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Erschienen in: Soft Computing 3/2016

14.12.2014 | Methodologies and Application

Modelling and predicting partial orders from pairwise belief functions

verfasst von: Marie-Hélène Masson, Sébastien Destercke, Thierry Denoeux

Erschienen in: Soft Computing | Ausgabe 3/2016

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Abstract

In this paper, we introduce a generic way to represent and manipulate pairwise information about partial orders (representing rankings, preferences, ...) with belief functions. We provide generic and practical tools to make inferences from this pairwise information and illustrate their use on the machine learning problems that are label ranking and multi-label prediction. Our approach differs from most other quantitative approaches handling complete or partial orders, in the sense that partial orders are here considered as primary objects and not as incomplete specifications of ideal but unknown complete orders.

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Fußnoten
1
\((\lambda _i, \lambda _j),(\lambda _j,\lambda _k) \in R \Rightarrow (\lambda _i,\lambda _k) \in R\).
 
3
The software can be downloaded from https://​www.​hds.​utc.​fr/​~tdenoeux/​.
 
Literatur
Zurück zum Zitat Blockeel H, Raedt LD, Ramon J (1998) Top-down induction of clustering trees. Proceedings of the 15th international conference on machine learning. Morgan Kaufmann Publishers Inc., San Francisco, pp 55–63 Blockeel H, Raedt LD, Ramon J (1998) Top-down induction of clustering trees. Proceedings of the 15th international conference on machine learning. Morgan Kaufmann Publishers Inc., San Francisco, pp 55–63
Zurück zum Zitat Boutell MR, Luo J, Shen X, Brown CM (2004) Learning multi-label scene classification. Pattern Recogn 37(9):1757–1771CrossRef Boutell MR, Luo J, Shen X, Brown CM (2004) Learning multi-label scene classification. Pattern Recogn 37(9):1757–1771CrossRef
Zurück zum Zitat Boutilier C, Brafman RI, Domshlak C, Hoos HH, Poole D (2004) CP-nets: a tool for representing and reasoning with conditional ceteris paribus preference statements. J Artif Intell Res (JAIR) 21:135–191MathSciNetMATH Boutilier C, Brafman RI, Domshlak C, Hoos HH, Poole D (2004) CP-nets: a tool for representing and reasoning with conditional ceteris paribus preference statements. J Artif Intell Res (JAIR) 21:135–191MathSciNetMATH
Zurück zum Zitat Cheng W, Rademaker M, De Baets B, Hüllermeier E (2010) Predicting partial orders: ranking with abstention. Machine learning and knowledge discovery in databases. Springer, Berlin, Heidelberg, pp 215–230CrossRef Cheng W, Rademaker M, De Baets B, Hüllermeier E (2010) Predicting partial orders: ranking with abstention. Machine learning and knowledge discovery in databases. Springer, Berlin, Heidelberg, pp 215–230CrossRef
Zurück zum Zitat Cheng W, Waegeman W, Welker V, Hüllermeier E (2012) Label ranking with partial abstention based on thresholded probabilistic models. In: Advances in neural information processing systems, pp 2510–2518. Cheng W, Waegeman W, Welker V, Hüllermeier E (2012) Label ranking with partial abstention based on thresholded probabilistic models. In: Advances in neural information processing systems, pp 2510–2518.
Zurück zum Zitat Chow C (1970) On optimum recognition error and reject tradeoff. IEEE Trans Inf Theory 16(1):41–46CrossRefMATH Chow C (1970) On optimum recognition error and reject tradeoff. IEEE Trans Inf Theory 16(1):41–46CrossRefMATH
Zurück zum Zitat Clare A, King RD (2001) Knowledge discovery in multi-label phenotype data. Principles of data mining and knowledge discovery. Springer, New York, pp 42–53CrossRef Clare A, King RD (2001) Knowledge discovery in multi-label phenotype data. Principles of data mining and knowledge discovery. Springer, New York, pp 42–53CrossRef
Zurück zum Zitat Cobb BR, Shenoy PP (2006) On the plausibility transformation method for translating belief function models to probability models. Int J Approx Reason 41(3):314–330CrossRefMathSciNetMATH Cobb BR, Shenoy PP (2006) On the plausibility transformation method for translating belief function models to probability models. Int J Approx Reason 41(3):314–330CrossRefMathSciNetMATH
Zurück zum Zitat Dekel O, Singer Y, Manning CD (2003) Log-linear models for label ranking. In: Advances in neural information processing systems, pp 497–504. Dekel O, Singer Y, Manning CD (2003) Log-linear models for label ranking. In: Advances in neural information processing systems, pp 497–504.
