# Binary matrix factorization

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Binary matrix factorization | |

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**Binary matrix factorization** is a machine learning algorithm that takes a matrix and factorizes it into matrices.
One or more of the matrices should be binary matrices.
There are different binary matrix factorizations.

Meeds et al.^{[1]}
considers the following condition

- <math>\mathbf{X | UWV}'</math>

where **U** and **V** are binary matrices, **W** contains weights and **X** may be real-valued, binary or categorical.

Other type of binary factorization is considered Zhang et al.^{[2]}

- <math>\mathbf{X \approx WH}</math>

where all three matrices are binary.
This form can be regarded as a specialization of non-negative matrix factorization.
Rank-one binary matrix factorization of Zhang's kind is considered by Shen et al.^{[3]}

Related to the Zhang binary matrix factorization is Boolean matrix factorization.

## [edit] References

- ↑ Edward Meeds, Zoubin Ghahramani, Radford Neal, Sam Roweis(2006). "Modeling dyadic data with binary latent factors".
*Advances in Neural Information Processing Systems*. [1] - ↑ Zhongyuan Zhang, Tao Li, Chris Ding, Xiangsun Zhang(2007). "Binary matrix factorization with applications". Pages 391-400 in
*Seventh IEEE International Conference on Data Mining, 2007. ICDM 2007*. doi: 10.1109/ICDM.2007.99. - ↑ Bao-Hong Shen, Shuiwang Ji, Jieping Ye(2009). "Mining discrete patterns via binary matrix factorization".