Analysis of Credal-C4.5 for classification in noisy domains

The robustness of Credal-C4.5 in noisy domains is analyzed. Credal-C4.5 depends on the 's' parameter.The relation between noise level and value of s is studied in terms of accuracy.A large experimental study is carried out varying the values of s.The correct selection of s can improve notably the results for each noise level. Credal Decision Trees (CDTs) are algorithms to design classifiers based on imprecise probabilities and uncertainty based information measures. These algorithms are suitable when noisy data sets are classified. This fact is explained in this paper in terms of the split criterion used in the new procedure of a special type of CDT, called Credal-C4.5. This criterion is more robust to noise than the split criteria of the classic decision trees. On the other hand, all the CDTs depend on a parameter s that has a direct relation with the size of the tree built. The known C4.5 and the Credal-C4.5 procedures are equivalent when the value s = 0 is used. The relation between the value of this parameter s and the capacity of the Credal-C4.5 to classify data sets with label noise is studied. Also, an experimental research is carried out where Credal-C4.5 with different values for s are compared when they classify data sets with distinct label noise levels. From this experimentation we can conclude that, if it is possible to estimate the noise level of a data set, the choice of the correct value for s is a key point in order to obtain notably better results.

[1]  Nenad Koncar,et al.  A note on the Gamma test , 1997, Neural Computing & Applications.

[2]  M. Verleysen,et al.  Classification in the Presence of Label Noise: A Survey , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[3]  George J. Klir,et al.  Disaggregated total uncertainty measure for credal sets , 2006, Int. J. Gen. Syst..

[4]  Andrés R. Masegosa,et al.  Imprecise Classification with Credal Decision Trees , 2012, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[5]  Serafín Moral,et al.  Building classification trees using the total uncertainty criterion , 2003, Int. J. Intell. Syst..

[6]  Joaquín Abellán,et al.  Improving experimental studies about ensembles of classifiers for bankruptcy prediction and credit scoring , 2014, Expert Syst. Appl..

[7]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[8]  อนิรุธ สืบสิงห์,et al.  Data Mining Practical Machine Learning Tools and Techniques , 2014 .

[9]  Jean-Marc Bernard,et al.  An introduction to the imprecise Dirichlet model for multinomial data , 2005, Int. J. Approx. Reason..

[10]  Kurt Weichselberger.  The theory of interval-probability as a unifying concept for uncertainty , 2000, Int. J. Approx. Reason..

[11]  Serafín Moral,et al.  Upper entropy of credal sets. Applications to credal classification , 2005, Int. J. Approx. Reason..

[12]  Joaquín Abellán,et al.  Credal-C4.5: Decision tree based on imprecise probabilities to classify noisy data , 2014, Expert Syst. Appl..

[13]  Andrés R. Masegosa,et al.  A Filter-Wrapper Method to Select Variables for the Naive Bayes Classifier Based on Credal Decision Trees , 2009, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[14]  Janez Demsar,et al.  Statistical Comparisons of Classifiers over Multiple Data Sets , 2006, J. Mach. Learn. Res..

[15]  Andrés R. Masegosa,et al.  Bagging schemes on the presence of class noise in classification , 2012, Expert Syst. Appl..

[16]  Serafín Moral,et al.  An Algorithm to Compute the Upper Entropy for Order-2 Capacities , 2006, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[17]  E. Jaynes.  On the rationale of maximum-entropy methods , 1982, Proceedings of the IEEE.

[18]  Andrés R. Masegosa,et al.  Requirements for total uncertainty measures in Dempster–Shafer theory of evidence , 2008, Int. J. Gen. Syst..

[19]  Khaled Mellouli,et al.  Belief decision trees: theoretical foundations , 2001, Int. J. Approx. Reason..

[20]  Joaquín Abellán,et al.  Analysis and extension of decision trees based on imprecise probabilities: Application on noisy data , 2014, Expert Syst. Appl..

[21]  J. Ross Quinlan,et al.  Induction of Decision Trees , 1986, Machine Learning.

[22]  María José del Jesús,et al.  KEEL: a software tool to assess evolutionary algorithms for data mining problems , 2008, Soft Comput..

[23]  Joaquín Abellán,et al.  Uncertainty measures on probability intervals from the imprecise Dirichlet model , 2006, Int. J. Gen. Syst..

[24]  P. Walley.  Inferences from Multinomial Data: Learning About a Bag of Marbles , 1996 .

[25]  Andrés R. Masegosa,et al.  An Experimental Study about Simple Decision Trees for Bagging Ensemble on Datasets with Classification Noise , 2009, ECSQARU.

[26]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[27]  Yan Wang.  Imprecise Probabilities based on Generalized Intervals , 2008 .

[28]  M. Friedman.  A Comparison of Alternative Tests of Significance for the Problem of $m$ Rankings , 1940 .

[29]  M. Friedman.  The Use of Ranks to Avoid the Assumption of Normality Implicit in the Analysis of Variance , 1937 .

[30]  Marco Zaffalon.  The naive credal classifier , 2002 .