Author(s)

Qingquan Sun, Peng Wu, Yeqing Wu, Mengcheng Guo, Jiang Lu

Department of Electrical and Computer Engineering, The University of Alabama, Tuscaloosa, USA.
School of Information Engineering, Wuhan University of Technology, Wuhan, China.

Rank determination issue is one of the most significant issues in non-negative matrix factorization (NMF) research. However, rank determination problem has not received so much emphasis as sparseness regularization problem. Usually, the rank of base matrix needs to be assumed. In this paper, we propose an unsupervised multi-level non-negative matrix factorization model to extract the hidden data structure and seek the rank of base matrix. From machine learning point of view, the learning result depends on its prior knowledge. In our unsupervised multi-level model, we construct a three-level data structure for non-negative matrix factorization algorithm. Such a construction could apply more prior knowledge to the algorithm and obtain a better approximation of real data structure. The final bases selection is achieved through L₂-norm optimization. We implement our experiment via binary datasets. The results demonstrate that our approach is able to retrieve the hidden structure of data, thus determine the correct rank of base matrix.

Non-Negative Matrix Factorization; Bayesian Model; Rank Determination; Probabilistic Model

Q. Sun, P. Wu, Y. Wu, M. Guo and J. Lu, "Unsupervised Multi-Level Non-Negative Matrix Factorization Model: Binary Data Case," Journal of Information Security, Vol. 3 No. 4, 2012, pp. 245-250. doi: 10.4236/jis.2012.34031.