Online Matrix Factorization via Broyden Updates
This work addresses the need for scalable matrix factorization in streaming or large-scale data applications, though it appears incremental as it builds on existing online and batch methods.
The authors tackled the problem of computing matrix factorizations in an online setting by proposing an algorithm that updates the dictionary matrix and coefficients with each new observation, also extending it for missing data and mini-batch processing. They demonstrated its efficiency on a real dataset, comparing it with methods like stochastic gradient matrix factorization and NMF.
In this paper, we propose an online algorithm to compute matrix factorizations. Proposed algorithm updates the dictionary matrix and associated coefficients using a single observation at each time. The algorithm performs low-rank updates to dictionary matrix. We derive the algorithm by defining a simple objective function to minimize whenever an observation is arrived. We extend the algorithm further for handling missing data. We also provide a mini-batch extension which enables to compute the matrix factorization on big datasets. We demonstrate the efficiency of our algorithm on a real dataset and give comparisons with well-known algorithms such as stochastic gradient matrix factorization and nonnegative matrix factorization (NMF).