SavedAdd your journal

Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 72 Issue: 3

A new measure of preferred direction for circular data using angular wrapping

Özge Tezel(KARADENIZ TECHNICAL UNIVERSITY, FACULTY OF SCIENCE)0000-0003-2815-686X
Buğra Kaan Tiryaki(KARADENIZ TECHNICAL UNIVERSITY, FACULTY OF SCIENCE)0000-0003-0995-7389
Eda Özkul(KARADENIZ TECHNICAL UNIVERSITY, FACULTY OF SCIENCE)0000-0002-9840-8818
Orhan Kesemen(KARADENIZ TECHNICAL UNIVERSITY, FACULTY OF SCIENCE)0000-0002-5160-1178
Pages
—
Publication Date
2023-09-30
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The results demonstrate the superiority of the proposed methods in terms of the absolute error and absolute percentage error.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The statistical techniques which are developed for the analysis of data in the linear number system cannot be applied to directional data directly.
📊
Key Findings & Data:Four different artificial and three real datasets are employed to evaluate the performance of the proposed methods.
💡
Conclusion & Impact:The results demonstrate the superiority of the proposed methods in terms of the absolute error and absolute percentage error.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Angular wrapping · circular data · angular circular mean

Abstract

The statistical techniques which are developed for the analysis of data in the linear number system cannot be applied to directional data directly. Circular data may be discontinuous in some principal interval. These discontinuities cause failure results in the circular statistics. Because of that the proposed wrapping operator must be used for data, which are defined in the discontinuous range. However, in both continuity and discontinuity, the wrapping operator works correctly. The most common preferred directions for circular data are circular mean and variance summarizing and comparing them. Although circular data has a very important role in statistics, the literature is weak in terms of statistical analysis of circular data. It creates a gap in this field. This study examines the preferred direction of circular data to fill this gap and presents a new measure of preferred direction for circular data using angular wrapping. Four different artificial and three real datasets are employed to evaluate the performance of the proposed methods. The results demonstrate the superiority of the proposed methods in terms of the absolute error and absolute percentage error. Consequently, it has been seen that the proposed methods giv e more consistent and more accurate results than thevectorial methods.

🔖

Cite This Article

Tezel, Ö., Tiryaki, B. K., Özkul, E., Kesemen, O. (2023). A new measure of preferred direction for circular data using angular wrapping. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 72 Issue: 3. https://doi.org/10.31801/cfsuasmas.1159269

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (44)

