The Boosting and Bootstrap Ensembles for the Pair Classifier Based on the Dual Indiscernibility Matrix

In search for subsets of data sets relevant in the classification of data tasks, we have exploited the betweenness relation adopted from axiomatic elementary geometry. It has turned out that this relation can partition data into two subsets, one of them dense in the sense that each object in this set is a convex combination of a finite number of objects in it, the other, to the contrary, consisting of objects endowed with outliers, i.e., pairs of (attribute, value) not possessed by any other object. A technical tool for singling out those subsets is the Dual Indiscernibility Matrix defined as a counterpart to a well-known Discernibility Matrix of Skowron-Rauszer. On the basis of those ideas, the pair Classifier has been introduced. It is its main feature that test objects are approximated to a certain degree by pairs of training objects which are not required to cover the object completely. In this chapter, we examine selected methods for stabilization of the Pair Classifier like Bootstrap Ensemble, Arcing based Bootstrap, Ada–Boost with Monte Carlo split. We present results of experiments with some standard data sets. Consecutive sections are dedicated to basics of the method: Dual Indiscernibility Matrix, Kernel and residuum in data sets, Pair Classifier, Experiments, Discussion of results, Conclusion and Perspectives.

[1]  Z. Pawlak.  Rough Sets: Theoretical Aspects of Reasoning about Data , 1991 .

[2]  Piotr Artiemjew,et al.  A New Classifier Based on the Dual Indiscernibility Matrix , 2016, ICIST.

[3]  L. Breiman.  Arcing classifier (with discussion and a rejoinder by the author) , 1998 .

[4]  Jerzy W. Grzymala-Busse,et al.  Rough Sets , 1995, Commun. ACM.

[5]  G. Leibniz,et al.  Philosophical papers and letters. , 2011 .

[6]  Robert E. Schapire,et al.  The Boosting Approach to Machine Learning An Overview , 2003 .

[7]  Leo Breiman,et al.  Bagging Predictors , 1996, Machine Learning.

[8]  Bartosz A. Nowak,et al.  Betweenness, Łukasiewicz Rough Inclusions, Euclidean Representations in Information Systems, Hyper-granules and Conflict Resolution , 2016, Fundam. Informaticae.

[9]  Zhi-Hua Zhou,et al.  Ensemble Methods: Foundations and Algorithms , 2012 .

[10]  Yoav Freund,et al.  A Short Introduction to Boosting , 1999 .

[11]  Johan van Benthem,et al.  The Logic of Time , 1983 .

[12]  Yoav Freund,et al.  A decision-theoretic generalization of on-line learning and an application to boosting , 1997, EuroCOLT.

[13]  Robert E. Schapire,et al.  Using output codes to boost multiclass learning problems , 1997, ICML.

[14]  Lech Polkowski,et al.  Mereology in Engineering and Computer Science , 2014 .

[15]  Alfred Tarski,et al.  Tarski's System of Geometry , 1999, Bulletin of Symbolic Logic.

[16]  Lech Polkowski,et al.  Approximate Reasoning by Parts - An Introduction to Rough Mereology , 2011, Intelligent Systems Reference Library.

[17]  Yoav Freund,et al.  Experiments with a New Boosting Algorithm , 1996, ICML.

[18]  P. Kleingeld,et al.  The Stanford Encyclopedia of Philosophy , 2013 .

[19]  Andrzej Skowron,et al.  Rough mereology: A new paradigm for approximate reasoning , 1996, Int. J. Approx. Reason..

[20]  Andrzej Skowron,et al.  Rough Mereology , 1994, ISMIS.