Online simplex-structured matrix factorization

Abstract: Simplex-structured matrix factorization (SSMF) is a common task encountered in signal processing and machine learning. Minimum-volume constrained unmixing (MVCU) algorithms are among the most widely used methods to perform this task. While MVCU algorithms generally perform well in an offline setting, their direct application to online scenarios suffers from scalability limitations due to memory and computational demands. To overcome these limitations, this paper proposes an approach which can build upon any off-the-shelf MVCU algorithm to operate sequentially, i.e., to handle one observation at a time. The key idea of the proposed method consists in updating the solution of MVCU only when necessary, guided by an online check of the corresponding optimization problem constraints. It only stores and processes observations identified as informative with respect to the geometrical constraints underlying SSMF. We demonstrate the effectiveness of the approach when analyzing synthetic and real datasets, showing that it achieves estimation accuracy comparable to the offline MVCU method upon which it relies, while significantly reducing the computational cost.