Principal Component Analysis Methods and Teaching Reform Paths in Precision Teaching of Vocal Music Education in Colleges and Universities

Abstract

In the exploration of the precise teaching reform of college vocal music, this paper takes the influencing factors of teachers as the research entry point. Aiming at the problems of the principal component analysis network, such as the inability to reflect the complete structural information of the data and the sensitivity to noise, the two-way two-dimensional principal component analysis is used as a filter, and the robust and non-greedy two-way two-dimensional principal component analysis network based on the L1-paradigm distance metric is proposed, and then a principal component analysis network model is constructed. Meanwhile, in order to improve the robustness of principal component analysis, the MCD algorithm, which calculates the robust covariance matrix, is added to the model. Combined with the actual situation, a set of teacher influence factor indicator system containing 7 secondary indicators and 27 tertiary indicators is constructed from the three aspects of teachers' basic situation, teachers' classroom performance and teaching management. Applying the principal component analysis network model to the index system of teachers' influencing factors, the cumulative contribution rate of the six extracted index factors (teachers' situation, teaching attitude, teaching methods and means, teaching organization, system management, process management) has reached 83.61%, indicating that the six aspects are the main entry point for the precise reform of vocal music teaching.