Learning the kernel matrix in discriminant analysis via quadratically constrained quadratic programming
Learning the kernel matrix in discriminant analysis via quadratically constrained quadratic programming
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DOI：
10.1145/1281192.1281283
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发表时间：
2007-08
期刊：
影响因子：
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通讯作者：
Jieping Ye;Shuiwang Ji;Jianhui Chen
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文献类型：
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作者：
Jieping Ye;Shuiwang Ji;Jianhui Chen
核函数在核方法中起着核心作用。在本文中，我们考虑的核矩阵的自动学习在一个凸组合的预先指定的核矩阵正则核判别分析（RKDA），它执行线性判别分析的特征空间通过核技巧。以前的研究表明，这个核学习问题可以用半定规划（SDP）来表示，但即使内点方法取得了最新的进展，这在计算上也是昂贵的。基于RKDA和最小二乘问题之间的等价关系，在二进制类的情况下，我们提出了一个二次约束二次规划（QCQP）制定的核学习问题，它可以更有效地解决比SDP。虽然大多数现有的工作只处理二进制类问题的内核学习，我们表明，我们的QCQP制定可以自然地扩展到多类的情况下。在二进制和多类基准数据集上的实验结果表明了所提出的QCQP公式的有效性。
The kernel function plays a central role in kernel methods. In this paper, we consider the automated learning of the kernel matrix over a convex combination of pre-specified kernel matrices in Regularized Kernel Discriminant Analysis (RKDA), which performs lineardiscriminant analysis in the feature space via the kernel trick. Previous studies have shown that this kernel learning problem can be formulated as a semidefinite program (SDP), which is however computationally expensive, even with the recent advances in interior point methods. Based on the equivalence relationship between RKDA and least square problems in the binary-class case, we propose a Quadratically Constrained Quadratic Programming (QCQP) formulation for the kernel learning problem, which can be solved more efficiently than SDP. While most existing work on kernel learning deal with binary-class problems only, we show that our QCQP formulation can be extended naturally to the multi-class case. Experimental results on both binary-class and multi-class benchmarkdata sets show the efficacy of the proposed QCQP formulations.