Matrix completion and extrapolation via kernel regression
This provides a more efficient solution for matrix completion tasks in data analysis, though it appears incremental as it builds on existing kernel-based methods.
The paper tackled matrix completion and extrapolation by formulating it as kernel ridge regression in reproducing kernel Hilbert spaces, resulting in a faster algorithm that reduces recovery error, especially with noisy data, as shown in tests on synthetic and real datasets.
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.