A Fuzzy Classifier Network with Ellipsoidal Epanechnikovs

Our new fuzzy classifier network can be trained with a set of labeled feature vectors without adjusting any weights. Further, it checks for consistency of the labels for the various feature vectors. It is a trade-off between two extreme cases. First, if a circular Gaussian is centered on each labeled feature vector, then a large number of Gaussians may be required but the accuracy is high in the absence of outliers. At the other extreme is the use of a single radial Gaussian for each class that is centered on the average vector of the class. This is very efficient, but the class may have a noncircular shape and outliers can bias the location, both of which affect the accuracy. We extend Epanechnikov functions to be multivariate ellipsoidal fuzzy set membership functions. To develop methods that are efficient and yet accurate, we center an ellipsoidal Gaussian or Epanechnikov on the weighted fuzzy average vector of each class. These fuzzy centers are immune to outliers. The ellipsoidal shapes are rotated, dilated and contracted along the principal axes by the inverse covariance matrices for the respective classes. The inverses of these symmetric matrices are computed efficiently, which completes the training. A test vector to be classified is put through all ellipsoidal fuzzy set membership functions for the respective classes and the maximum value (fuzzy truth) determines the winner. Tests are done on the iris and other data sets.

[1]  Ke Chen,et al.  A method of combining multiple probabilistic classifiers through soft competition on different feature sets , 1998, Neurocomputing.

[2]  Donald F. Specht,et al.  Probabilistic neural networks , 1990, Neural Networks.

[3]  Moti Schneider,et al.  On the use of fuzzy sets in histogram equalization , 1992 .

[4]  Carl G. Looney,et al.  Radial basis functional link nets and fuzzy reasoning , 2002, Neurocomputing.

[5]  Shigeo Abe DrEng.  Pattern Classification , 2001, Springer London.

[6]  Fouad Badran,et al.  Probabilistic self-organizing map and radial basis function networks , 1998, Neurocomputing.

[7]  M. Ait Kbir,et al.  Hierarchical fuzzy partition for pattern classification with fuzzy if-then rules , 2000, Pattern Recognit. Lett..

[8]  Multiple hierarchicall classifier system with self GA invocation , 1997 .

[9]  D. F. Specht,et al.  Probabilistic neural networks for classification, mapping, or associative memory , 1988, IEEE 1988 International Conference on Neural Networks.

[10]  Shigeo Abe,et al.  A fuzzy classifier with ellipsoidal regions , 1997, IEEE Trans. Fuzzy Syst..

[11]  Krzysztof J. Cios,et al.  Certainty factors versus Parzen windows as reliability measures in RBF networks , 1998, Neurocomputing.

[12]  Yoshiki Uchikawa,et al.  A Fuzzy Classifier System for evolutionary learning of robot behaviors , 1998 .

[13]  Hisao Ishibuchi,et al.  Selecting fuzzy if-then rules for classification problems using genetic algorithms , 1995, IEEE Trans. Fuzzy Syst..

[14]  Witold Pedrycz,et al.  Fuzzy clustering preprocessor in neural classifiers , 1998 .

[15]  Ching-Chang Wong,et al.  K-means-based fuzzy classifier design , 2000, Ninth IEEE International Conference on Fuzzy Systems. FUZZ- IEEE 2000 (Cat. No.00CH37063).

[16]  John Moody,et al.  Fast Learning in Networks of Locally-Tuned Processing Units , 1989, Neural Computation.

[17]  Abraham Kandel,et al.  Feature-based fuzzy classification for interpretation of mammograms , 2000, Fuzzy Sets Syst..

[18]  Ioannis Anagnostopoulos,et al.  A neural network and fuzzy logic system for face detection on RGB images , 2001, Computers and Their Applications.

[19]  Luc Boullart,et al.  An implementation of genetic algorithms for rule based machine learning , 2000 .

[20]  David S. Broomhead,et al.  Multivariable Functional Interpolation and Adaptive Networks , 1988, Complex Syst..

[21]  Carl G. Looney,et al.  Pattern recognition using neural networks , 1997 .

[22]  James M. Keller,et al.  A fuzzy K-nearest neighbor algorithm , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[23]  Korris Fu-Lai Chung,et al.  Fuzzy competitive learning , 1994, Neural Networks.

[24]  J. Bednar,et al.  Alpha-trimmed means and their relationship to median filters , 1984 .

[25]  Hazem Tawfik,et al.  Handoff algorithms based on fuzzy classifiers , 2000, IEEE Trans. Veh. Technol..