FLSOM with individual kernel radii formation and application to optimization of a pickling line

Updating individually the kernel radii of the neurons according to Van Hulle's approach in the Fuzzy Labeled Self-Organizing Map (FLSOM) algorithm can produce a significant reduction of the mean quantization error as it is demonstrated in this paper using four datasets. The algorithm takes advantage of the available classification of the instances of the dataset since FLSOM is a version of SOM algorithm where the prototype vectors are influenced by the labeling data vectors that define the clusters of the dataset. In this work, the proposed modified version of the FLSOM is able to achieve a better approximation to the numerical variables by means of decreasing the mean quantization error using an individual adaptation of the kernel radii. The aim of this paper is to apply this idea to a pickling line of the steel industry to obtain a model trained with categorical and numerical process variables preserving the topological distribution of the output space in order to reach a visualization of the industrial process and estimate the optimum line speed that minimizes the pickling defects over the steel strip.