A taxonomy of monotonicity properties for the aggregation of multidimensional data
- Author
- Raul Perez Fernandez (UGent) , Bernard De Baets (UGent) and Marek Gagolewski
- Organization
- Abstract
- The property of monotonicity, which requires a function to preserve a given order, has been considered the standard in the aggregation of real numbers for decades. In this paper, we argue that, for the case of multidimensional data, an order-based definition of monotonicity is far too restrictive. We propose several meaningful alternatives to this property not involving the preservation of a given order by returning to its early origins stemming from the field of calculus. Numerous aggregation methods for multidimensional data commonly used by practitioners are studied within our new framework.
- Keywords
- Monotonicity, Aggregation, Multidimensional data, Centroid, Spatial median, WEAK MONOTONICITY, ORTHOGONALIZATION
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8626846
- MLA
- Perez Fernandez, Raul, et al. “A Taxonomy of Monotonicity Properties for the Aggregation of Multidimensional Data.” INFORMATION FUSION, vol. 52, 2019, pp. 322–34, doi:10.1016/j.inffus.2019.05.006.
- APA
- Perez Fernandez, R., De Baets, B., & Gagolewski, M. (2019). A taxonomy of monotonicity properties for the aggregation of multidimensional data. INFORMATION FUSION, 52, 322–334. https://doi.org/10.1016/j.inffus.2019.05.006
- Chicago author-date
- Perez Fernandez, Raul, Bernard De Baets, and Marek Gagolewski. 2019. “A Taxonomy of Monotonicity Properties for the Aggregation of Multidimensional Data.” INFORMATION FUSION 52: 322–34. https://doi.org/10.1016/j.inffus.2019.05.006.
- Chicago author-date (all authors)
- Perez Fernandez, Raul, Bernard De Baets, and Marek Gagolewski. 2019. “A Taxonomy of Monotonicity Properties for the Aggregation of Multidimensional Data.” INFORMATION FUSION 52: 322–334. doi:10.1016/j.inffus.2019.05.006.
- Vancouver
- 1.Perez Fernandez R, De Baets B, Gagolewski M. A taxonomy of monotonicity properties for the aggregation of multidimensional data. INFORMATION FUSION. 2019;52:322–34.
- IEEE
- [1]R. Perez Fernandez, B. De Baets, and M. Gagolewski, “A taxonomy of monotonicity properties for the aggregation of multidimensional data,” INFORMATION FUSION, vol. 52, pp. 322–334, 2019.
@article{8626846,
abstract = {{The property of monotonicity, which requires a function to preserve a given order, has been considered the standard in the aggregation of real numbers for decades. In this paper, we argue that, for the case of multidimensional data, an order-based definition of monotonicity is far too restrictive. We propose several meaningful alternatives to this property not involving the preservation of a given order by returning to its early origins stemming from the field of calculus. Numerous aggregation methods for multidimensional data commonly used by practitioners are studied within our new framework.}},
author = {{Perez Fernandez, Raul and De Baets, Bernard and Gagolewski, Marek}},
issn = {{1566-2535}},
journal = {{INFORMATION FUSION}},
keywords = {{Monotonicity,Aggregation,Multidimensional data,Centroid,Spatial median,WEAK MONOTONICITY,ORTHOGONALIZATION}},
language = {{eng}},
pages = {{322--334}},
title = {{A taxonomy of monotonicity properties for the aggregation of multidimensional data}},
url = {{http://doi.org/10.1016/j.inffus.2019.05.006}},
volume = {{52}},
year = {{2019}},
}
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