Classifying matrices with a spectral regularization
Classifying matrices with a spectral regularization
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DOI：
10.1145/1273496.1273609
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发表时间：
2007-06
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通讯作者：
Ryota Tomioka;K. Aihara
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文献类型：
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作者：
Ryota Tomioka;K. Aihara
我们提出了一种矩阵分类的方法。我们使用线性分类器和基于其系数矩阵的谱 l1-范数的新颖正则化方案。谱正则化不仅提供了复杂性控制的原则性方法，而且还能够自动确定系数矩阵的秩。使用线性矩阵不等式技术，我们将推理任务表述为单个凸优化问题。我们将我们的方法应用于运动想象脑电图分类问题。该方法不仅在分类性能上改进了传统方法，而且无需任何额外的特征提取步骤即可确定信号中集中判别信息的子空间。通过改变损失函数，该方法可以很容易地推广到回归问题。还讨论了与其他方法的连接。
We propose a method for the classification of matrices. We use a linear classifier with a novel regularization scheme based on the spectral l1-norm of its coefficient matrix. The spectral regularization not only provides a principled way of complexity control but also enables automatic determination of the rank of the coefficient matrix. Using the Linear Matrix Inequality technique, we formulate the inference task as a single convex optimization problem. We apply our method to the motor-imagery EEG classification problem. The method not only improves upon conventional methods in the classification performance but also determines a subspace in the signal that concentrates discriminative information without any additional feature extraction step. The method can be easily generalized to regression problems by changing the loss function. Connections to other methods are also discussed.