Tunable equivalence fuzzy associative memories

This paper introduces a new class of fuzzy associative memories (FAMs) called tunable equivalence fuzzy associative memories, for short tunable E-FAMs or TE-FAMs, that are determined by the application of parametrized equivalence measures in the hidden nodes. Tunable E-FAMs belong to the class of ?-FAMs that have recently appeared in the literature. In contrast to previous ?-FAM models, tunable E-FAMs allow for the extraction of a fundamental memory set from the training data by means of an algorithm that depends on the evaluation of equivalence measures. Furthermore, we are able to optimize not only the weights corresponding to the contributions of the hidden nodes but also the contributions of the attributes of the data by tuning the parametrized equivalence measures used in a TE-FAM model. The computational effort involved in training tunable TE-FAMs is very low compared to the one of the previous ?-FAM training algorithm.

[1]  Humberto Bustince,et al.  Restricted equivalence functions , 2006, Fuzzy Sets Syst..

[2]  J. Goguen.  L-fuzzy sets , 1967 .

[3]  Divyendu Sinha,et al.  Fuzzy mathematical morphology , 1992, J. Vis. Commun. Image Represent..

[4]  Peter Sussner,et al.  Fuzzy Associative Memories and Their Relationship to Mathematical Morphology , 2008 .

[5]  Antonio González Muñoz,et al.  Table Ii Tc Pattern Recognition Result for 120 Eir Satellite Image Cases Selection of Relevant Features in a Fuzzy Genetic Learning Algorithm , 2001 .

[6]  Wenyi Zeng,et al.  Inclusion measures, similarity measures, and the fuzziness of fuzzy sets and their relations , 2006, Int. J. Intell. Syst..

[7]  Jesús Alcalá-Fdez,et al.  A Fuzzy Association Rule-Based Classification Model for High-Dimensional Problems With Genetic Rule Selection and Lateral Tuning , 2011, IEEE Transactions on Fuzzy Systems.

[8]  Jesús Alcalá-Fdez,et al.  KEEL Data-Mining Software Tool: Data Set Repository, Integration of Algorithms and Experimental Analysis Framework , 2011, J. Multiple Valued Log. Soft Comput..

[9]  Wynne Hsu,et al.  Integrating Classification and Association Rule Mining , 1998, KDD.

[10]  Athanasios Kehagias,et al.  Fuzzy Inference System (FIS) Extensions Based on the Lattice Theory , 2014, IEEE Transactions on Fuzzy Systems.

[11]  Leo Breiman,et al.  Random Forests , 2001, Machine Learning.

[12]  Edward R. Dougherty,et al.  Design and analysis of fuzzy morphological algorithms for image processing , 1997, IEEE Trans. Fuzzy Syst..

[13]  Jiawei Han,et al.  CPAR: Classification based on Predictive Association Rules , 2003, SDM.

[14]  Mokhtar S. Bazaraa,et al.  Nonlinear Programming: Theory and Algorithms , 1993 .

[15]  Humberto Bustince,et al.  Construction of fuzzy indices from fuzzy DI-subsethood measures: Application to the global comparison of images , 2007, Inf. Sci..

[16]  Thomas F. Coleman,et al.  On the convergence of interior-reflective Newton methods for nonlinear minimization subject to bounds , 1994, Math. Program..

[17]  Siti Zaiton Mohd Hashim,et al.  Memetic multiobjective particle swarm optimization-based radial basis function network for classification problems , 2013, Inf. Sci..

[18]  Henk J. A. M. Heijmans,et al.  The algebraic basis of mathematical morphology. I Dilations and erosions , 1990, Comput. Vis. Graph. Image Process..

[19]  Junior Barrera,et al.  Decomposition of mappings between complete lattices by mathematical morphology, Part I. General lattices , 1993, Signal Process..

[20]  Peter Sussner,et al.  Classification of Fuzzy Mathematical Morphologies Based on Concepts of Inclusion Measure and Duality , 2008, Journal of Mathematical Imaging and Vision.

[21]  Peter Sussner,et al.  A general framework for fuzzy morphological associative memories , 2008, Fuzzy Sets Syst..

[22]  Alexander J. Smola,et al.  Learning with Kernels: support vector machines, regularization, optimization, and beyond , 2001, Adaptive computation and machine learning series.

[23]  Manuel Graña,et al.  Lattice independent component analysis for functional magnetic resonance imaging , 2011, Inf. Sci..

[24]  Peter Sussner,et al.  Fuzzy Associative Memories Based on Subsethood and Similarity Measures with Applications to Speaker Identification , 2012, HAIS.

[25]  Dimitri P. Bertsekas,et al.  Nonlinear Programming , 1997 .

[26]  Korris Fu-Lai Chung,et al.  On fuzzy associative memory with multiple-rule storage capacity , 1996, IEEE Trans. Fuzzy Syst..

[27]  Puyin Liu,et al.  The fuzzy associative memory of max-min fuzzy neural network with threshold , 1999, Fuzzy Sets Syst..

[28]  Wen-Xiu Zhang,et al.  Hybrid monotonic inclusion measure and its use in measuring similarity and distance between fuzzy sets , 2009, Fuzzy Sets Syst..

[29]  Weixin Xie,et al.  Subsethood measure: new definitions , 1999, Fuzzy Sets Syst..

