Hierarchical Kernel and Sub-kernels

This paper shows the theoretical development of hierarchy by kernels and an algorithm used to obtain an interesting class or partition from a hierarchy. Also shown is the theorem about the Kernels Optimal Criterion and how it is expressed as a function of the masses of the points of the vector space and product scale points, the inertia of the cloud formed by those two points or hierarchical nodes, which are called subcores or sub-kernels. The application is made on the terminal efficiency of postgraduate degrees at ESIA, IPN Mexico, along its first 48 years of academic and scientific life and the development of students´ graduation.