Kendall transformation brings a robust categorical representation of ordinal data
Abstract Kendall transformation is a conversion of an ordered feature into a vector of pairwise order relations between individual values. This way, it preserves ranking of observations and represents it in a categorical form. Such transformation allows for generalisation of methods requiring strict...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2022-05-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-022-12224-2 |
| _version_ | 1828806805818441728 |
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| author | Miron Bartosz Kursa |
| author_facet | Miron Bartosz Kursa |
| author_sort | Miron Bartosz Kursa |
| collection | DOAJ |
| description | Abstract Kendall transformation is a conversion of an ordered feature into a vector of pairwise order relations between individual values. This way, it preserves ranking of observations and represents it in a categorical form. Such transformation allows for generalisation of methods requiring strictly categorical input, especially in the limit of small number of observations, when quantisation becomes problematic. In particular, many approaches of information theory can be directly applied to Kendall-transformed continuous data without relying on differential entropy or any additional parameters. Moreover, by filtering information to this contained in ranking, Kendall transformation leads to a better robustness at a reasonable cost of dropping sophisticated interactions which are anyhow unlikely to be correctly estimated. In bivariate analysis, Kendall transformation can be related to popular non-parametric methods, showing the soundness of the approach. The paper also demonstrates its efficiency in multivariate problems, as well as provides an example analysis of a real-world data. |
| first_indexed | 2024-12-12T08:15:06Z |
| format | Article |
| id | doaj.art-1dc0940176fb497abb5f22145c24034c |
| institution | Directory Open Access Journal |
| issn | 2045-2322 |
| language | English |
| last_indexed | 2024-12-12T08:15:06Z |
| publishDate | 2022-05-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj.art-1dc0940176fb497abb5f22145c24034c2022-12-22T00:31:37ZengNature PortfolioScientific Reports2045-23222022-05-011211810.1038/s41598-022-12224-2Kendall transformation brings a robust categorical representation of ordinal dataMiron Bartosz Kursa0Interdisciplinary Centre for Mathematical and Computational Modelling, University of WarsawAbstract Kendall transformation is a conversion of an ordered feature into a vector of pairwise order relations between individual values. This way, it preserves ranking of observations and represents it in a categorical form. Such transformation allows for generalisation of methods requiring strictly categorical input, especially in the limit of small number of observations, when quantisation becomes problematic. In particular, many approaches of information theory can be directly applied to Kendall-transformed continuous data without relying on differential entropy or any additional parameters. Moreover, by filtering information to this contained in ranking, Kendall transformation leads to a better robustness at a reasonable cost of dropping sophisticated interactions which are anyhow unlikely to be correctly estimated. In bivariate analysis, Kendall transformation can be related to popular non-parametric methods, showing the soundness of the approach. The paper also demonstrates its efficiency in multivariate problems, as well as provides an example analysis of a real-world data.https://doi.org/10.1038/s41598-022-12224-2 |
| spellingShingle | Miron Bartosz Kursa Kendall transformation brings a robust categorical representation of ordinal data Scientific Reports |
| title | Kendall transformation brings a robust categorical representation of ordinal data |
| title_full | Kendall transformation brings a robust categorical representation of ordinal data |
| title_fullStr | Kendall transformation brings a robust categorical representation of ordinal data |
| title_full_unstemmed | Kendall transformation brings a robust categorical representation of ordinal data |
| title_short | Kendall transformation brings a robust categorical representation of ordinal data |
| title_sort | kendall transformation brings a robust categorical representation of ordinal data |
| url | https://doi.org/10.1038/s41598-022-12224-2 |
| work_keys_str_mv | AT mironbartoszkursa kendalltransformationbringsarobustcategoricalrepresentationofordinaldata |