Graph Non-negative Matrix Factorization Based on Self-representation Learning Update for Clustering

Non-negative Matrix Factorization (NMF) is a dimensionality reduction technique based on matrix factorization, used to find linear representations based on latent features. Although Graph Nonnegative Matrix Factorization (GNMF), which is proposed to address the issue of NMF ignoring the local geometric structure of data, can improve the geometric relationship between data in high-dimensional spaces relatively well, the graph information it follows - that is, the adjacency matrix - is constructed based on the distance relationship of the observable space of the original samples and cannot reflect the true distance relationship between objects. To address this issue, we integrate the graph information based on self-representation into the algorithm framework of NMF and propose Graph Non-negative Matrix Factorization based on Self-representation Learning Update (GNMFSLU). This method updates the adjacency matrix of the graph in each iteration, thereby making the graph information closer to the true distance relationship between objects and enhancing the clustering performance of NMF.