The ontology sparse vector learning algorithm is essentially a dimensionality reduction trick, i.e., the key components in the p-dimensional vector are taken out, and the remaining components are set to zero, so as to obtain the key information in a certain ontology application background. In the early stage of ontology data processing, the goal of the algorithm is to find the location of key components through the learning of some ontology sample points, if the relevant concepts and structure information of each ontology vertex with p-dimensional vectors are expressed. The ontology sparse vector itself contains a certain structure, such as the symmetry between components and the binding relationship between certain components, and the algorithm can also be used to dig out the correlation and decisive components between the components. In this paper, the graph structure is used to express these components and their interrelationships, and the optimal solution is obtained by using spectral graph theory and graph optimization techniques. The essence of the proposed ontology learning algorithm is to find the decisive vertices in the graph Gβ. Finally, two experiments show that the given ontology learning algorithm is effective in similarity calculation and ontology mapping in some specific engineering fields. © 2020 by the authors.