Nonnegative matrix factorization is comprehensively used in recommendation systems. In an effort to reduce the recommended cost of newly added samples, incremental nonnegative matrix factorization and its variants have been extensively studied in recommendation systems. However, the recommendation performance is incapable of particular applications in terms of data sparsity and sample diversity. In this paper, we propose a new incremental recommend algorithm by improving incremental nonnegative matrix factorization based on three-way decision, called Three-way Decision Recommendations Based on Incremental Non-negative Matrix Factorization (3WD-INMF), in which the concept of positive, negative, and boundary regions are employed to update the new coming samples’ features. Finally, experiments on six public data sets demonstrate the error induced by 3WD-INMF is decreasing as the addition of new samples and deliver state-of-the-art performance compared with existing recommendation algorithms. The results indicate our method is more reasonable and efficient by leveraging the idea of three-way decision to perform the recommendation decision process.

非负矩阵分解广泛应用于推荐系统。为了降低新添加样本的推荐成本，推荐系统中广泛研究了增量非负矩阵分解及其变体。然而，推荐性能在数据稀疏性和样本多样性方面无法满足特定应用需求。在本文中，我们通过改进基于三向决策的增量非负矩阵分解提出了一种新的增量推荐算法，称为基于增量非负矩阵分解的三向决策推荐（3WD-INMF），其中正的概念、负和边界区域被用来更新新样本的特征。最后，在六个公共数据集上的实验表明，与现有推荐算法相比，随着新样本的添加和提供最先进的性能，3WD-INMF 引起的错误正在减少。结果表明，通过利用三向决策的思想来执行推荐决策过程，我们的方法更加合理和有效。