Multi-objective evolutionary optimization for constructing neural networks for virtual reality visual data mining: Application to geophysical prospecting

A method for the construction of virtual reality spaces for visual data mining using multi-objective optimization with genetic algorithms on nonlinear discriminant (NDA) neural networks is presented. Two neural network layers (the output and the last hidden) are used for the construction of simultaneous solutions for: (i) a supervised classification of data patterns and (ii) an unsupervised similarity structure preservation between the original data matrix and its image in the new space. A set of spaces are constructed from selected solutions along the Pareto front. This strategy represents a conceptual improvement over spaces computed by single-objective optimization. In addition, genetic programming (in particular gene expression programming) is used for finding analytic representations of the complex mappings generating the spaces (a composition of NDA and orthogonal principal components). The presented approach is domain independent and is illustrated via application to the geophysical prospecting of caves.

[1]  Graham Kendall,et al.  Search Methodologies: Introductory Tutorials in Optimization and Decision Support Techniques , 2013 .

[2]  Anil K. Jain,et al.  Discriminant analysis neural networks , 1993, IEEE International Conference on Neural Networks.

[3]  John R. Koza,et al.  Genetic programming - on the programming of computers by means of natural selection , 1993, Complex adaptive systems.

[4]  John R. Koza,et al.  Genetic Programming III: Darwinian Invention & Problem Solving , 1999 .

[5]  Cândida Ferreira,et al.  Gene Expression Programming: Mathematical Modeling by an Artificial Intelligence , 2014, Studies in Computational Intelligence.

[6]  I. Borg.  Multidimensional similarity structure analysis , 1987 .

[7]  John R. Koza,et al.  Genetic programming 2 - automatic discovery of reusable programs , 1994, Complex Adaptive Systems.

[8]  Anil K. Jain,et al.  Artificial neural network for nonlinear projection of multivariate data , 1992, [Proceedings 1992] IJCNN International Joint Conference on Neural Networks.

[9]  David Lowe,et al.  The optimised internal representation of multilayer classifier networks performs nonlinear discriminant analysis , 1990, Neural Networks.

[10]  Anil K. Jain,et al.  Artificial neural networks for feature extraction and multivariate data projection , 1995, IEEE Trans. Neural Networks.

[11]  Patrick Brézillon,et al.  Lecture Notes in Artificial Intelligence , 1999 .

[12]  John R. Koza,et al.  Hierarchical Genetic Algorithms Operating on Populations of Computer Programs , 1989, IJCAI.

[13]  William H. Press,et al.  Numerical recipes in C , 2002 .

[14]  Kalyanmoy Deb,et al.  A Fast Elitist Non-dominated Sorting Genetic Algorithm for Multi-objective Optimisation: NSGA-II , 2000, PPSN.

[15]  John W. Sammon,et al.  A Nonlinear Mapping for Data Structure Analysis , 1969, IEEE Transactions on Computers.

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

[17]  Cândida Ferreira,et al.  Gene Expression Programming: Mathematical Modeling by an Artificial Intelligence (Studies in Computational Intelligence) , 2006 .

[18]  P. Nordin.  Genetic Programming III - Darwinian Invention and Problem Solving , 1999 .

[19]  J. Kruskal.  Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis , 1964 .

[20]  Charles Gide,et al.  Cours d'économie politique , 1911 .

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

[22]  J.J. Valdes,et al.  Virtual reality visual data mining with nonlinear discriminant neural networks: application to leukemia and Alzheimer gene expression data , 2005, Proceedings. 2005 IEEE International Joint Conference on Neural Networks, 2005..

[23]  J. Gower.  A General Coefficient of Similarity and Some of Its Properties , 1971 .