Zurück zum Zitat Denœux T (1995) A k-nearest neighbor classification rule based on Dempster-Shafer theory. IEEE Trans Syst Man Cybern 25(5):804–813CrossRef Denœux T (1995) A k-nearest neighbor classification rule based on Dempster-Shafer theory. IEEE Trans Syst Man Cybern 25(5):804–813CrossRef
Zurück zum Zitat Destercke S (2013) A pairwise label ranking method with imprecise scores and partial predictions. Machine learning and knowledge discovery in databases. Springer, New York, pp 112–127CrossRef Destercke S (2013) A pairwise label ranking method with imprecise scores and partial predictions. Machine learning and knowledge discovery in databases. Springer, New York, pp 112–127CrossRef
Zurück zum Zitat El Zoghby N, Cherfaoui V, Denœux T (2013) Optimal object association from pairwise evidential mass functions. 16th international conference on information fusion (FUSION). IEEE, New York, pp 774–780 El Zoghby N, Cherfaoui V, Denœux T (2013) Optimal object association from pairwise evidential mass functions. 16th international conference on information fusion (FUSION). IEEE, New York, pp 774–780
Zurück zum Zitat Elisseeff A, Weston J (2001) A kernel method for multi-labelled classification. In: Advances in neural information processing systems, pp 681–687. Elisseeff A, Weston J (2001) A kernel method for multi-labelled classification. In: Advances in neural information processing systems, pp 681–687.
Zurück zum Zitat Fürnkranz J, Hüllermeier E (2010) Preference learning. Springer, New YorkMATH Fürnkranz J, Hüllermeier E (2010) Preference learning. Springer, New YorkMATH
Zurück zum Zitat Fürnkranz J, Hüllermeier E, Mencía EL, Brinker K (2008) Multilabel classification via calibrated label ranking. Mach Learn 73(2):133–153CrossRef Fürnkranz J, Hüllermeier E, Mencía EL, Brinker K (2008) Multilabel classification via calibrated label ranking. Mach Learn 73(2):133–153CrossRef
Zurück zum Zitat Grabisch M, Labreuche C (2008) A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid. 4OR 6(1):1–44. Grabisch M, Labreuche C (2008) A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid. 4OR 6(1):1–44.
Zurück zum Zitat Greco S, Kadziński M, SŁowiński R (2011) Selection of a representative value function in robust multiple criteria sorting. Comput Oper Res 38(11):1620–1637CrossRefMathSciNetMATH Greco S, Kadziński M, SŁowiński R (2011) Selection of a representative value function in robust multiple criteria sorting. Comput Oper Res 38(11):1620–1637CrossRefMathSciNetMATH
Zurück zum Zitat Har-Peled S, Roth D, Zimak D (2003) Constraint classification for multiclass classification and ranking. Adv Neural Inf Process Syst 809–816. Har-Peled S, Roth D, Zimak D (2003) Constraint classification for multiclass classification and ranking. Adv Neural Inf Process Syst 809–816.
Zurück zum Zitat Hüllermeier E, Furnkranz J, Cheng W, Brinker K (2008) Label ranking by learning pairwise preferences. Artif Intell 172(16–17):1897–1916CrossRefMATH Hüllermeier E, Furnkranz J, Cheng W, Brinker K (2008) Label ranking by learning pairwise preferences. Artif Intell 172(16–17):1897–1916CrossRefMATH
Zurück zum Zitat Kamishima T, Kazawa H, Akaho S (2011) A survey and empirical comparison of object ranking methods. Preference learning. Springer, New York, pp 181–201 Kamishima T, Kazawa H, Akaho S (2011) A survey and empirical comparison of object ranking methods. Preference learning. Springer, New York, pp 181–201
Zurück zum Zitat Kocev D, Vens C, Struyf J, Džeroski S (2007) Ensembles of multi-objective decision trees. Mach Learn ECML 2007:624–631 Kocev D, Vens C, Struyf J, Džeroski S (2007) Ensembles of multi-objective decision trees. Mach Learn ECML 2007:624–631
Zurück zum Zitat Labreuche C (2010) On the robustness for the Choquet integral. Computational intelligence for knowledge-based systems design. Springer, New York, pp 484–493CrossRef Labreuche C (2010) On the robustness for the Choquet integral. Computational intelligence for knowledge-based systems design. Springer, New York, pp 484–493CrossRef
Zurück zum Zitat Li T, Ogihara M (2006) Toward intelligent music information retrieval. IEEE Trans Multimed 8(3):564–574CrossRef Li T, Ogihara M (2006) Toward intelligent music information retrieval. IEEE Trans Multimed 8(3):564–574CrossRef
Zurück zum Zitat Loza Mencía E, Park S-H, Fürnkranz J (2010) Efficient voting prediction for pairwise multilabel classification. Neurocomputing 73(7):1164–1176CrossRef Loza Mencía E, Park S-H, Fürnkranz J (2010) Efficient voting prediction for pairwise multilabel classification. Neurocomputing 73(7):1164–1176CrossRef
