Weakly Supervised Regression Using Manifold Regularization and Low-Rank Matrix Representation

Vladimir Berikov, Alexander Litvinenko

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

Abstract

We solve a weakly supervised regression problem. Under “weakly” we understand that for some training points the labels are known, for some unknown, and for others uncertain due to the presence of random noise or other reasons such as lack of resources. The solution process requires to optimize a certain objective function (the loss function), which combines manifold regularization and low-rank matrix decomposition techniques. These low-rank approximations allow us to speed up all matrix calculations and reduce storage requirements. This is especially crucial for large datasets. Ensemble clustering is used for obtaining the co-association matrix, which we consider as the similarity matrix. The utilization of these techniques allows us to increase the quality and stability of the solution. In the numerical section, we applied the suggested method to artificial and real datasets using Monte-Carlo modeling.

Original languageEnglish
Title of host publicationMathematical Optimization Theory and Operations Research - 20th International Conference, MOTOR 2021, Proceedings
EditorsPanos Pardalos, Michael Khachay, Alexander Kazakov
PublisherSpringer Science and Business Media Deutschland GmbH
Pages447-461
Number of pages15
ISBN (Print)9783030778750
DOIs
Publication statusPublished - 2021
Event20th International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2021 - Irkutsk, Russian Federation
Duration: 5 Jul 202110 Jul 2021

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12755 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference20th International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2021
CountryRussian Federation
CityIrkutsk
Period05.07.202110.07.2021

Keywords

  • Cluster ensemble
  • Co-association matrix
  • Low-rank matrix decomposition
  • Manifold regularization
  • Weakly supervised learning

OECD FOS+WOS

  • 1.02 COMPUTER AND INFORMATION SCIENCES
  • 1.01 MATHEMATICS

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