Adaptive factorization rank selection-based NMF and its application in tumor recognition

The nonnegative matrix factorization (NMF) has been widely used because it can accomplish both feature representation learning and dimension reduction. However, there are two critical and challenging issues affecting the performance of NMF models. One is the selection of matrix factorization rank, while most of the existing methods are based on experiments or experience. For tackling this issue, an adaptive and stable NMF model is constructed based on an adaptive factorization rank selection (AFRS) strategy, which skillfully and simply integrates a row constraint similar to the generalized elastic net. The other is the sensitivity to the initial value of the iteration, which seriously affects the result of matrix factorization. This issue is alleviated by complementing NMF and deep learning each other and avoiding complex network structure. The proposed NMF model is called deep AFRS-NMF model for short, and the corresponding optimization solution, convergence and stability are analyzed. Moreover, the statistical consistency is discussed between the rank obtained by the proposed model and the ideal rank. The performance of the proposed deep AFRS-NMF model is demonstrated by applying in genetic data-based tumor recognition. Experiments show that the factorization rank obtained by the deep AFRS-NMF model is stable and superior to classical and state-of-the-art methods.