Binary matrix factorization

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Binary matrix factorization
Abbreviations: BMF
Category: Binary matrix factorization

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

  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.
  3. Bao-Hong Shen, Shuiwang Ji, Jieping Ye(2009). "Mining discrete patterns via binary matrix factorization".
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