A New Classifier Based on the Dual Indiscernibility Matrix

A new approach to classifier synthesis was proposed by Polkowski and in this work we propose an implementation of this idea. The idea is based on usage of a dual indiscernibility matrix which allows to determine for each test object in the data, pairs of training objects which cover in a sense the given test object. A family of pairs best covering the given object pass their decisions for majority voting on decision for the test object. We present results obtained by our classifier on standard data from UCI Repository and compare them with results obtained by means of k-NN and Bayes classifiers. The results are validated by multiple cross-validation. We find our classifier on par with k-NN and Bayes classifiers.

[1]  Krzysztof Sopyla,et al.  Different Orderings and Visual Sequence Alignment Algorithms for Image Classification , 2014, ICAISC.

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

[3]  Andrzej Skowron,et al.  Boolean Reasoning for Decision Rules Generation , 1993, ISMIS.

[4]  Marcin Zalasinski,et al.  New Algorithm for On-line Signature Verification Using Characteristic Hybrid Partitions , 2015, ISAT.

[5]  中澤 真,et al.  Devroye, L., Gyorfi, L. and Lugosi, G. : A Probabilistic Theory of Pattern Recognition, Springer (1996). , 1997 .

[6]  Marcin Korytkowski,et al.  AdaBoost Ensemble of DCOG Rough-Neuro-Fuzzy Systems , 2011, ICCCI.

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

[8]  Lech Polkowski,et al.  Granular Computing in Decision Approximation - An Application of Rough Mereology , 2015, Intelligent Systems Reference Library.

[9]  L. Polkowski Rough Sets: Mathematical Foundations , 2013 .

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

[11]  Jerzy W. Grzymala-Busse,et al.  LERS-A System for Learning from Examples Based on Rough Sets , 1992, Intelligent Decision Support.

[12]  Andrzej Skowron,et al.  The Discernibility Matrices and Functions in Information Systems , 1992, Intelligent Decision Support.

[13]  Zdzislaw Pawlak,et al.  An Inquiry into Anatomy of Conflicts , 1998, Inf. Sci..

[14]  Marcin Gabryel,et al.  Modified Merge Sort Algorithm for Large Scale Data Sets , 2013, ICAISC.

[15]  László Györfi,et al.  A Probabilistic Theory of Pattern Recognition , 1996, Stochastic Modelling and Applied Probability.

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

[17]  Janusz T. Starczewski,et al.  Genetic fuzzy classifier with fuzzy rough sets for imprecise data , 2014, 2014 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE).

[18]  Christian Napoli,et al.  Multi-class Nearest Neighbour Classifier for Incomplete Data Handling , 2015, ICAISC.