Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Graph-Based Semi-Supervised Segregated Lipschitz Learning

Farid Bozorgnia, Yassine Belkheiri, Abderrahim Elmoataz

TL;DR

This paper develops a graph-based semi-supervised learning framework that leverages the properties of the infinity Laplacian to propagate labels in a dataset where only a few samples are labeled, and provides a robust method for dealing with class imbalance.

Abstract

This paper presents an approach to semi-supervised learning for the classification of data using the Lipschitz Learning on graphs. We develop a graph-based semi-supervised learning framework that leverages the properties of the infinity Laplacian to propagate labels in a dataset where only a few samples are labeled. By extending the theory of spatial segregation from the Laplace operator to the infinity Laplace operator, both in continuum and discrete settings, our approach provides a robust method for dealing with class imbalance, a common challenge in machine learning. Experimental validation on several benchmark datasets demonstrates that our method not only improves classification accuracy compared to existing methods but also ensures efficient label propagation in scenarios with limited labeled data.

Graph-Based Semi-Supervised Segregated Lipschitz Learning

TL;DR

This paper develops a graph-based semi-supervised learning framework that leverages the properties of the infinity Laplacian to propagate labels in a dataset where only a few samples are labeled, and provides a robust method for dealing with class imbalance.

Abstract

This paper presents an approach to semi-supervised learning for the classification of data using the Lipschitz Learning on graphs. We develop a graph-based semi-supervised learning framework that leverages the properties of the infinity Laplacian to propagate labels in a dataset where only a few samples are labeled. By extending the theory of spatial segregation from the Laplace operator to the infinity Laplace operator, both in continuum and discrete settings, our approach provides a robust method for dealing with class imbalance, a common challenge in machine learning. Experimental validation on several benchmark datasets demonstrates that our method not only improves classification accuracy compared to existing methods but also ensures efficient label propagation in scenarios with limited labeled data.

Paper Structure

This paper contains 17 sections, 1 theorem, 47 equations, 7 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Mathematical preliminaries on Infinity Laplacian
  3. Local continuous infinity Laplacian
  4. Non-local continuous infinity Laplacian
  5. Calculus on Graphs
  6. Infinity Laplace equation
  7. Minimal Lipshitz extension
  8. Infinity Laplacian abderrahim2014nonlocal
  9. Related Works on Graph-Based Semi-Supervised Learning
  10. Infinity Segregation
  11. Schemes
  12. Infinity Learning Schemes
  13. Infinity Segregated Learning Schemes
  14. Implementation
  15. SNNkoch2015siamese
  16. ...and 2 more sections

Key Result

Lemma 5.1

Let $U=(u_{1},\ldots,u_{k})$ be the minimizer and $\Omega_{1},\ldots,\Omega_{k}$ be the corresponding supports then the following differential inequalities hold in $\Omega$

Figures (7)

  • Figure 1: The first picture on top-left shows the initial value, the right indicates the solution of Problem eq1 and the last picture is the solution of infinity Laplacian with the same boundary condition.
  • Figure 2: .
  • Figure 3: Classification results on 4 Moons with 1 label per class for InfSL, InfL, and Poisson Learning.
  • Figure 4: Classification results on 4 Moons with 3 labels per class for InfSL, InfL, and Poisson Learning.
  • Figure 5: Classification results on 4 Moons with 5 labels per class for InfSL, InfL, and Poisson Learning.
  • ...and 2 more figures

Theorems & Definitions (9)

  • Definition 2.1
  • Lemma 5.1
  • proof
  • Remark 5.2
  • Example 7.1
  • Example 7.2
  • Example 7.3
  • Example 7.4
  • Example 7.5