On Approximating Metric Nearness Through Deep Learning

Magzhan Gabidolla, Alisher Iskakov, M. Fatih Demirci, Adnan Yazici

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)


Many problems require a notion of distance between a set of points in a metric space, e.g., clustering data points in an N-dimensional space, object retrieval in pattern recognition, and image segmentation. However, these applications often require that the distances must be a metric, meaning that they must satisfy a set of conditions, with triangle inequality being the focus of this paper. Given an dissimilarity matrix with triangle inequality violations, the metric nearness problem requires to find a closest distance matrix, which satisfies the triangle inequality condition. This paper introduces a new deep learning approach for approximating a nearest matrix with more efficient runtime complexity than existing algorithms. We have experimented with several deep learning architectures, and our experimental results demonstrate that deep neural networks can learn to construct a close-distance matrix efficiently by removing most of the triangular inequality violations.

Original languageEnglish
Title of host publicationArtificial Intelligence and Soft Computing - 18th International Conference, ICAISC 2019, Proceedings
EditorsJacek M. Zurada, Witold Pedrycz, Leszek Rutkowski, Rafał Scherer, Marcin Korytkowski, Ryszard Tadeusiewicz
PublisherSpringer Verlag
Number of pages11
ISBN (Print)9783030209117
Publication statusPublished - Jan 1 2019
Event18th International Conference on Artificial Intelligence and Soft Computing, ICAISC 2019 - Zakopane, Poland
Duration: Jun 16 2019Jun 20 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11508 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference18th International Conference on Artificial Intelligence and Soft Computing, ICAISC 2019


  • Convolutional neural networks
  • Deep learning
  • Matrix analysis
  • Metric nearness problem

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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