[30]  W. Pedrycz,et al.  Fuzzy Relation Equations and Their Applications to Knowledge Engineering , 1989, Theory and Decision Library.

[31]  Bart Kosko,et al.  Fuzzy associative memories , 1991 .

[32]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[33]  G. Grätzer,et al.  Lattice Theory: First Concepts and Distributive Lattices , 1971 .

[34]  Lluis Godo,et al.  Restoring Consistency in Systems of Fuzzy Gradual Rules Using Similarity Relations , 2002, SBIA.

[35]  Luciano Vieira Dutra,et al.  Classification of Schistosomiasis Prevalence Using Fuzzy Case-Based Reasoning , 2009, IWANN.

[36]  Bing Liu,et al.  Classification Using Association Rules: Weaknesses and Enhancements , 2001 .

[37]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[38]  Humberto Bustince,et al.  Theta-Fuzzy Associative Memories (Theta-FAMs) , 2015, IEEE Transactions on Fuzzy Systems.

[39]  J. A. Leonard,et al.  Radial basis function networks for classifying process faults , 1991, IEEE Control Systems.

[40]  David J. Sheskin,et al.  Handbook of Parametric and Nonparametric Statistical Procedures , 1997 .

[41]  R. Yager,et al.  Fuzzy Set-Theoretic Operators and Quantifiers , 2000 .

[42]  F. Wilcoxon.  Individual Comparisons by Ranking Methods , 1945 .

[43]  George J. Klir,et al.  Fuzzy sets, uncertainty and information , 1988 .

[44]  Richard P. Lippmann,et al.  An introduction to computing with neural nets , 1987 .

[45]  Marc Roubens,et al.  Fuzzy Preference Modelling and Multicriteria Decision Support , 1994, Theory and Decision Library.

[46]  Peter Sussner,et al.  Quantale-based autoassociative memories with an application to the storage of color images , 2013, Pattern Recognit. Lett..

[47]  Thomas F. Coleman,et al.  An Interior Trust Region Approach for Nonlinear Minimization Subject to Bounds , 1993, SIAM J. Optim..

[48]  Sandra A. Sandri,et al.  A method for deriving order compatible fuzzy relations from convex fuzzy partitions , 2014, Fuzzy Sets Syst..

[49]  Christopher M. Bishop,et al.  Neural networks for pattern recognition , 1995 .

[50]  Shi Yan,et al.  A learning rule for fuzzy associative memories , 1994, Proceedings of 1994 IEEE International Conference on Neural Networks (ICNN'94).

[51]  J. Buckley,et al.  Fuzzy neural networks: a survey , 1994 .

[52]  Peter Sussner,et al.  Implicative Fuzzy Associative Memories , 2006, IEEE Transactions on Fuzzy Systems.

[53]  Weixin Xie,et al.  Some notes on similarity measure and proximity measure , 1999, Fuzzy Sets Syst..

[54]  Mohamad H. Hassoun,et al.  A two-level Hamming network for high performance associative memory , 2001, Neural Networks.

[55]  Vladimir Vapnik,et al.  Statistical learning theory , 1998 .

[56]  Eghbal G. Mansoori,et al.  SGERD: A Steady-State Genetic Algorithm for Extracting Fuzzy Classification Rules From Data , 2008, IEEE Transactions on Fuzzy Systems.

[57]  Liu Xuecheng,et al.  Entropy, distance measure and similarity measure of fuzzy sets and their relations , 1992 .

[58]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[59]  Hisao Ishibuchi,et al.  Hybridization of fuzzy GBML approaches for pattern classification problems , 2005, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[60]  J. Ross Quinlan,et al.  C4.5: Programs for Machine Learning , 1992 .

[61]  George A. Papakostas,et al.  Lattice Computing Extension of the FAM Neural Classifier for Human Facial Expression Recognition , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[62]  Max A. Woodbury,et al.  Individualizing user interfaces: application of the Grade of Membership (GoM) model for development of fuzzy user classes , 1994 .

[63]  Etienne E. Kerre,et al.  Interval-Valued and Intuitionistic Fuzzy Mathematical Morphologies as Special Cases of $\mathbb{L}$-Fuzzy Mathematical Morphology , 2012, Journal of Mathematical Imaging and Vision.

[64]  Isabelle Bloch,et al.  Fuzzy mathematical morphologies: A comparative study , 1995, Pattern Recognit..

[65]  George J. Klir,et al.  Fuzzy sets and fuzzy logic - theory and applications , 1995 .

[66]  Bart Kosko,et al.  Neural networks and fuzzy systems: a dynamical systems approach to machine intelligence , 1991 .

[67]  Mohamad H. Hassoun,et al.  A Weighted Voting Model of Associative Memory , 2007, IEEE Transactions on Neural Networks.

[68]  Jian Pei,et al.  CMAR: accurate and efficient classification based on multiple class-association rules , 2001, Proceedings 2001 IEEE International Conference on Data Mining.

[69]  D. Dubois,et al.  Fundamentals of fuzzy sets , 2000 .

[70]  Manuel Graña,et al.  The Kosko Subsethood Fuzzy Associative Memory (KS-FAM): Mathematical Background and Applications in Computer Vision , 2011, Journal of Mathematical Imaging and Vision.

[71]  Etienne E. Kerre,et al.  Connections between binary, gray-scale and fuzzy mathematical morphologies , 2001, Fuzzy Sets Syst..