  1. Jammalamadaka, S. R., SenGupta, A., Topics in Circular Statistics, World Scientific Publishing Co. Pte. Ltd., 2001.
  2. Bowers, J. A., Morto, I. D., Mould, G. I., Directional statistics of the wind and waves, Appl. Ocean. Res., 22(1) (2000), 13-30. https://doi.org/10.1016/S0141-1187(99)00025-5
  3. Mardia, K. V., Statistics of Directional Data, Academic Press, 1972.
  4. Fisher, N., Statistical Analysis of Circular Data, Cambridge University Press, 1993.
  5. Mardia, K. V., Jupp, P. E., Directional Statistics, John Wiley & Sons Inc., 2000.
  6. Lark, L. M., Clifford, D., Waters, C. N., Modelling complex geological circular data with the projected normal distribution and mixtures of von Mises distribution, Solid Earth, 5(2) (2014) 631-639. https://doi.org/10.5194/se-5-631-2014
  7. Kempter, R., Leibold, C., Buzs´aki, G., Diba, K., Schmidt, R., Quantifying circular–linear associations: Hippocampal phase precession, J. Neurosci. Methods, 207(1) (2012), 113-124. https://doi.org/10.1016/j.jneumeth.2012.03.007
  8. La Sorte, F. A., Mannan, R. W., Reynolds, R. T., Grubb, T. G., Habitat associations ofsympatric red-tailed hawks and northern goshawks on the Kaibab Plateau, J. Wildl. Manage., 68(2) (2004), 307-317. https://doi.org/10.2193/0022-541X(2004)068[0307:HAOSRH]2.0.CO;2
  9. Jones, M. C., Pewsey, A., Inverse Batschelet distributions for circular data, Biometrics, 68(1) (2012), 183-193. https://doi.org/10.1111/j.1541-0420.2011.01651.x
  10. Baayen, C., Klugkist, I., Mechsner, F., Test of order-constrained hypotheses for circular data with applications to human movement science, J. Mot. Behav., 44(5) (2012), 351-363. https://doi.org/10.1080/00222895.2012.709549
  11. Traa, J., Smaragdis, P., Multichannel source separation and tracking with RANSAC and directional statistics, IEEE/ACM Trans. Audio Speech. Lang. Process., 22(12) (2014), 2233-2243. https://doi.org/10.1109/TASLP.2014.2365701
  12. Ehler, M., Galanis, J., Frame theory in directional statistics, Stat. Probab. Lett., 81(2) (2011), 1046-1051. https://doi.org/10.1016/j.spl.2011.02.027
  13. Hawkins, D. M., Lombard, F., Segmentation of circular data, J. Appl. Stat., 42(1) (2015), 88-97. https://doi.org/10.1080/02664763.2014.934665
  14. Klugkist, I., Bullens, J., Postma, A., Evaluating order-constrained hypotheses for circulardata using permutation tests, Br. J. Math. Stat. Psychol., 65(2) (2012), 222-236. https://doi.org/10.1111/j.2044-8317.2011.02018.x
  15. Tasdan, F., Cetin, M., A simulation study on the influence of ties on uniform scores test for circular data, J. Appl. Stat., 41(5) (2014), 1137-1146. https://doi.org/10.1080/02664763.2013.862224
  16. Thompson, L. M., van Manen, F. T., King, T. L., Geostatistical analysis of allele presence patterns among American black bears in eastern North Carolina, Ursus, 16(1) (2005), 59-69. https://doi.org/10.2192/1537-6176(2005)016[0059:GAOAPP]2.0.CO;2
  17. Kubiak, T., Jonas, C., Applying circular statistics to the analysis of monitoring data, Eur. J. Psychol. Assess., 23(4) (2007), 227-237. https://doi.org/10.1027/1015-5759.23.4.227
  18. Brunsdon, C., Corcoran, J., Using circular statistics to analyse time patterns in crime incidence, Comput. Environ. Urban Syst., 30(3) (2006), 300-319. https://doi.org/10.1016/j.compenvurbsys.2005.11.001
  19. Huang, L., Helmke, B. P., A Semi-automatic method for image analysis of edge dynamics in living cells, Cell. Mol. Bioeng., 4(2) (2011), 205-219. https://doi.org/10.1007/s12195-010-0141-z
  20. Abraham, C., Molinari, N., Servien, R., Unsupervised clustering of multivariate circular data, Stat. Med., 32(8) (2013), 1376-1382. https://doi.org/10.1002/sim.5589
  21. Rocchi, M. B., Perlini, C., Is the time of suicide a random choice? A new statistical perspective, Crisis, 23(4) (2002), 161. https://doi.org/10.1027/0227-5910.23.4.161
  22. Le, C. T., Liu, P., Lindgren, B. R., Daly, K. A., Giebink, G. S., Some statistical methods for investigating the date of birth as a disease indicator, Stat. Med., 22(13) (2003), 2127-2135. https://doi.org/10.1002/sim.1343
