Graph Laplacian for Semi-supervised Learning

Or Streicher, Guy Gilboa

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Semi-supervised learning is highly useful in common scenarios where labeled data is scarce but unlabeled data is abundant. The graph (or nonlocal) Laplacian is a fundamental smoothing operator for solving various learning tasks. For unsupervised clustering, a spectral embedding is often used, based on graph-Laplacian eigenvectors. For semi-supervised problems, the common approach is to solve a constrained optimization problem, regularized by a Dirichlet energy, based on the graph-Laplacian. However, as supervision decreases, Dirichlet optimization becomes suboptimal. We therefore would like to obtain a smooth transition between unsupervised clustering and low-supervised graph-based classification. In this paper, we propose a new type of graph-Laplacian which is adapted for Semi-Supervised Learning (SSL) problems. It is based on both density and contrastive measures and allows the encoding of the labeled data directly in the operator. Thus, we can perform successfully semi-supervised learning using spectral clustering. The benefits of our approach are illustrated for several SSL problems.

Original languageEnglish
Title of host publicationScale Space and Variational Methods in Computer Vision - 9th International Conference, SSVM 2023, Proceedings
EditorsLuca Calatroni, Marco Donatelli, Serena Morigi, Marco Prato, Matteo Santacesaria
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages13
ISBN (Print)9783031319747
StatePublished - 2023
Event9th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2023 - Santa Margherita di Pula, Italy
Duration: 21 May 202325 May 2023

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume14009 LNCS


Conference9th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2023
CitySanta Margherita di Pula


  • Graph Representation
  • Nonlocal Laplacian
  • Semi-Supervise Learning
  • Spectral Clustering

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science


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