TY - GEN

T1 - On Approximating Metric Nearness Through Deep Learning

AU - Gabidolla, Magzhan

AU - Iskakov, Alisher

AU - Demirci, M. Fatih

AU - Yazici, Adnan

N1 - Publisher Copyright:
© 2019, Springer Nature Switzerland AG.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - Convolutional neural networks

KW - Deep learning

KW - Matrix analysis

KW - Metric nearness problem

UR - http://www.scopus.com/inward/record.url?scp=85066743086&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85066743086&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-20912-4_6

DO - 10.1007/978-3-030-20912-4_6

M3 - Conference contribution

AN - SCOPUS:85066743086

SN - 9783030209117

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 62

EP - 72

BT - Artificial Intelligence and Soft Computing - 18th International Conference, ICAISC 2019, Proceedings

A2 - Zurada, Jacek M.

A2 - Pedrycz, Witold

A2 - Rutkowski, Leszek

A2 - Scherer, Rafał

A2 - Korytkowski, Marcin

A2 - Tadeusiewicz, Ryszard

PB - Springer Verlag

T2 - 18th International Conference on Artificial Intelligence and Soft Computing, ICAISC 2019

Y2 - 16 June 2019 through 20 June 2019

ER -