Abstract
As is well-known, collinearity in data sets has long been recognized as a factor that significantly influences data mining processes in various aspects, particularly in high-dimensional cases. To effectively address this issue, especially in contemporary models where collinearity often arises, we aim to modify a classic data compression technique. Specifically, our study focuses on the least-squares model of the nonnegative matrix factorization (NMF) problem, with the goal of improving the condition number of the decomposition elements. This improvement is intended to reduce the collinearity level in the resulting output matrices. Our approach involves embedding penalty terms into the traditional NMF model, integrating two recently proposed penalty frameworks to form a hybrid model. To solve this extended model, we develop a revised version of the Hestenes–Stiefel (HS) conjugate gradient (CG) algorithm, by modifying the classic parameter of the algorithm while ensuring that its anti-jamming property is preserved. We further discuss how such a modification reinforces the anti-jamming characteristic of the HS method. We test our theoretical claims on both standard benchmark problems and randomly generated test problems, evaluating the results to assess the effectiveness of our approach. The findings generally demonstrate that the proposed modifications yield promising results.