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Matrix Completion in the Unit Hypercube via Structured Matrix Factorization

机译:通过结构矩阵分解在单元HyperCube中完成矩阵完成

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摘要

Several complex tasks that arise in organizations can be simplified by mapping them into a matrix completion problem. In this paper, we address a key challenge faced by our company: predicting the efficiency of artists in rendering visual effects (VFX) in film shots. We tackle this challenge by using a two-fold approach: first, we transform this task into a constrained matrix completion problem with entries bounded in the unit interval; second, we propose two novel matrix factorization models that leverage our knowledge of the VFX environment. Our first approach, expertise matrix factorization (EMF), is an interpretable method that structures the latent factors as weighted user-item interplay. The second one, survival matrix factorization (SMF), is instead a probabilistic model for the underlying process defining employees' efficiencies. We show the effectiveness of our proposed models by extensive numerical tests on our VFX dataset and two additional datasets with values that are also bounded in the [0, 1] interval.
机译:通过将它们映射到矩阵完成问题,可以简化组织中出现的几个复杂任务。在本文中,我们解决了公司所面临的关键挑战:预测艺术家在胶片镜头中的视觉效果(VFX)的效率。我们通过使用双倍方法来解决这一挑战:首先,我们将此任务转换为在单元间隔中界定的条目的约束矩阵完成问题;其次,我们提出了两种新的矩阵分解模型,可以利用我们对VFX环境的了解。我们的第一种方法,专业知识矩阵分解(EMF)是一种可解释的方法,可以将潜在的因素构成作为加权用户项目的相互作用。第二个,生存矩阵分解(SMF)是潜在的过程,用于定义员工效率的底层过程。我们在VFX数据集和两个附加数据集中展示了我们提出的模型的有效性,以及两个具有在[0,1]间隔中的值的附加数据集。

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