Online Simplex-Structured Matrix Factorization

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...

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Bibliographic Details
Published in:IEEE signal processing letters Vol. 32; pp. 3705 - 3709
Main Authors: Kouakou, Hugues, Goulart, Jose Henrique de Morais, Vitale, Raffaele, Oberlin, Thomas, Rousseau, David, Ruckebusch, Cyril, Dobigeon, Nicolas
Format: Journal Article
Language:English
Published: New York IEEE 2025
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Institute of Electrical and Electronics Engineers
Subjects:
Algorithms
Computational efficiency
Computer Science
Computing costs
Constraints
Data mining
Factorization
Frequency measurement
Iterative methods
low-rank approximation
Machine learning
Methodology
online processing
Protocols
Redundancy
Signal and Image Processing
Signal processing algorithms
Simplex-structured matrix factorization
Statistics
Structured matrices
Training
Vectors
online processing
low-rank approximation
Simplex-structured matrix factorization
ISSN:1070-9908, 1558-2361
Online Access:Get full text
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Summary: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 letter 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.
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ISSN:1070-9908
1558-2361
DOI:10.1109/LSP.2025.3611695