On Approximating Metric Nearness Through Deep Learning

Gabidolla M., Iskakov A., Demirci M. F. , YAZICI A.

18th International Conference on Artificial Intelligence and Soft Computing, ICAISC 2019, Zakopane, Poland, 16 - 20 June 2019, vol.11508 LNAI, pp.62-72 identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 11508 LNAI
  • Doi Number: 10.1007/978-3-030-20912-4_6
  • City: Zakopane
  • Country: Poland
  • Page Numbers: pp.62-72
  • Keywords: Convolutional neural networks, Deep learning, Matrix analysis, Metric nearness problem


© 2019, Springer Nature Switzerland AG.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.