Finsler Metrics Induced by a Similarity Function

Main Article Content

Nisachon Kumankat*
Praiboon Pantaragphong
Sorin V. Sabau

Abstract

In the present paper, the geometrical properties of a topological space endowed with a similarity was studied. Its relation with weighted quasi-metrics and Finsler metrics of Randers type was discussed. Finally, some applications to bioinformatics and computer science by relating similarities to dynamic programming algorithms are considered. In conclusion, the space containing the real-world data is non-symmetric and non-linear.


 


Keywords:  Finsler metrics; similarity function; weighted quasi-metrics

*Corresponding author: Tel.:  +66 91 8517097


                                             E-mail:  Nisachon.Kumankat@gmail.com


m

Downloads

Download data is not yet available.

Article Details

Section
Research Articles

References

[1] Sabau, S.V., Shibuya, K. and Shimada, H., 2014. Metric structures associated to Finsler metrics. Publications Mathematicae Debrecen, 84 (1-2), 89-103.
[2] Shanker, G. and Rani, S., 2018. Weighted quasi-metrics associated with Finsler metrics. [online]Available at : https://www.researchgate.net/publication/322567912_Weighted_quasi-metrics_associated_with_Finsler_metrics
[3] Vitolo, P., 1999. The representation of weighted quasi-metric spaces. Rendiconti dell'Istituto di Matematica dell'Università di Trieste, 31, 95-100.
[4] Stojmirovic, A., 2008. Quasi-metrics, Similarities and Searches: Aspects of Geometry of Protein Datasets. Ph.D. Victoria University of Wellington.
[5] Stojmirovic, A., 2004. Quasi-metric space with measure. Topology Proceedings, 28 (2), 655-671.
[6] Pevsner, J., 2017. Bioinformatics and Functional Genomics. 3rd ed. New Delhi: Wiley India.
[7] Vitolo, P., 1995. A representation theorem for quasi-metric spaces. Topology and Its Applications, 65, 101-104.
[8] Bao, D., Chern, S.S. and Shen, Z., 2000. An Introduction to Riemann-Finsler Geometry. New York: Springer-Verlag.
[9] Chern, S.S. and Shen, Z., 2005. Riemann-Finsler Geometry. 6th ed. Singapore: World Scientific.