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Optimal monotone relabelling of partially non-monotone ordinal data

Michaël Rademaker (UGent) , Bernard De Baets (UGent) and Hans De Meyer (UGent)
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Abstract
Noise in multi-criteria data sets can manifest itself as non-monotonicity. Work on the remediation of such non-monotonicity is rather scarce. Nevertheless, errors are often present in real-life data sets, and several monotone classification algorithms are unable to use such partially non-monotone data sets. Fortunately, as we will show here, it is possible to restore monotonicity in an optimal way, by relabelling part of the data set. By exploiting the properties of a (minimum) flow network, and identifying pleasing properties of some maximum cuts, an elegant single-pass optimal ordinal relabelling algorithm is formulated.
Keywords
monotonicity, ordinal data, monotone relabelling, flow network, maximum independent set, maximum cut, AGGREGATION OPERATORS, RANKING, SETS

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Please use this url to cite or link to this publication:

MLA
Rademaker, Michaël, Bernard De Baets, and Hans De Meyer. “Optimal Monotone Relabelling of Partially Non-monotone Ordinal Data.” OPTIMIZATION METHODS & SOFTWARE 27.1 (2012): 17–31. Print.
APA
Rademaker, M., De Baets, B., & De Meyer, H. (2012). Optimal monotone relabelling of partially non-monotone ordinal data. OPTIMIZATION METHODS & SOFTWARE, 27(1), 17–31.
Chicago author-date
Rademaker, Michaël, Bernard De Baets, and Hans De Meyer. 2012. “Optimal Monotone Relabelling of Partially Non-monotone Ordinal Data.” Optimization Methods & Software 27 (1): 17–31.
Chicago author-date (all authors)
Rademaker, Michaël, Bernard De Baets, and Hans De Meyer. 2012. “Optimal Monotone Relabelling of Partially Non-monotone Ordinal Data.” Optimization Methods & Software 27 (1): 17–31.
Vancouver
1.
Rademaker M, De Baets B, De Meyer H. Optimal monotone relabelling of partially non-monotone ordinal data. OPTIMIZATION METHODS & SOFTWARE. 2012;27(1):17–31.
IEEE
[1]
M. Rademaker, B. De Baets, and H. De Meyer, “Optimal monotone relabelling of partially non-monotone ordinal data,” OPTIMIZATION METHODS & SOFTWARE, vol. 27, no. 1, pp. 17–31, 2012.
@article{2918678,
  abstract     = {Noise in multi-criteria data sets can manifest itself as non-monotonicity. Work on the remediation of such non-monotonicity is rather scarce. Nevertheless, errors are often present in real-life data sets, and several monotone classification algorithms are unable to use such partially non-monotone data sets. Fortunately, as we will show here, it is possible to restore monotonicity in an optimal way, by relabelling part of the data set. By exploiting the properties of a (minimum) flow network, and identifying pleasing properties of some maximum cuts, an elegant single-pass optimal ordinal relabelling algorithm is formulated.},
  author       = {Rademaker, Michaël and De Baets, Bernard and De Meyer, Hans},
  issn         = {1055-6788},
  journal      = {OPTIMIZATION METHODS & SOFTWARE},
  keywords     = {monotonicity,ordinal data,monotone relabelling,flow network,maximum independent set,maximum cut,AGGREGATION OPERATORS,RANKING,SETS},
  language     = {eng},
  number       = {1},
  pages        = {17--31},
  title        = {Optimal monotone relabelling of partially non-monotone ordinal data},
  url          = {http://dx.doi.org/10.1080/10556788.2010.507272},
  volume       = {27},
  year         = {2012},
}

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