中文摘要：

研究一类特殊的矩阵分解问题：对由多个对象在一组连续时间点上产生的数据构成的矩阵R，寻求把它近似地分解为两个低秩矩阵U和V的乘积，即R≈U^T×V．有为数众多的时间序列分析问题都可归结为所研究问题的求解，如金融数据矩阵的因子分析、缺失交通流数据的估计等．提出了该问题的概率图模型，进而由此导出了其约束优化模型，最终给出了模型的求解算法．在不同的数据集上进行实验验证了该模型的有效性．

英文摘要：

The paper studies a matrix faetorization problem for time series data, where the target matrix R consists of the equal length time series data generated by a set of objects. The goal is to find two low rank matrices U and V, such that R≈U^T×V. Many time series analysis problems, such as finance data analysis and missing traffic data imputation, can be reduced to the proposed model. A probabilistic graphical representation for the problem is proposed, and a constrained optimization model from the graphical representation is derived. The solution algorithms for the proposed model is also presented. Empirical studies show that the proposed model is superior to the baselines.