Robustness of Minimum-Volume Nonnegative Matrix Factorization under an Expanded Sufficiently Scattered Condition
This addresses a long-standing open problem in applications like hyperspectral imaging and topic modeling, though it appears incremental as it extends existing conditions.
The paper tackles the robustness of minimum-volume nonnegative matrix factorization to noise by proving that it identifies groundtruth factors under an expanded sufficiently scattered condition, which requires data points to be well-scattered in a latent simplex.
Minimum-volume nonnegative matrix factorization (min-vol NMF) has been used successfully in many applications, such as hyperspectral imaging, chemical kinetics, spectroscopy, topic modeling, and audio source separation. However, its robustness to noise has been a long-standing open problem. In this paper, we prove that min-vol NMF identifies the groundtruth factors in the presence of noise under a condition referred to as the expanded sufficiently scattered condition which requires the data points to be sufficiently well scattered in the latent simplex generated by the basis vectors.