Andri Mirzal , A. Mirzal is with the Faculty of Computing, Universiti Teknologi Malaysia, 81310 Johor Bahru, Malaysia.(email:email@example.com)
The Tikhonov regularized nonnegative matrix factorization (TNMF) is an NMF objective function that enforces smoothness on the computed solutions, and has been successfully applied to many problem domains including text mining, spectral data analysis, and cancer clustering. There is, however, an issue that is still insufficiently addressed in the development of TNMF algorithms, i.e., how to develop mechanisms that can learn the regularization parameters directly from the datasets. The common approach is to use fixed values based on a priori knowledge about the problem domains. However, from the linear inverse problems study it is known that the quality of the solutions of the Tikhonov regularized least square problems depends heavily on the choosing of appropriate regularization parameters. Since least squares are the building blocks of the NMF, it can be expected that similar situation also applies to the NMF. In this paper, we propose two formulas to automatically learn the regularization parameters from the dataset based on the L-curve approach. We also develop a convergent algorithm for the TNMF based on the additive update rules. Finally, we demonstrate the use of the proposed algorithm in cancer clustering tasks.
Andri Mirzal, "Nonparametric Tikhonov Regularized NMF and Its Application in Cancer Clustering", IEEE/ACM Transactions on Computational Biology and Bioinformatics, , no. 1, pp. 1, PrePrints PrePrints, doi:10.1109/TCBB.2014.2328342