Abstract
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 Z = X ⊤ Y, with the constraint that X = Y. 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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Hu, EL., Kwok, J.T. (2013). Flexible Nonparametric Kernel Learning with Different Loss Functions. In: Lee, M., Hirose, A., Hou, ZG., Kil, R.M. (eds) Neural Information Processing. ICONIP 2013. Lecture Notes in Computer Science, vol 8227. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-42042-9_15
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DOI: https://doi.org/10.1007/978-3-642-42042-9_15
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