In this paper, we consider the generalized nonnegative tensor factorization (GNTF) problem, which arises in multiple-tissue gene expression and multi-target tracking. Based on the Karhsh-Kuhn-Tucker conditions, the necessary condition of the local solution for the GNTF problem is given. The proximal alternating nonnegative least squares method is designed to solve it, and its convergence theorem is also derived. Numerical examples show that the new method is feasible and effective.

中文翻译：

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广义非负张量分解问题的数值方法

在本文中，我们考虑了广义非负张量因子分解（GNTF）问题，该问题出现在多组织基因表达和多目标跟踪中。基于Karhsh-Kuhn-Tucker条件，给出了GNTF问题局部解的必要条件。设计了近端交替非负最小二乘法求解，并推导了其收敛定理。数值算例表明，该方法是可行和有效的。