Zurück zum Zitat Madjarov G, Kocev D, Gjorgjevikj D, Džeroski S (2012) An extensive experimental comparison of methods for multi-label learning. Pattern Recogn 45(9):3084–3104CrossRef Madjarov G, Kocev D, Gjorgjevikj D, Džeroski S (2012) An extensive experimental comparison of methods for multi-label learning. Pattern Recogn 45(9):3084–3104CrossRef
Zurück zum Zitat Marden JI (1995) Analyzing and modeling rank data, vol 64. Chapman & Hall, LondonMATH Marden JI (1995) Analyzing and modeling rank data, vol 64. Chapman & Hall, LondonMATH
Zurück zum Zitat Rademaker M, De Baets B (2010) A threshold for majority in the context of aggregating partial order relations. 2010 IEEE international conference on fuzzy systems (FUZZ). IEEE, New York, pp 1–4 Rademaker M, De Baets B (2010) A threshold for majority in the context of aggregating partial order relations. 2010 IEEE international conference on fuzzy systems (FUZZ). IEEE, New York, pp 1–4
Zurück zum Zitat Read J, Pfahringer B, Holmes G, Frank E (2011) Classifier chains for multi-label classification. Mach Learn 85(3):333–359CrossRefMathSciNet Read J, Pfahringer B, Holmes G, Frank E (2011) Classifier chains for multi-label classification. Mach Learn 85(3):333–359CrossRefMathSciNet
Zurück zum Zitat Shafer G (1976) A mathematical theory of evidence. Princeton University Press, New JerseyMATH Shafer G (1976) A mathematical theory of evidence. Princeton University Press, New JerseyMATH
Zurück zum Zitat Smets P (1993) Belief functions: the disjunctive rule of combination and the generalized Bayesian theorem. Int J Approx Reason 9(1):1–35CrossRefMathSciNetMATH Smets P (1993) Belief functions: the disjunctive rule of combination and the generalized Bayesian theorem. Int J Approx Reason 9(1):1–35CrossRefMathSciNetMATH
Zurück zum Zitat Tsoumakas G, Katakis I (2007) Multi-label classification: an overview. Int J Data Wareh Min (IJDWM) 3(3):1–13CrossRef Tsoumakas G, Katakis I (2007) Multi-label classification: an overview. Int J Data Wareh Min (IJDWM) 3(3):1–13CrossRef
Zurück zum Zitat Tsoumakas G, Katakis I, Vlahavas I (2008) Effective and efficient multilabel classification in domains with large number of labels. In: Proceedings of the ECML/PKDD 2008 workshop on mining multidimensional data (MMD08), pp 30–44. Tsoumakas G, Katakis I, Vlahavas I (2008) Effective and efficient multilabel classification in domains with large number of labels. In: Proceedings of the ECML/PKDD 2008 workshop on mining multidimensional data (MMD08), pp 30–44.
Zurück zum Zitat Tsoumakas G, Katakis I, Vlahavas I (2010) Mining multi-label data. Data mining and knowledge discovery handbook. Springer, New York, pp 667–685 Tsoumakas G, Katakis I, Vlahavas I (2010) Mining multi-label data. Data mining and knowledge discovery handbook. Springer, New York, pp 667–685
Zurück zum Zitat Tsoumakas G, Vlahavas I (2007) Random k-labelsets: an ensemble method for multilabel classification. Machine learning: ECML 2007. Springer, New York, pp 406–417CrossRef Tsoumakas G, Vlahavas I (2007) Random k-labelsets: an ensemble method for multilabel classification. Machine learning: ECML 2007. Springer, New York, pp 406–417CrossRef
Zurück zum Zitat Ueda N, Saito K (2002) Parametric mixture models for multi-labeled text. In: Advances in neural information processing systems, pp 721–728. Ueda N, Saito K (2002) Parametric mixture models for multi-labeled text. In: Advances in neural information processing systems, pp 721–728.
Zurück zum Zitat Utkin LV (2009) A new ranking procedure by incomplete pairwise comparisons using preference subsets. Intell Data Anal 13(2):229–241MathSciNet Utkin LV (2009) A new ranking procedure by incomplete pairwise comparisons using preference subsets. Intell Data Anal 13(2):229–241MathSciNet
Zurück zum Zitat Vembu S, Gärtner T (2011) Label ranking algorithms: a survey. In: Preference learning, pp 45–64. Springer, New York. Vembu S, Gärtner T (2011) Label ranking algorithms: a survey. In: Preference learning, pp 45–64. Springer, New York.
Zurück zum Zitat Zhang M-L, Zhou Z-H (2007) ML-KNN: a lazy learning approach to multi-label learning. Pattern Recogn 40(7):2038–2048CrossRefMATH Zhang M-L, Zhou Z-H (2007) ML-KNN: a lazy learning approach to multi-label learning. Pattern Recogn 40(7):2038–2048CrossRefMATH
Metadaten
Titel
Modelling and predicting partial orders from pairwise belief functions
verfasst von
Marie-Hélène Masson
Sébastien Destercke
Thierry Denoeux
Publikationsdatum
14.12.2014
Verlag
Springer Berlin Heidelberg
Erschienen in
Soft Computing / Ausgabe 3/2016
Print ISSN: 1432-7643
Elektronische ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-014-1553-9

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