论文标题
新的惩罚标准，用于平滑的非负张量分解，缺少条目
New penalized criteria for smooth non-negative tensor factorization with missing entries
论文作者
论文摘要
张量分解模型广泛用于许多应用领域，例如化学计量学，心理计量学，计算机视觉或通信网络。现实生活数据收集通常会遇到错误，导致数据丢失。在这里，我们专注于理解如何处理此问题以进行非负张量分解。在缺少某些条目的情况下，我们研究了用于非负张量分解的几个标准。特别是我们展示了如何平滑性惩罚能够补偿缺失值的存在，以确保最佳的存在。这使我们提出了具有有效数值优化算法的新标准。进行数值实验以支持我们的主张。
Tensor factorization models are widely used in many applied fields such as chemometrics, psychometrics, computer vision or communication networks. Real life data collection is often subject to errors, resulting in missing data. Here we focus in understanding how this issue should be dealt with for nonnegative tensor factorization. We investigate several criteria used for non-negative tensor factorization in the case where some entries are missing. In particular we show how smoothness penalties can compensate the presence of missing values in order to ensure the existence of an optimum. This lead us to propose new criteria with efficient numerical optimization algorithms. Numerical experiments are conducted to support our claims.
