Analysis of G-Transformation Modes for Building Neuro-like Parallel–Hierarchical Network Identification of Rail Surface Defects

This work presents the construction of a transformation for the identification of surface defects on rails, starting with the selection of elements from the matrix and the creation of different matrices. It further elaborates on the recursive formulation of the transformation and demonstrates that, regardless of the elements’ uniqueness, the sum of the transformed matrix remains equal to the sum of the original matrix. This study also addresses the handling of matrices with repeated elements and proves that the G-transformation preserves information, ensuring the integrity of data without any loss or redundancy.