Nonlinear Matrix Decomposition

Nonlinear Matrix Decomposition (NMD) seeks to approximate a sparse, nonnegative matrix using a low-rank matrix transformed by an element-wise nonlinear function, often the Rectified Linear Unit (ReLU). Current research emphasizes developing efficient algorithms, such as accelerated methods incorporating momentum and three-block decompositions, to address challenges like overfitting and computational cost, particularly within the context of ReLU-based NMD. These advancements are driven by applications in diverse fields, including neuroscience (e.g., analyzing fMRI data) and machine learning, where NMD offers improved model interpretability and reduced complexity compared to fully connected deep learning architectures. The development of robust and scalable NMD methods is thus crucial for advancing these fields.