Forecasting project expenses is a crucial step for businesses to avoid budget overruns and project failures. Traditionally, this has been done by financial analysts or data science techniques such as time-series analysis. However, these approaches can be uncertain and produce results that differ from the planned budget, especially at the start of a project with limited data points. This paper proposes a constrained non-negative matrix completion model that predicts expenses by learning the likelihood of the project correlating with certain expense patterns in the latent space. The model is constrained on three probability simplexes, two of which are on the factor matrices and the third on the missing entries. Additionally, the predicted expense values are guaranteed to meet the budget constraint without the need of post-processing. An inexact alternating optimization algorithm is developed to solve the associated optimization problem and is proven to converge to a stationary point. Results from two real datasets demonstrate the effectiveness of the proposed method in comparison to state-of-the-art algorithms.

提出一种受限非负矩阵完成模型，通过学习项目与潜在空间中某些费用模式的相关性概率，预测费用，并且保证预测的费用值满足预算约束，无需后处理。通过对关联优化问题的不精确交替优化算法求解，证明其收敛于稳定点。两个真实数据集的结果表明该方法比现有算法更有效。

三重单纯形矩阵补全用于费用预测