基于特征距离的组合核矩阵模型选择标准

核矩阵的组合方法是核函数构造和核方法学习的崭新的、重要的方法。目前，组合核矩阵的模型选择标准并不多见，应用较多的是核目标匹配，但该标准并不严格，尚具有较大的冗余性。针对这一问题，本文提出一个有效的基于特征距离的组合核矩阵模型选择标准。本文首先讨论核目标匹配标准及其局限性，然后提出基于特征距离的核矩阵模型型选择标准并分析该标准的计算性能，最后通过实验验证所提出的模型选择标准在核参数选择和组合系数选择两方面的效能。理论分析和实验结果表明，所提出的基于特征距
离的组合核矩阵模型选择标准是合理且有效的。

A Feature-Distance-Based Model Selection Criterion for the Combinatorial Kernel Matrix

Combinatorial construction is an effective and promising kernel construction approach.We study a criterion for selecting an optimal combinatorial kernel matrix in the feature space.Different from the previously popular kernel target alignment criteria,the new criterion overcomes the limitation and measures the performance of a combinatorial kernel matrix based on feature distance.We first introduce the kernel target alignment and discuss its limitation for the combinatorial kernel matrix.Then we present the feature-distance-based combinatorial kernel matrix evaluation criterion formally.Finally,we analyze the properties of the proposed criterion and examine its performance based on the simulated data.Both the theoretical analysis and the experimental results demonstrate that the proposed combinatorial kernel matrix evaluation criterion is sound and effective.