核选择直接影响核方法的性能.已有高斯核选择方法的计算复杂度为Ω(n2),阻碍大规模核方法的发展.文中提出高斯核选择的线性性质检测方法,不同于传统核选择方法,询问复杂度为O(ln(1/δ)/∈2),计算复杂度独立于样本规模.文中首先给出函数∈线性水平的定义,证明可使用∈线性水平近似度量一个函数与线性函数类之间的距离,并以此为基础提出高斯核选择的线性性质检测准则.然后应用该准则,在随机傅里叶特征空间中有效评价并选择高斯核.理论分析与实验表明,应用性质检测以实现高斯核选择的方法有效可行.%Kernel selection is critical to the performance of kernel methods. The computational complexity of the existing approaches to Gaussian kernel selection is Ω( n2 ) . Therefore, it is an impediment to the development of large-scale kernel methods. To address this issue, a linearity property testing approach to Gaussian kernel selection is proposed. Completely different from the existing approaches, the proposed approach only needs O( ln(1/δ)/∈2 ) query complexity, and its computational complexity is independent of the sample size. Firstly, a concept called ∈linearity level is defined. It is proved that ∈linearity level can approximate the distance between a function and the linear function class, and the linearity property testing criterion for Gaussian kernel selection is presented via the concept of ∈linearity level and the approximate distance. The linearity property testing criterion can be applied in random Fourier feature space to assess and select a suitable Gaussian kernel. Theoretical and experimental results demonstrate that the linearity property testing approach to Gaussian kernel selection is feasible and effective.
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