Radial basis functions for multidimensional learning with an application to nondestructive sizing of defects

A computational intelligence problem with mapping of multiple classes for a given input feature is addressed in this paper. The objective is to classify a vector of class for a given vector of input features. Each class is a member of disjoint set called dimension and hence, it is called multidimensional learning. Dependency between the classes and dimensions are usually not taken into account while constructing independent classifiers for each component class of vector. In this paper, two methods of adaption of radial basis functions (RBF) neural network for multidimensional learning are proposed. In first method, the prototype vector of hidden layer is formed by cluster analysis on instance belong to each class of each dimension. By this way the dependencies of classes is considered. In second method, the prototype vector of hidden layer are formed by cluster analysis on instance belong to each new classes by taking the Cartesian product of each dimension. With this method, the dependency between each dimension is concentrated. A comparison study with these two methods of adaptations with independent uni-dimensional RBF is presented. Studies are carried out with real world multidimensional dataset (with >2 classes in each dimension) obtained from simulated eddy current non-destructive evaluation (NDE) of a stainless steel plate having sub-surface defects of different dimensions. This dataset is used for estimating three characteristics (three dimensions) of defects namely, length, depth and height. The performance evaluation using metrics such as mean accuracy and global accuracy clearly reveals that the proposed multidimensional RBF is superior to the uni-dimensional RBF used individually for each dimensions.