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

Abstract

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
Pages62-72
Number of pages11
ISBN (Print)9783030209117
DOIs
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

Conference

Conference18th International Conference on Artificial Intelligence and Soft Computing, ICAISC 2019
CountryPoland
CityZakopane
Period6/16/196/20/19

Fingerprint

Triangle inequality
Distance Matrix
Metric
Data Clustering
Dissimilarity
Image Segmentation
Set of points
Pattern Recognition
Metric space
Triangular
Retrieval
Image segmentation
Neural Networks
Pattern recognition
Experimental Results
Demonstrate
Learning
Deep learning

Keywords

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

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Gabidolla, M., Iskakov, A., Demirci, M. F., & Yazici, A. (2019). On Approximating Metric Nearness Through Deep Learning. In J. M. Zurada, W. Pedrycz, L. Rutkowski, R. Scherer, M. Korytkowski, & R. Tadeusiewicz (Eds.), Artificial Intelligence and Soft Computing - 18th International Conference, ICAISC 2019, Proceedings (pp. 62-72). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11508 LNAI). Springer Verlag. https://doi.org/10.1007/978-3-030-20912-4_6

On Approximating Metric Nearness Through Deep Learning. / Gabidolla, Magzhan; Iskakov, Alisher; Demirci, M. Fatih; Yazici, Adnan.

Artificial Intelligence and Soft Computing - 18th International Conference, ICAISC 2019, Proceedings. ed. / Jacek M. Zurada; Witold Pedrycz; Leszek Rutkowski; Rafał Scherer; Marcin Korytkowski; Ryszard Tadeusiewicz. Springer Verlag, 2019. p. 62-72 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11508 LNAI).

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

Gabidolla, M, Iskakov, A, Demirci, MF & Yazici, A 2019, On Approximating Metric Nearness Through Deep Learning. in JM Zurada, W Pedrycz, L Rutkowski, R Scherer, M Korytkowski & R Tadeusiewicz (eds), Artificial Intelligence and Soft Computing - 18th International Conference, ICAISC 2019, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11508 LNAI, Springer Verlag, pp. 62-72, 18th International Conference on Artificial Intelligence and Soft Computing, ICAISC 2019, Zakopane, Poland, 6/16/19. https://doi.org/10.1007/978-3-030-20912-4_6
Gabidolla M, Iskakov A, Demirci MF, Yazici A. On Approximating Metric Nearness Through Deep Learning. In Zurada JM, Pedrycz W, Rutkowski L, Scherer R, Korytkowski M, Tadeusiewicz R, editors, Artificial Intelligence and Soft Computing - 18th International Conference, ICAISC 2019, Proceedings. Springer Verlag. 2019. p. 62-72. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-030-20912-4_6
Gabidolla, Magzhan ; Iskakov, Alisher ; Demirci, M. Fatih ; Yazici, Adnan. / On Approximating Metric Nearness Through Deep Learning. Artificial Intelligence and Soft Computing - 18th International Conference, ICAISC 2019, Proceedings. editor / Jacek M. Zurada ; Witold Pedrycz ; Leszek Rutkowski ; Rafał Scherer ; Marcin Korytkowski ; Ryszard Tadeusiewicz. Springer Verlag, 2019. pp. 62-72 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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