Fitting aggregation functions to data: Part I-Linearization and regularization

Maciej Bartoszuk , Gleb Beliakov , Marek Gągolewski , Simon James

Abstract

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.
Author Maciej Bartoszuk (FMIS / DAICM)
Maciej Bartoszuk,,
- Department of Artificial Intelligence and Computational Methods
, Gleb Beliakov - [Deakin University]
Gleb Beliakov,,
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, Marek Gągolewski (FMIS / DIE) - [Systems Research Institute (IBS PAN) [Polska Akademia Nauk (PAN)]]
Marek Gągolewski,,
- Department of Integral Equations
- Instytucie Badań Systemowych
, Simon James - [Deakin University]
Simon James,,
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Pages767-779
Publication size in sheets0.6
Book Carvalho Joao Paulo, Lesot Marie-Jeanne, Kaymak Uzay, Vieira Susana, Bouchon-Meunier Bernadette, Yager Ronald R. (eds.): INFORMATION PROCESSING AND MANAGEMENT OF UNCERTAINTY IN KNOWLEDGE-BASED SYSTEMS, IPMU 2016, PT II, Communications in Computer and Information Science, vol. 611, 2016, SPRINGER INT PUBLISHING AG, ISBN 978-3-319-40581-0, [ 978-3-319-40580-3]
Keywords in EnglishAggregation functions; Weighted quasi-arithmetic means; Least squares fitting; Regularization; Linearization
ASJC Classification2600 General Mathematics; 1700 General Computer Science
DOIDOI:10.1007/978-3-319-40581-0_62
URL https://link.springer.com/chapter/10.1007/978-3-319-40581-0_62
Languageen angielski
Score (nominal)15
ScoreMinisterial score = 15.0, 04-09-2019, BookChapterSeriesAndMatConfByConferenceseries
Ministerial score (2013-2016) = 15.0, 04-09-2019, BookChapterSeriesAndMatConfByConferenceseries
Publication indicators Scopus Citations = 4; Scopus SNIP (Source Normalised Impact per Paper): 2016 = 0.317
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