Multifactor Association Analysis Model of Preschool Education Based on Multivariate Nonlinear Matrix Theory

This paper uses the multivariate nonlinear matrix theory to conduct an in-depth study and analysis of the multifactor correlation in preschool education, and designs a multifactor correlation analysis model to be applied to the actual preschool education process. A nonlinear approach is used to define the dynamics of a planar segmented smooth system with visible folds on a switching surface, and conditions are given for the system to have a sliding periodic orbit through this visible fold. A curriculum relatedness analysis algorithm based on Euclidean distance is proposed, which takes distance as a perspective and calculates the curriculum relatedness by measuring the difference of the curriculum in different dimensions; a curriculum relatedness analysis algorithm based on cosine similarity is proposed, which takes a vector as a perspective and calculates the curriculum relatedness by measuring the cosine of the angle between different curriculum vectors; a curriculum relatedness analysis algorithm based on correlation coefficient is proposed. The course relevance analysis algorithm based on the correlation coefficient evaluates the relevance of different courses from a centralized perspective. After preprocessing the course results, two different types of datasets were selected for the experiments of the three algorithms. The results show that all three algorithms can calculate the correlation degree of the courses, which can provide scientific data support for the curriculum arrangement of the school so that the school can scientifically verify and optimize the curriculum arrangement. The three algorithms are compared from the calculation results and theories, among which the correlation coefficient correlation analysis algorithm has the best effect. This study proposes suggestions to promote students’ noncognitive ability development from the perspective of preschool education development; grasp the critical period of children’s noncognitive ability development and pay attention to preschool education investment; further develop inclusive preschool education to ensure the educational opportunities of disadvantaged groups; promote regional preschool education reform to ensure the quality of preschool education in rural areas; and guide parents’ participation and cooperate with schools to cultivate children’s noncognitive ability.