Canlı toplumlarının derecelendirilmesi için nispi entropi, boolean operatörleri ve temel bileşenler analizi kardeşliği
Abstract
Canlı toplumların sayısal olarak birbirlerine göre derecelendirilmiş verileri toplum-çevre ilişkilerini incelemek ve açıklamak için temel girdilerdir. Bu çalışmada iki olasılık dağılımı olan p ve q arasındaki simetrik olmayan farkın ölçümü olarak tanımlanan nispi entropiyi D[p(x) | |q(x)] kullanarak temel bileşenler analizinin ordinasyon eksenleri boyunca canlı toplumların derecelendirilmesinin nasıl gerçekleştirileceği sorusuna cevap bulmak amaçlanmıştır. Çalışmada ilk olarak üç bitki toplumundan oluşan hipotetik bir veri matrisi kullanılarak bitki toplum çiftlerinin nispi entropi hesaplarına girişilmiştir. Fakat bu işlem sonunda, orijinal veri matrisinde “0” verilerinin varlığı sebebiyle toplum çiftleri arasında nispi entropi hesapları gerçekleştirilememiştir. Bu sebepten veri matrisi her bir toplumun marjinal entropilerini arttırmak suretiyle tekrar düzenlenmiştir. Böylece toplum çiftleri arasında gölgeli nispi entropi (D∎[p(x) || q(x)]) başarılı bir şekilde hesaplanmıştır. Bu aşamadan sonra, toplum çiftleri arasında entropik ölçüm değerlerini içeren matriste, her bir toplumun kendi ile çakıştığı köşegen elemanlarının entropik değerlerini bulmak için devreye Boolean operatörleri ve temel bileşenler analizi (TBA) sokulmuştur. En son aşamada elde edilen veri grubuna son bir kez TBA uygulanmış, toplumlar TBA’nın ordinasyon ekseninde konumlandırılmıştır. Bu yaklaşımla elde edilen çıktılar, orijinal veriye kümeleme analizi kullanarak elde edilen çıktılar ile çok benzer bulunmuştur. Bu sonuç, nispi entropi, Boolean operatörleri ve TBA birlikteliği ile canlı toplumlarının birbirlerine göre konumlanmasının veya derecelenmesinin başarılı bir şekilde uygulanabileceğine dair bir kanaatin oluşmasını sağlamıştır.
References
- Arpasi, J.P., 2003. A Brief intrduction of ternary logic. http://www.docslides.com/luanne-stotts/a-brief-introduction-to-ternary. Accessed: 07.09.2017
- Ben-Ari, M., 1993. Mathematical Logic for Computer Science. Third Edition, Springer London Heidelberg New York Dordrecht.
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- Hill, M.O., Gauch, H.G., 1980. Detrended correspondence analysis: An improved ordination technique. Classification and ordination. Springer, Dordrecht. pp. 47-58.
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Brotherhoods of relative entropy, boolean operators and principle component analysis for a gradient of living communities
Abstract
It is well known that gradient values of the living communities are the most important and valuable data to examine and explain community-environmental relationships. On this context, the purpose of the present study is to find an answer to the question that is how to generate a gradient of living communities along the PCA (Principal Component Analysis) ordination axes by using relative entropy (D[p(x) | |q(x)]), a measure of the non-symmetric difference between two probability distributions, p and q. A hypothetic data matrix composed of 3 plant communities was subjected to relative entropy. Relative entropy could not be calculated from original data since the hypothetic data matrix includes zero values. The data matrix was, therefore, re-arranged by increasing the marginal entropy of each of the communities. Thus shaded relative entropies (D∎[p(x) || q(x)]) among the communities were successfully calculated. Next, the locations of the resulted matrix in which each community shares a cell with itself were analyzed using Boolean Operators and principle component analysis (PCA). Lastly, the last PCA was applied in order to determine the locations of the plant communities along the ordination axes. The results of such approach were compared to the results obtained from the original data by using cluster analysis. The results were found very similar as a result of this comparison and, it was formed an opinion to be able to successfully use the combinations of shaded relative entropy and Boolean operators for a gradient of the living communities along the PCA ordination axes.
Keywords
Information theory Probability theory The Kullback–Leibler divergence Information gain Information divergence
References
- Arpasi, J.P., 2003. A Brief intrduction of ternary logic. http://www.docslides.com/luanne-stotts/a-brief-introduction-to-ternary. Accessed: 07.09.2017
- Ben-Ari, M., 1993. Mathematical Logic for Computer Science. Third Edition, Springer London Heidelberg New York Dordrecht.
- Boc, A., Diallo A.B., Makarenkov, V., 2012. T-REX: a wep server for inferring validating and visualizing phylogenetic trees and networks. Nucleic Acids Reseach, 40: 573-579.
- Cover, T.M., Thomas, J.A., 1991. Elements of information theory. Wiley, Network., http://coltech.vnu.edu.vn/~ thainp/books/Wiley_-_2006_ Elements_of_Information_ Theory_2nd_Ed.pdf; Erişim tarihi: 14.03.2016.
- Ejrnæs, R., 2000. Can we trust gradients extracted by detrended correspondence analysis? Journal of Vegetation Science, 11(4): 565-572.
- Hill, M.O., Gauch, H.G., 1980. Detrended correspondence analysis: An improved ordination technique. Classification and ordination. Springer, Dordrecht. pp. 47-58.
- Özkan, K., 2016. Application of information theory for an entropic gradient of ecological sites. Entropy, 18(10): 340.
- Pathak, R.P., Baniya, C.B., 2017. Species diversity and tree carbon stock pattern in a community-managed tropical shorea forest in Nawalparasi, Nepal. International Journal of Ecology and Environmental Sciences, 42(5): 3-17.
- Peet, R.K., Knox, R.G., Case, J.S., Allen, R., 1988. Putting things in order: The advantages of detrended correspondence analysis. The American Naturalist, 131(6): 924-934.
- Schumacher, B., Westmoreland, M.D., 2002. Relative entropy in quantum information theory. Contemporary Mathematics, 305, 265-290.
- Vedral, V., 2002. The role of relative entropy in quantum information theory. Reviews of Modern Physics, 74(1): 197.
Details
| Primary Language | Turkish |
|---|---|
| Journal Section | Orijinal Araştırma Makalesi |
| Authors | |
| Publication Date | July 21, 2018 |
| Acceptance Date | May 21, 2018 |
| Published in Issue | Year 2018 Volume: 19 Issue: 2 |
