Identifying clusters in Czekanowski's diagram

• Autorzy: Bartoszek Krzysztof , Luo Ying

Identyfikatory

DOI

10.14708/ma.v51i2.7259

Warianty tytułu

PL

Identyfikacja skupień w diagramie Czekanowskiego

• Języki publikacji: EN

Abstrakty

EN

Visualizing data through Czekanowski's diagram has as its aim to present how objects are related to each other. Often, obvious clusters of observations are directly visible. However, exactly delimiting them is not a straightforward task. We present here a development of the RMaCzek package that includes cluster identification in Czekanowski's diagrams.

PL

Diagram Czekanowskiego ma na celu zaprezentowanie podobieństw wewnątrz próbki statystycznej. Najczęściej widać na nim wyraźne grupowania elementów. Jednakże dokładne wyznaczenie granic między skupieniami nie jest trywialnym zagdnieniem. W niniejszej pracy przedstawiamy rozszerzoną wersję pakietu RMaCzek, która pozwala na analizę skupień w diagramach Czekanowskiego.

Słowa kluczowe

EN

change point analysis; cluster analysis; Czekanowski's diagram; fuzzy clustering; multivariate distance methods; R; RMaCzek

PL

diagram czekanowskiego; kraniometria; metody odległości wielocechowych; rozwój ludzkości

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Mathematica Applicanda
• Rocznik: 2023
• Tom: Vol. 51, no. 2
• Strony: 183--198
• Opis fizyczny: Bibliogr. 22 poz., rys., tab., wykr.

Twórcy

autor

Bartoszek Krzysztof

• Linköping University Department of Computer and Information Science The Division of Statistics and Machine Learning Linköping University, 581 83, Linköping, Sweden

• https://orcid.org/0000-0002-5816-4345+

autor

Luo Ying

• Linköping University The Division of Bioinformatics, Department of Physics, Chemistry and Biology 581 83, Linköping, Sweden

• https://orcid.org/0009-0002-1298-0037+

Bibliografia

• [1] D. Aliyev and C. L. Zirbel. Seriation using tree-penalized path length. Eur. J. Oper. Res., 305(2):617–629, 2023.
• [2] Z. Bar-Joseph, E. D. Demaine, D. K. Gifford, and T. Jaakkola. Fast optimal leaf ordering for hierarchical clustering. Bioinformatics, 17(1):22–29, 2001.
• [3] K. Bartoszek. Revisiting the nowosiółka skull with RMaCzek. Mathematica Applicanda, 50(2):255–266, 2022.
• [4] K. Bartoszek and A. Västerlund. “Old Techniques for New Times”: the RMaCzek package. Biometrical Letters, 57(2):89–118, 2020.
• [5] J. C. Bezdek. Pattern Recognition with Fuzzy Objective Function Algorithms, chapter Objective Function Clustering, pages 43–93.
• [6] J. C. Bezdek, R. Ehrlich, and W. Full. FCM: The fuzzy C–means clustering algorithm. Comput. Geosci., 10(2):191–203, 1984.
• [7] J. Czekanowski. Zur Differentialdiagnose der Neandertalgruppe. Korespondentblatt der Deutschen Gesellschaft für Anthropologie, Ethnologie und Urgeschichte, XL(6/7):44–47, 1909.
• [8] J. Czekanowski. Zarys Metod Statystycznych w Zastosowaniu do Antroplogii (Introduction to Statistics for Anthropology, in Polish). Towarzystwo Naukowe Warszawskie, Warsaw, 1913.
• [9] G. Gruvaeus and H. Wainer. Two additions to hierarchical cluster analysis. British Journal of Mathematical and Statistical Psychology, 25(2):200–206, 1972.
• [10] M. Hahsler, K. Hornik, and C. Buchta. Getting things in order: An introduction to the R package seriation. J. Stat. Softw., 25(3):1–34, 2008.
• [11] H. Henderson and P. F. Velleman. Building multiple regression models interactively. Biometrics, 37(2):391–411, 1981.
• [12] N. A. James and D. S. Matteson. ecp: An R package for nonparametric multiple change point analysis of multivariate data. J. Stat. Softw., 62(7):1–25, 2014.
• [13] Y. Luo. Czekanowski’s clustering: Development of visualization possibilities of the RMaCzek package, 2022. URL http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-182576. MSc thesis, Division for Statistics and Machine Learning, Department of Computer and Information Science, Linköping University.
• [14] D. Matteson and N. James. A nonparametric approach for multiple change point analysis of multivariate data. J. Am. Stat. Assoc., 109 (505):334–345, 2014.
• [15] D. Meyer, E. Dimitriadou, K. Hornik, A. Weingessel, and F. Leisch. e1071: Misc functions of the Department of Statistics, Probability Theory Group (formerly: E1071) TU Wien, 2022. URL https://CRAN.R-project.org/package=e1071. R package version 1.7-11.
• [16] R Core Team. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria, 2019. URL https://www.R-project.org/.
• [17] A. Sołtysiak and P. Jaskulski. Czekanowski’s diagram. A method of multidimensional clustering. In New Techniques for Old Times. CAA 98. Computer Applications and Quantitative Methods in Archaeology. Proceedings of the 26th Conference, Barcelona, March 1998, pages 175–184. Oxford, number 757 in BAR International Series, 1999.
• [18] D. Tsafrir, I. Tsafrir, L. Ein-Dor, O. Zuk, D. A. Notterman, and E. Domany. Sorting points into neighborhoods (SPIN): data analysis and visualization by ordering distance matrices. Bioinformatics, 21(10):2301–2208, 2005.
• [19] A. Västerlund. Czekanowski’s Diagram: Implementing and exploring Czekanowski’s Diagram with different seriation methods, 2019. MSc thesis, Division for Statistics and Machine Learning, Department of Computer and Information Science, Linköping University.
• [20] K. Warzecha. The use of quantitative methods in research on selected behavioral addictions of young people. Studia Ekonomiczne, 247:121–139, 2015.
• [21] S. Wierzchoń and M. Kłopotek. Algorytmy Analizy Skupień (Cluster Analysis Algorithms, in Polish). PWN, Warsaw, 2015.
• [22] W. Wolberg. Breast Cancer Wisconsin (original), 1992. URL http://dx.doi.org/10.24432/C5HP4Z. UCI Machine Learning Repository.

Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).