A polynomial time algorithm for the construction and training of a class of multilayer perceptrons

This paper presents a polynomial time algorithm for the construction and training of a class of multilayer perceptrons for classification. It uses linear programming models to incrementally generate the hidden layer in a restricted higher-order perceptron. Polynomial time complexity of the method is proven. Computational results are provided for several well-known applications in the areas of speech recognition, medical diagnosis, and target detection. In all cases, very small nets were created that had error rates similar to those reported so far.

[1]  Robert R. Sokal,et al.  A statistical method for evaluating systematic relationships , 1958 .

[2]  Richard Lippmann,et al.  Neural Net and Traditional Classifiers , 1987, NIPS.

[3]  Richard O. Duda,et al.  Pattern classification and scene analysis , 1974, A Wiley-Interscience publication.

[4]  Alan J. Gross,et al.  Self-Organizing Methods in Modeling , 1988 .

[5]  Brian Everitt,et al.  Cluster analysis , 1974 .

[6]  Terrence J. Sejnowski,et al.  Analysis of hidden units in a layered network trained to classify sonar targets , 1988, Neural Networks.

[7]  George B. Dantzig,et al.  Linear programming and extensions , 1965 .

[8]  O. Mangasarian,et al.  Pattern Recognition Via Linear Programming: Theory and Application to Medical Diagnosis , 1989 .

[9]  Ned Freed,et al.  EVALUATING ALTERNATIVE LINEAR PROGRAMMING MODELS TO SOLVE THE TWO-GROUP DISCRIMINANT PROBLEM , 1986 .

[10]  Fred Glover,et al.  Applications and Implementation , 1981 .

[11]  Teuvo Kohonen,et al.  An introduction to neural computing , 1988, Neural Networks.

[12]  FRED W. SMITH,et al.  Pattern Classifier Design by Linear Programming , 1968, IEEE Transactions on Computers.

[13]  G. E. Peterson,et al.  Control Methods Used in a Study of the Vowels , 1951 .

[14]  Julius T. Tou,et al.  Pattern Recognition Principles , 1974 .

[15]  L. Khachiyan.  Polynomial algorithms in linear programming , 1980 .

[16]  Fred Glover,et al.  A NEW CLASS OF MODELS FOR THE DISCRIMINANT PROBLEM , 1988 .

[17]  Teuvo Kohonen,et al.  Self-Organization and Associative Memory , 1988 .

[18]  Stephen Grossberg,et al.  Art 2: Self-Organization Of Stable Category Recognition Codes For Analog Input Patterns , 1988, Other Conferences.

[19]  John A. Hartigan,et al.  Clustering Algorithms , 1975 .

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

[21]  Narendra Karmarkar,et al.  A new polynomial-time algorithm for linear programming , 1984, Comb..