Combining topographic map formation with projection pursuit learning for nonparametric regression analysis

The original Self-Organizing Map (SOM) algorithm is known to perform poorly on regression problems due to the occurrence of nonfunctional mappings. Recently, we have introduced an unsupervised learning rule, called the Maximum Entropy learning Rule (MER), which performs topographic map formation without using a neighborhood function. In the present paper, MER is extended with a neighborhood function and applied to nonparametric projection pursuit regression. The extended rule, called eMER, alleviates the occurrence of nonfunctional mappings. The performance of our regression procedure is quantified and compared to other neural network-based parametric and nonparametric regression procedures.

[1]  Teuvo Kohonen,et al.  Self-organized formation of topologically correct feature maps , 2004, Biological Cybernetics.

[2]  J. Friedman,et al.  FLEXIBLE PARSIMONIOUS SMOOTHING AND ADDITIVE MODELING , 1989 .

[3]  P. Hall.  On Polynomial-Based Projection Indices for Exploratory Projection Pursuit , 1989 .

[4]  Allen Gersho,et al.  Asymptotically optimal block quantization , 1979, IEEE Trans. Inf. Theory.

[5]  Teuvo Kohonen,et al.  Self-Organizing Maps , 2010 .

[6]  H. Ritter.  Combining self-organizing maps , 1989, International 1989 Joint Conference on Neural Networks.

[7]  T. Kohonen.  Self-organized formation of topographically correct feature maps , 1982 .

[8]  Jenq-Neng Hwang,et al.  Regression modeling in back-propagation and projection pursuit learning , 1994, IEEE Trans. Neural Networks.

[9]  Marc M. Van Hulle,et al.  The Formation of Topographic Maps That Maximize the Average Mutual Information of the Output Responses to Noiseless Input Signals , 1997, Neural Computation.

[10]  J. Friedman,et al.  Projection Pursuit Regression , 1981 .

[11]  Hilbert J. Kappen,et al.  Self-organization and nonparametric regression , 1995 .

[12]  Stephen P. Luttrell.  Code vector density in topographic mappings: Scalar case , 1991, IEEE Trans. Neural Networks.

[13]  Vladimir Cherkassky,et al.  Constrained topological mapping for nonparametric regression analysis , 1991, Neural Networks.

[14]  T. Kohonen.  Self-Organized Formation of Correct Feature Maps , 1982 .

[15]  Helge Ritter.  Asymptotic level density for a class of vector quantization processes , 1991, IEEE Trans. Neural Networks.

[16]  Robert M. Gray,et al.  An Algorithm for Vector Quantizer Design , 1980, IEEE Trans. Commun..

[17]  M. Hulle.  Globally-ordered topology-preserving maps achieved with a learning rule performing local weight updates only , 1995 .