  23. Chen, L., Singh, V. P., Guo, S., Fang, B., Liu, P., A new method for identification of flood seasons using directional statistics, Hydrol. Sci. J., 58(1) (2013), 28-40. https://doi.org/10.1080/02626667.2012.743661
  24. Wang F., Gelfand, A. E., Modeling space and space-time directional data using projected Gaussian processes, J. Atmos. Ocean. Technol., 8(11) (2014), 1466-1485. https://doi.org/10.1080/01621459.2014.934454
  25. Yurovskaya, M. V., Dulov, V. A., Chapron, B., Kudryavtsev, V. N., Directional short wind wave spectra derived from the sea surface photography, J. Geophys. Res. Oceans., 118(9) (2013), 4380-4394. https://doi.org/10.1002/jgrc.20296
  26. Costa, M., Koivunen, V., Poor, H. V., Estimating directional statistics using wavefield modeling and mixtures of von-mises distributions, IEEE Signal Process. Lett., 21(12) (2014), 1496-1500. https://doi.org/10.1109/LSP.2014.2341651
  27. Minguez, R., Espejo, A., Tomas, A., Mendez, F. J., Losada, I. J., Directional calibration of wave reanalysis databases using instrumental data, J. Atmos. Ocean. Technol., 28(11) (2011), 1466-1485. https://doi.org/10.1175/JTECH-D-11-00008.1
  28. Schwartz, R. S., Barbosa, R. R. R., Meratnia, N., Heijenk, G., Scholten, H., A directional data dissemination protocol for vehicular environments, Comput. Commun., 34(17), (2011), 2057-2071. https://doi.org/10.1016/j.comcom.2011.03.007
  29. Guo, C., Wu, X., Feng, C., Zeng, Z., Spectrum sensing for cognitive radios based on directionalstatistics of polarization vectors, IEEE J. Sel. Areas Commun., 31(3) (2013), 379-393. https://doi.org/10.1109/JSAC.2013.130305
  30. Batschelet, E., Circular Statistics in Biology, Academic Press, 1981.
  31. Zar, J. H., Biostatistical Analysis 4th edition, Prentice Hill, 1999.
  32. Easton Jr, R. L., Topics in Circular Statistics, John Wiley & Sons, 2010.
  33. Rhoad, R., Milauskas G., Whipple, R., Geometry for Enjoyment and Challenge, McDougal Littell & Co., 1991.
  34. Ackermann, H., A note on circular nonparametrical classification, Biom. J., 39(5) (1997), 577-587. https://doi.org/10.1002/bimj.4710390506
  35. Lund, U., Cluster analysis for directional data, Commun. Stat.–Simul. Comput., 28(4) (1999), 1001-1009. https://doi.org/10.1080/03610919908813589
  36. Jander, R., Die optische richtungsorientierung der roten waldameise (formica ruea l.), Z. Vgl. Physiol., 40(2) (1957), 162-238. https://doi.org/10.1007/BF00297947
  37. Chapman, M., Assessment of some controls in experimental transplants of intertidal gastropods, Journal of J. Exp. Mar. Biol. Ecol., 103(1-3) (1986), 181-201. https://doi.org/10.1016/0022-0981(86)90140-1
  38. Chapman, M., Underwood, A., Experimental designs for analyses of movements by molluscs, Proceedings of the third international symposium on littorinid biology, (1992), 169-180.
  39. Wehner R., Strasser, S., The POL area of the honey bee’s eye: behavioural evidence, Physiol. Entomol., 10(3) (1985), 337-349. https://doi.org/10.1111/j.1365-3032.1985.tb00055.x
  40. Ravindran, P., Ghosh, S. K., Bayesian analysis of circular data using wrapped distributions, J. Stat. Theory Pract., 5(4) (2011), 547-561. https://doi.org/10.1080/15598608.2011.10483731
  41. Otieno, B. S., Anderson-Cook, C. M., Measures of preferred direction for environmental and ecological circular data, Environ. Ecol. Stat., 13(3)(2006), 311-324. https://doi.org/10.1007/s10651-004-0014-5
  42. Rossel, S., Wehner, R., Polarization vision in bees, Nature, 323(6084) (1986), 128-131. https://doi.org/10.1038/323128a0
  43. Rossel, S., Wehner, R., The bee’s map of the e-vector pattern in the sky, Proc. Natl. Acad. Sci. U.S.A., 79(14) (1982), 4451-4455. https://doi.org/10.1073/pnas.79.14.4451
  44. Brines, M. L., Gould, J. L., Bees have rules, Science, 206(4418) (1979), 571-573. https://doi.org/10.1126/science.206.4418.571