Side information is highly useful in the learning of a nonparametric kernel matrix. However, this often leads to an expensive semidefinite program (SDP). In recent years, a number of dedicated solvers have been proposed. Though much better than off-the-shelf SDP solvers, they still cannot scale to large data sets. In this paper, we propose a novel solver based on the alternating direction method of multipliers (ADMM). The key idea is to use a low-rank decomposition of the kernel matrix $\K = \V^\top \U$, with the constraint that $\V=\U$. The resultant optimization problem, though non-convex, has favorable convergence properties and can be efficiently solved without requiring eigen-decomposition in each iteration. Experimental results on a number of real-world data sets demonstrate that the proposed method is as accurate as directly solving the SDP, but can be one to two orders of magnitude faster.

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