https://github.com/advestis/nmf-rank-determination

https://github.com/advestis/nmf-rank-determination

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• Host: GitHub
• URL: https://github.com/advestis/nmf-rank-determination
• Owner: Advestis
• Created: 2023-10-20T12:56:46.000Z (about 1 year ago)
• Default Branch: main
• Last Pushed: 2023-11-13T09:25:23.000Z (about 1 year ago)
• Last Synced: 2023-11-13T10:34:06.967Z (about 1 year ago)
• Language: Python
• Size: 3.16 MB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
## On Rank Selection in Non-Negative Matrix Factorization using ConcordanceOfficial *GitHub* repository for the original *MDPI Mathematics* paper

![Graphical_abstract](images/graphical_abstract.png)

*Credits*: DALL·E 3

**On Rank Selection in Non-Negative Matrix Factorization using Concordance**


Paul Fogel, Christophe Geissler, Nicolas Morizet and George Luta


**DOI**: https://doi.org/10.3390/math11224611

This article belongs to the Special Issue [Advances in Applied Probability and Statistical Inference](https://www.mdpi.com/journal/mathematics/special_issues/Advances_Applied_Probability_Statistical_Inference).

**Abstract**: The choice of the factorization rank of a matrix is critical, e.g., in dimensionality reduction,

filtering, clustering, deconvolution, etc., because selecting a rank that is too high amounts to adjusting the noise,

while selecting a rank that is too low results in the oversimplification of the signal.

Numerous methods for selecting the factorization rank of a non-negative matrix have been proposed.

One of them is the cophenetic correlation coefficient (*ccc*), widely used in data science to evaluate the number of

clusters in a hierarchical clustering. In previous work, it was shown that 𝑐𝑐𝑐 performs better than other methods

for rank selection in non-negative matrix factorization (NMF) when the underlying structure of the matrix consists

of orthogonal clusters. In this article, we show that using the ratio of *ccc* to the approximation error significantly

improves the accuracy of the rank selection. We also propose a new criterion, *concordance*, which, like *ccc*,

benefits from the stochastic nature of NMF; its accuracy is also improved by using its ratio-to-error form.

Using real and simulated data, we show that *concordance*, with a CUSUM-based automatic detection algorithm

for its original or ratio-to-error forms, significantly outperforms *ccc*.

It is important to note that the new criterion works for a broader class of matrices,

where the underlying clusters are not assumed to be orthogonal.

**Datasets used in the study**

- Swimmer

- Sausage

- Brunet

- MNIST

**Requirements**

- Python 3.9.0

- scikit-learn 

- pandas 

- numpy 

- scipy 

- tqdm

## Citation

```

@Article{math11224611,

AUTHOR = {Fogel, Paul and Geissler, Christophe and Morizet, Nicolas and Luta, George},

TITLE = {On Rank Selection in Non-Negative Matrix Factorization Using Concordance},

JOURNAL = {Mathematics},

VOLUME = {11},

YEAR = {2023},

NUMBER = {22},

ARTICLE-NUMBER = {4611},

URL = {https://www.mdpi.com/2227-7390/11/22/4611},

ISSN = {2227-7390},

DOI = {10.3390/math11224611}

}

```