Fuzzy regularized generalized eigenvalue classifier with a novel membership function

Supervised classification of data affected by noise or error, with unknown probability distribution, is a challenging task. To this extend, we propose the Fuzzy Regularized Eigenvalue Classifier, based on a recent technique to classify data in two or more classes. We compare the execution time and accuracy of the classifier with other de facto standard methods. With the adoption of a novel membership function, the classifier is capable to produce more accurate models that well compare with results obtained by other methods, and fuzzy weighting functions, on benchmark datasets.

[1]  Panos M. Pardalos,et al.  A classification method based on generalized eigenvalue problems , 2007, Optim. Methods Softw..

[2]  J. MacQueen.  Some methods for classification and analysis of multivariate observations , 1967 .

[3]  Jiun-Hung Chen,et al.  Fuzzy kernel perceptron , 2002, IEEE Trans. Neural Networks.

[4]  Olvi L. Mangasarian,et al.  Multisurface proximal support vector machine classification via generalized eigenvalues , 2006, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[5]  Yi Lin,et al.  Support Vector Machines for Classification in Nonstandard Situations , 2002, Machine Learning.

[6]  Nikos A. Vlassis,et al.  The global k-means clustering algorithm , 2003, Pattern Recognit..

[7]  Reshma Khemchandani,et al.  Twin Support Vector Machines for Pattern Classification , 2007, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[8]  Panos M. Pardalos,et al.  Robust generalized eigenvalue classifier with ellipsoidal uncertainty , 2014, Ann. Oper. Res..

[9]  Mario Rosario Guarracino,et al.  Multiclass Generalized Eigenvalue Proximal Support Vector Machines , 2010, 2010 International Conference on Complex, Intelligent and Software Intensive Systems.

[10]  O. Mangasarian.  Linear and Nonlinear Separation of Patterns by Linear Programming , 1965 .

[11]  Trevor Hastie,et al.  Regularized linear discriminant analysis and its application in microarrays. , 2007, Biostatistics.

[12]  T. Mexia,et al.  Author ' s personal copy , 2009 .

[13]  Pat Langley,et al.  Estimating Continuous Distributions in Bayesian Classifiers , 1995, UAI.

[14]  Sheng-De Wang,et al.  Fuzzy support vector machines , 2002, IEEE Trans. Neural Networks.

[15]  Mangui Liang,et al.  Fuzzy support vector machine based on within-class scatter for classification problems with outliers or noises , 2013, Neurocomputing.

[16]  Bodo Manthey,et al.  k-Means Has Polynomial Smoothed Complexity , 2009, 2009 50th Annual IEEE Symposium on Foundations of Computer Science.

[17]  H. L. Le Roy,et al.  Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability; Vol. IV , 1969 .

[18]  Jeng-Shyang Pan,et al.  Kernel class-wise locality preserving projection , 2008, Inf. Sci..

[19]  Nello Cristianini,et al.  An Introduction to Support Vector Machines and Other Kernel-based Learning Methods , 2000 .

[20]  B. C. Brookes,et al.  Information Sciences , 2020, Cognitive Skills You Need for the 21st Century.

[21]  Lipo Wang,et al.  Support Vector Machines: Theory and Applications (Studies in Fuzziness and Soft Computing) , 2005 .

[22]  Chih-Jen Lin,et al.  LIBSVM: A library for support vector machines , 2011, TIST.

[23]  Mary Inaba,et al.  Applications of weighted Voronoi diagrams and randomization to variance-based k-clustering: (extended abstract) , 1994, SCG '94.

[24]  Reshma Khemchandani,et al.  Fuzzy multi-category proximal support vector classification via generalized eigenvalues , 2007, Soft Comput..

[25]  Glenn Fung,et al.  Proximal support vector machine classifiers , 2001, KDD '01.

[26]  Jeng-Shyang Pan,et al.  Kernel Self-optimized Locality Preserving Discriminant Analysis for feature extraction and recognition , 2011, Neurocomputing.

[27]  J. Hadamard.  Sur les problemes aux derive espartielles et leur signification physique , 1902 .

[28]  Chih-Jen Lin,et al.  A Practical Guide to Support Vector Classication , 2008 .

[29]  C.-fu Lin,et al.  Fuzzy Support Vector Machines with Automatic Membership Setting , 2005 .

[30]  Vladimir N. Vapnik,et al.  The Nature of Statistical Learning Theory , 2000, Statistics for Engineering and Information Science.

[31]  Lei Wang,et al.  Fuzzy Passive-Aggressive classification: A robust and efficient algorithm for online classification problems , 2013, Inf. Sci..