Summary of Randomized Algorithms For Symmetric Nonnegative Matrix Factorization, by Koby Hayashi et al.
Randomized Algorithms for Symmetric Nonnegative Matrix Factorization
by Koby Hayashi, Sinan G. Aksoy, Grey Ballard, Haesun Park
First submitted to arxiv on: 13 Feb 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Numerical Analysis (math.NA); Optimization and Control (math.OC)
GrooveSquid.com Paper Summaries
GrooveSquid.com’s goal is to make artificial intelligence research accessible by summarizing AI papers in simpler terms. Each summary below covers the same AI paper, written at different levels of difficulty. The medium difficulty and low difficulty versions are original summaries written by GrooveSquid.com, while the high difficulty version is the paper’s original abstract. Feel free to learn from the version that suits you best!
| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This paper introduces two randomized algorithms designed to accelerate Symmetric Nonnegative Matrix Factorization (SymNMF), a technique used in data analysis and machine learning. The first algorithm uses matrix sketching to compute an initial low-rank approximation, followed by rapid computation of the SymNMF. The second algorithm employs leverage score sampling to approximately solve constrained least squares problems. These methods are crucial for solving sequences of constrained least squares problems that underlie many successful SymNMF approaches. Theoretical guarantees are provided for the accuracy and efficiency of these algorithms, which are then demonstrated in practice through graph clustering tasks on large real-world datasets. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Symmetric Nonnegative Matrix Factorization is a way to break down big matrices into smaller pieces. This helps us understand and work with very large datasets. To make this process faster and more efficient, the authors created two new methods that use random numbers to help solve the problem. The first method starts by breaking down the matrix into a simpler version, then uses that version to get an answer quickly. The second method uses a special kind of sampling to find the right pieces of the puzzle. Both methods are tested on big datasets and show great results, giving us new ways to work with very large amounts of data. |
Keywords
* Artificial intelligence * Clustering * Machine learning
