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Fitting aggregation functions to data: part I-linearization and regularization

Bartoszuk, Maciej, Beliakov, Gleb, Gagolewski, Marek and James, Simon 2016, Fitting aggregation functions to data: part I-linearization and regularization. In Carvalho, Joao Paulo, Lesot, Marie-Jeanne, Kaymak, Uzay, Vieira, Susana, Bouchon-Meunier, Bernadette and Yager, Ronald R. (ed), Information processing and management of uncertainty in knowledge-based systems, Springer, Berlin, Germany, pp.767-779, doi: 10.1007/978-3-319-40581-0_62.

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Title Fitting aggregation functions to data: part I-linearization and regularization
Author(s) Bartoszuk, Maciej
Beliakov, GlebORCID iD for Beliakov, Gleb
Gagolewski, Marek
James, SimonORCID iD for James, Simon
Title of book Information processing and management of uncertainty in knowledge-based systems
Editor(s) Carvalho, Joao Paulo
Lesot, Marie-Jeanne
Kaymak, Uzay
Vieira, Susana
Bouchon-Meunier, Bernadette
Yager, Ronald R.
Publication date 2016
Series Communications in computer and information science
Chapter number 62
Total chapters 67
Start page 767
End page 779
Total pages 12
Publisher Springer
Place of Publication Berlin, Germany
Keyword(s) aggregation functions
weighted quasi-arithmetic means
least squares fitting
Summary The use of supervised learning techniques for fitting weights and/or generator functions of weighted quasi-arithmetic means – a special class of idempotent and nondecreasing aggregation functions – to empirical data has already been considered in a number of papers. Nevertheless, there are still some important issues that have not been discussed in the literature yet. In the first part of this two-part contribution we deal with the concept of regularization, a quite standard technique from machine learning applied so as to increase the fit quality on test and validation data samples. Due to the constraints on the weighting vector, it turns out that quite different methods can be used in the current framework, as compared to regression models. Moreover, it is worth noting that so far fitting weighted quasi-arithmetic means to empirical data has only been performed approximately, via the so-called linearization technique. In this paper we consider exact solutions to such special optimization tasks and indicate cases where linearization leads to much worse solutions.
Notes This publication is part II of the 16th IPMU International Conference held on 20-24 June 2016, Eindhoven, The Netherlands.
ISBN 9783319405803
ISSN 1865-0929
Language eng
DOI 10.1007/978-3-319-40581-0_62
Field of Research 080109 Pattern Recognition and Data Mining
Socio Economic Objective 970108 Expanding Knowledge in the Information and Computing Sciences
HERDC Research category B1 Book chapter
ERA Research output type B Book chapter
Copyright notice ©2016, Springer
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Document type: Book Chapter
Collection: School of Information Technology
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