On the weak monotonicity of Gini means and other mixture functions

Weak monotonicity was recently proposed as a relaxation of the monotonicity condition for averaging aggregation, and weakly monotone functions were shown to have desirable properties when averaging data corrupted with outliers or noise. We extended the study of weakly monotone averages by analyzing...

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Bibliographic Details
Published in:Information sciences 2015-04, Vol.300, p.70-84
Main Authors: Beliakov, Gleb, Calvo, Tomasa, Wilkin, Tim
Format: Article
Language:English
Subjects:
Agglomeration
Aggregation function
Data processing
Gaussian
Gini mean
Image processing
Mean
Mixture function
Monotone functions
Monotonicity
Operators
Penalty-based function
Tasks
Weighting functions
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Summary:Weak monotonicity was recently proposed as a relaxation of the monotonicity condition for averaging aggregation, and weakly monotone functions were shown to have desirable properties when averaging data corrupted with outliers or noise. We extended the study of weakly monotone averages by analyzing their ϕ-transforms, and we established weak monotonicity of several classes of averaging functions, in particular Gini means and mixture operators. Mixture operators with Gaussian weighting functions were shown to be weakly monotone for a broad range of their parameters. This study assists in identifying averaging functions suitable for data analysis and image processing tasks in the presence of outliers.
ISSN:0020-0255
1872-6291
DOI:10.1016/j.ins.2014.12.030