HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Journal articles

Stochastic Subsampling for Factorizing Huge Matrices

Abstract : We present a matrix-factorization algorithm that scales to input matrices with both huge number of rows and columns. Learned factors may be sparse or dense and/or non-negative, which makes our algorithm suitable for dictionary learning, sparse component analysis, and non-negative matrix factorization. Our algorithm streams matrix columns while subsampling them to iteratively learn the matrix factors. At each iteration, the row dimension of a new sample is reduced by subsampling, resulting in lower time complexity compared to a simple streaming algorithm. Our method comes with convergence guarantees to reach a stationary point of the matrix-factorization problem. We demonstrate its efficiency on massive functional Magnetic Resonance Imaging data (2 TB), and on patches extracted from hyperspectral images (103 GB). For both problems, which involve different penalties on rows and columns, we obtain significant speed-ups compared to state-of-the-art algorithms.
Complete list of metadata

https://hal.archives-ouvertes.fr/hal-01431618
Contributor : Arthur Mensch Connect in order to contact the contributor
Submitted on : Monday, October 30, 2017 - 10:18:07 AM
Last modification on : Friday, January 28, 2022 - 9:02:03 PM
Long-term archiving on: : Wednesday, January 31, 2018 - 1:05:45 PM

Files

modl_tsp.pdf
Files produced by the author(s)

Identifiers

Citation

Arthur Mensch, Julien Mairal, Bertrand Thirion, Gaël Varoquaux. Stochastic Subsampling for Factorizing Huge Matrices. IEEE Transactions on Signal Processing, Institute of Electrical and Electronics Engineers, 2018, 66 (1), pp.113-128. ⟨10.1109/TSP.2017.2752697⟩. ⟨hal-01431618v3⟩

Share

Metrics

Record views

2460

Files downloads

1321