标题： 矩阵完成与外推通过核回归 显示英文标题

标题： Matrix completion and extrapolation via kernel regression

摘要： 矩阵完成与外推（MCEX）在这里被处理为在再生核希尔伯特空间（RKHS）中，以便考虑可用数据中存在的先验信息。 旨在实现更快且低复杂度的求解器，该任务被公式化为核岭回归。 由此产生的MCEX算法还可以支持在线实现，而核函数类也涵盖了多个现有方法，这些方法利用先验信息进行矩阵完成（MC）。 在合成数据集和真实数据集上的数值测试表明，新方法比广泛使用的方法（如交替最小二乘法（ALS）或随机梯度下降（SGD））更快，并且恢复误差更小，尤其是在处理噪声数据时。 显示英文摘要

摘要： Matrix completion and extrapolation (MCEX) are dealt with here over reproducing kernel Hilbert spaces (RKHSs) in order to account for prior information present in the available data. Aiming at a faster and low-complexity solver, the task is formulated as a kernel ridge regression. The resultant MCEX algorithm can also afford online implementation, while the class of kernel functions also encompasses several existing approaches to MC with prior information. Numerical tests on synthetic and real datasets show that the novel approach performs faster than widespread methods such as alternating least squares (ALS) or stochastic gradient descent (SGD), and that the recovery error is reduced, especially when dealing with noisy data.