
| Mathematics, University of Bologna | |
| 2. | Serena Morigi
|
| University of Bologna | |
| 3. | Alessandro Lanza
|
| University of Bologna |
Abstract
The p-Laplacian is a non-linear generalization of the Laplace operator. In the graph context, its eigenfunctions are used for data clustering, spectral graph theory, dimensionality reduction and others problems, as non-linearity better captures the underlying geometry of the data.
We formulate the p-Laplacian nonlinear eigenproblem as an optimization problem under p-orthogonality constraints. The problem of computing multiple eigenvectors of the graph p-Laplacian is then solved by iteratively minimizing the constrained generalized Rayleigh quotient.
We analyze two different optimization algorithms to solve the variational problem. The first is a manifold gradient descent which solves a smooth unconstrained minimization over the p-orthogonality subspace. The second is an Alternate Direction Method of Multipliers which leverages the scaling invariance of Rayleigh quotient to solve a constrained minimization under a p-orthogonality constraint.
We demonstrate the effectiveness and accuracy of the proposed algorithms and compare them in terms of efficiency.
Keywords
- Large Scale Optimization
- Continuous Optimization
- Programming, Nonlinear
Status: accepted
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