Structural Tensor Construction And Decomposition Method And Its Application In Multivariate Relevance Analysis

With the continuous development of the Internet of Things and social networks in recent years,relevant data is growing rapidly at an explosive rate.The problem that bothers people is often not insufficiency of data,but overload of information.Tensors and knowledge graphs can effectively organize irregular heterogeneous data.How to dig out the hidden correlation characteristics of data from their structural characteristics is of great value in the field of multiple correlation analysis.However,the indirect and asymmetric relationships in actual data make it difficult to accurately predict the relationships between some entities.How to analyze these relationships has become an urgent problem to be solved.Most of the existing relationship analysis and prediction models mainly focus on the prediction of direct relationships and symmetric relationships.Excellent solutions for predicting indirect relationships and asymmetric relationships are rare.Some models rely on deep neural networks to predict local indirect relationships.But they usually have high time complexity and do not have good interpretability.Aiming at the indirect relationship in the data,this thesis proposes the ARCCS(Association Rule algorithm Combined with Classical Statistics)model,which regards tensors as the high-dimensional representation of matrices and uses the improved FGMD-GCD(Fast Greedy Multi-Dimensional Graph Community Detection)algorithm to perform low-dimensional single-matrix relational cluster analysis,Apriori algorithm to perform high-dimensional multi-matrix association analysis,and classical statistical testing algorithms to perform hypothesis testing on the results.Aiming at the asymmetric relationship in the data,this thesis proposes the CPE(CP decomposition and Embedding method)model,which uses tensor decomposition and word embedding representation to complete the prediction task of the relationship in the knowledge graph.Thanks to the model's giving different weights to two entities in asymmetric relationships,the CPE model is particularly suitable for capturing the characteristics of asymmetric relationships in the knowledge graph.Finally,this thesis combines the two models above and proposes the MAAH(Multiple Association Analysis Hybrid recommendation system,MAAH)model.This model combines the advantages of the two models and deeply digs into the indirect relationships and asymmetric relationships between movies and users in the movie recommendation system.The three models proposed in this thesis have made good predictions and analysis of the indirect and asymmetric relationships in the multivariate related data.The results on the related data sets show that the ARCCS model has an improvement of 2.98% compared to the earlier prioritized model.Compared with other latest linear models,the CPE model has an improvement of up to 10%.The MAAH recommended model has an improvement of about 10% compared to the previous model.