学术报告（陈文胜 2024.11.13）

摘要：Nonnegative matrix factorization (NMF) aims to extract nonnegative features for data representation and has been widely utilized for data analysis. Most NMF-based methods are iteration algorithms based on gradient descent. However, their step sizes are determined using a specific formula and cannot be optimally adjusted. The restriction on choosing the optimal iteration step size affects the flexible design of the algorithms and leads to slowing down their convergence. This talk will introduce a novel graph-regularized orthogonal quadratic nonnegative matrix factorization (GOQNMF) model to address these issues. The quadratic matrix factors allow for adaptive step size selection along the gradient descent direction. This model not only captures the local structure of the data but also eliminates the correlation between features. The optimization problem of the GOQNMF model is solved using the gradient descent method. We suggest a methodology to determine the optimal step size range for iterations and prove that the GOQNMF algorithm is convergent with strictly monotonically decreasing. Experimental results confirm the convergence and effectiveness of the GOQNMF algorithm under different types of step sizes. Among the NMF-based algorithms compared, the proposed GOQNMF algorithm demonstrates superior performance in both convergence speed and facial image recognition.