中文说明：逼近非线性内核使用特征映射获得了大量的利息在近年来由于在减少培训和测试次数支持向量机分类器和其他基于核的学习算法中的应用。我们将这条线的工作和目前的低失真嵌入的点积内核扩展到线性的欧几里得空间。我们我们的研究结果基于谐波分析表征所有的点积内核中的经典理论结果，并使用它来定义随机的特征映射到本机的点积为近似值的点积内核提供高信任度的显式低维欧几里得空间。
English Description：
Approximating non-linear kernels using feature maps has gained a lot of interest in recent years due to applications in reducing training and testing times of SVM classifiers and other kernel based learning algorithms. We extend this line of work and present low distortion embeddings for dot product kernels into linear Euclidean spaces. We base our results on a classical result in harmonic analysis characterizing all dot product kernels and use it to define randomized feature maps into explicit low dimensional Euclidean spaces in which the native dot product provides an approximation to the dot product kernel with high confidence.