Robust Non-Negative Matrix Factorization

Background

This is a repository to reproduce robust NMF algorithms:

1. Standard NMF[1]

2. HCNMF[2]

3. L21 -NMF[3]

4. RCNMF[4]

5. RNMF-L1​[5]

6. L_1​-NMF[3]

7. HuberNMF[6]

8. CIM-NMF[6]

Note that the HCNMF in this repository is simplified. In details, it uses two global learning rates instead of element-wise learning rates the paper proposed for backtracking line search. Thanks to AceKimi pointing it out and sharing his version. In the future, we will merge our versions if we have spare time.

Requirement

matplotlib-3.1.1
numpy-1.27.2
sklearn-0.21.3

Usage

Add noise

You can use nmf.preprocess.add_block_noise , nmf.preprocess.add_salt_noise to add two common types of image noise.

Fit NMF

You can use classes in nmf.nmfs to fit NMF model and nmf.evalute.inspect_dictionary to inspect the dictionary it learned.

Reconstruct images

You can use nmf.evalute.reconstruct to reconstruct images.

Cross Validation Experiment

It also provides function for CV experiments and plots the results.

An example can be found in the ./tutorial.ipynb.

References

[1]: Lee, Daniel D., and H. Sebastian Seung. "Algorithms for non-negative matrix factorization." In Advances in neural information processing systems, pp. 556-562. 2001.
[2]: Hamza, A. Ben, and David J. Brady. "Reconstruction of reflectance spectra using robust nonnegative matrix factorization." IEEE Transactions on Signal Processing 54, no. 9 (2006): 3637-3642.
[3]: Lam, Edmund Y. "Non-negative matrix factorization for images with Laplacian noise." In APCCAS 2008-2008 IEEE Asia Pacific Conference on Circuits and Systems, pp. 798-801. IEEE, 2008.
[4]: Gao, Hongchang, Feiping Nie, Weidong Cai, and Heng Huang. "Robust capped norm nonnegative matrix factorization: Capped norm nmf." In Proceedings of the 24th ACM International on Conference on Information and Knowledge Management, pp. 871-880. ACM, 2015.
[5]: Zhang, Lijun, Zhengguang Chen, Miao Zheng, and Xiaofei He. "Robust non-negative matrix factorization." Frontiers of Electrical and Electronic Engineering in China 6, no. 2 (2011): 192-200.
[6]: Du, Liang, Xuan Li, and Yi-Dong Shen. "Robust nonnegative matrix factorization via half-quadratic minimization." In 2012 IEEE 12th International Conference on Data Mining, pp. 201-210. IEEE, 2012.