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[2409.04994] Learning nonnegative matrix factorizations from compressed data
Summary
This paper presents a framework for scalable nonnegative matrix factorization (NMF) that operates directly on compressed data, allowing for efficient recovery of low-rank components with minimal access to original data.
Why It Matters
The ability to perform nonnegative matrix factorization from compressed data is crucial for applications in data science and machine learning, where data storage and processing efficiency are paramount. This research offers a theoretically grounded approach that could enhance performance in various real-world scenarios.
Key Takeaways
- Introduces a flexible framework for NMF from compressed data.
- Employs randomized sketching methods for effective data compression.
- Formulates optimization problems that only require compressed data.
- Demonstrates empirical success in real-world applications.
- Discusses algorithmic approaches, including multiplicative updates.
Mathematics > Optimization and Control arXiv:2409.04994 (math) [Submitted on 8 Sep 2024 (v1), last revised 15 Feb 2026 (this version, v2)] Title:Learning nonnegative matrix factorizations from compressed data Authors:Abraar Chaudhry, Elizaveta Rebrova View a PDF of the paper titled Learning nonnegative matrix factorizations from compressed data, by Abraar Chaudhry and Elizaveta Rebrova View PDF HTML (experimental) Abstract:We propose a flexible and theoretically supported framework for scalable nonnegative matrix factorization. The goal is to find nonnegative low-rank components directly from compressed measurements, accessing the original data only once or twice. We consider compression through randomized sketching methods that can be adapted to the data, or can be oblivious. We formulate optimization problems that only depend on the compressed data, but which can recover a nonnegative factorization which closely approximates the original matrix. The defined problems can be approached with a variety of algorithms, and in particular, we discuss variations of the popular multiplicative updates method for these compressed problems. We demonstrate the success of our approaches empirically and validate their performance in real-world applications. Subjects: Optimization and Control (math.OC); Machine Learning (cs.LG); Numerical Analysis (math.NA) MSC classes: 15A23, 68T10, 68W20, 65F30 Cite as: arXiv:2409.04994 [math.OC] (or arXiv:2409.04994v2 [math.OC] for this version) h...
