Summary of Orthogonal Nonnegative Matrix Factorization with the Kullback-leibler Divergence, by Jean Pacifique Nkurunziza et al.
Orthogonal Nonnegative Matrix Factorization with the Kullback-Leibler divergence
by Jean Pacifique Nkurunziza, Fulgence Nahayo, Nicolas Gillis
First submitted to arxiv on: 10 Oct 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Information Retrieval (cs.IR); Machine Learning (cs.LG); Signal Processing (eess.SP)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The proposed paper presents a new model and algorithm for orthogonal nonnegative matrix factorization (ONMF) that minimizes the Kullback-Leibler (KL) divergence, unlike most existing works which rely on the Frobenius norm. This approach is particularly suitable for modeling sparse vectors of word counts in document datasets or photo counting processes in imaging, as it assumes Poisson-distributed data. The algorithm, called KL-ONMF, uses alternating optimization and is shown to perform favorably with the traditional Frobenius-norm based ONMF for tasks such as document classification and hyperspectral image unmixing. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper creates a new way to do orthogonal nonnegative matrix factorization (ONMF) that’s better for certain types of data. Right now, most people use a method called the Frobenius norm to see how good their ONMF results are. But this new approach uses something called the Kullback-Leibler divergence instead. This is useful because it can handle data that has lots of zeros in it, which is important for things like counting words in documents or counting photos in images. |
Keywords
* Artificial intelligence * Classification * Optimization
