2023/01/30 by Zheng Zhai, Hengchao Chen, Zhai, Zheng +3
Computer Science · Engineering · #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #FOS: Mathematics #Face and Expression Recognition #Information Retrieval (cs.IR) #Machine Learning (cs.LG) #Medical Image Segmentation Techniques #Numerical Analysis (math.NA) #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.2301.12965
openalex publication_date 2023/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Matrix factorization is a popular framework for modeling low-rank data matrices. Motivated by manifold learning problems, this paper proposes a quadratic matrix factorization (QMF) framework to learn the curved manifold on which the dataset lies. Unlike local linear methods such as the local principal component analysis, QMF can better exploit the curved structure of the underlying manifold. Algorithmically, we propose an alternating minimization algorithm to optimize QMF and establish its theoretical convergence properties. Moreover, to avoid possible over-fitting, we then propose a regularized QMF algorithm and discuss how to tune its regularization parameter. Finally, we elaborate how to apply the regularized QMF to manifold learning problems. Experiments on a synthetic manifold learning dataset and two real datasets, including the MNIST handwritten dataset and a cryogenic electron microscopy dataset, demonstrate the superiority of the proposed method over its competitors.