Discriminant kernel and regularization parameter learning via semidefinite programming
Discriminant kernel and regularization parameter learning via semidefinite programming
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DOI：
10.1145/1273496.1273634
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发表时间：
2007-06
期刊：
影响因子：
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通讯作者：
Jieping Ye;Jianhui Chen;Shuiwang Ji
中科院分区：
文献类型：
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作者：
Jieping Ye;Jianhui Chen;Shuiwang Ji
正则化核判别分析（RKDA）通过核技巧在特征空间中执行线性判别分析。RKDA的性能取决于内核的选择。在本文中，我们考虑的问题，学习一个最佳的核在一个凸集的内核。我们表明，内核学习问题可以制定为一个半定规划（SDP）在二进制类的情况下。我们进一步扩展的SDP制定多类的情况下。它是基于本文建立的一个关键结果，即多类核学习问题可以分解成一组二进制类核学习问题。此外，我们提出了一个近似方案，以减少计算复杂性的多类SDP制定。RKDA的性能还取决于正则化参数的值。我们表明，这个值可以在框架中自动学习。基准数据集上的实验结果表明，所提出的SDP配方的有效性。
Regularized Kernel Discriminant Analysis (RKDA) performs linear discriminant analysis in the feature space via the kernel trick. The performance of RKDA depends on the selection of kernels. In this paper, we consider the problem of learning an optimal kernel over a convex set of kernels. We show that the kernel learning problem can be formulated as a semidefinite program (SDP) in the binary-class case. We further extend the SDP formulation to the multi-class case. It is based on a key result established in this paper, that is, the multi-class kernel learning problem can be decomposed into a set of binary-class kernel learning problems. In addition, we propose an approximation scheme to reduce the computational complexity of the multi-class SDP formulation. The performance of RKDA also depends on the value of the regularization parameter. We show that this value can be learned automatically in the framework. Experimental results on benchmark data sets demonstrate the efficacy of the proposed SDP formulations.