The Decision of the Optimal Rank of a Non-negative Matrix Factorization Model for Gene Expression Datasets Utilizing Unit Invariant Knee Method

BackgroundThere is a great need to develop a computational approach to analyze and exploit the information contained in gene expression data. Recent utilization of non-negative matrix factorization (NMF) in computational biology has served its capability to derive essential details from a high amount of data in particular gene expression microarrays. ObjectiveA common problem in NMF is finding the proper number rank (r) of factors. Thus, various techniques have been suggested to select the optimal value of rank factorization (r). MethodThis study focused on the unit invariant knee (UIK) method to calculate factorization rank (basis vector) of the non-negative matrix factorization (NMF) of gene expression data sets is employed. Because the UIK method requires an extremum distance estimator (EDE) that is eventually employed for inflection and identification of a knee point, this study finds the first inflection point of curvature of RSS of the proposed algorithms using the UIK method on gene expression datasets as a target matrix. ResultsComputation was conducted for the UIK task using the esGolub data set of R studio, and consequently, the distinct results of NMF was subjected to compare on different algorithms. The proposed UIK method is easy to perform, free of a priori rank value input, and does not require initial parameters that significantly influence the models functionality. ConclusionThis study demonstrates that the UIK method provides a credible prediction for both gene expression data and precisely estimating of simulated mutational processes data with known dimensions.