Z. Yang, Z. Zhu and E. Oja, “Automatic Rank Determination in Projective Non-negative Matrix Factorization,” Proceedings of 9th International Conference on LVA/ICA, St. Malo, 27-30 September 2010, pp. 514-521.

has been cited by the following article:

• TITLE: Unsupervised Multi-Level Non-Negative Matrix Factorization Model: Binary Data Case

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

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

  JOURNAL NAME: Journal of Information Security, Vol.3 No.4, October 31, 2012

  ABSTRACT: 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.