Abstract

We consider the problem of inductive matrix completion, i.e., the reconstruction of a matrix using side features of its rows and columns. In numerous applications, however, side information of this kind includes redundant or uninformative features, so feature selection is required. An approach based on matrix factorization with group LASSO regularization on the coefficients of the side features is proposed, which combines feature selection with matrix completion. It is proved that the theoretical sample complexity for the proposed approach is lower than for methods without sparsifying. A computationally efficient iterative procedure for simultaneous matrix completion and feature selection is proposed. Experiments on synthetic and real-world data demonstrate that, due to the feature selection procedure, the proposed approach outperforms other methods.

中文翻译：

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具有特征选择的归纳矩阵补全

摘要

我们考虑归纳矩阵补全的问题，即使用矩阵的行和列的边特征重建矩阵。然而，在许多应用中，这种辅助信息包括冗余或无信息特征，因此需要进行特征选择。提出了一种基于矩阵分解和侧特征系数组LASSO正则化的方法，将特征选择与矩阵补全相结合。事实证明，所提出的方法的理论样本复杂度低于没有稀疏化的方法。提出了一种用于同时矩阵完成和特征选择的计算高效的迭代过程。合成数据和真实数据的实验表明，由于特征选择过程，