# Binary matrix factorization

Topic (help)
Binary matrix factorization
Abbreviations: BMF
Variations:
Category: Binary matrix factorization
Parents:
Children:
Databases:
Search
Ontologies: MeSH NeuroLex Wikidata Wikipedia

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

$\mathbf{X | UWV}'$

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]

$\mathbf{X \approx WH}$

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.

##  References

1. Edward Meeds, Zoubin Ghahramani, Radford Neal, Sam Roweis(2006). "Modeling dyadic data with binary latent factors". Advances in Neural Information Processing Systems. [1]
2. 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.