Fusion of data dimensionality reduction algorithms based on category representation theory

For a long time, people have believed that representation problems are one of the bottlenecks in the field of machine learning. Therefore, it is a long-term and exploratory work to study machine learning representation methods. Due to this, we use category theory to study the fusion representation of data dimensionality reduction. We propose the basic concept of category representation for data dimensionality reduction and provide a data dimensionality reduction fusion representation framework. We have conducted research and analysis on algorithms such as PCA, KPCA, and LDA, identified the essential connection between PCA, KPCA, and LDA and proposed a data dimensionality reduction fusion representation algorithm based on a data dimensionality reduction fusion representation framework. Finally, we demonstrated the feasibility of the proposed method through experiments.