Ridgelet kernel regression
Ridgelet kernel regression
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DOI：
10.1016/j.neucom.2006.05.015
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发表时间：
2007-10
期刊：
影响因子：
6
通讯作者：
Shuyuan Yang;Min Wang;L. Jiao
中科院分区：
文献类型：
--
作者：
Shuyuan Yang;Min Wang;L. Jiao
本文提出了一种脊波核回归方法来逼近多维函数，特别是具有某种空间不均匀性的多维函数。该方法是基于脊波理论，核和正则化技术，从我们可以推导出一个正则核回归形式。通过表示这种形式与二次规划和获得的解决方案，以定义一个适应度函数，我们使用粒子群优化优化脊波的方向。脊波的性质保证了该方法在逼近多维函数时的稳定性，以及对线性奇异函数的优越性。此外，该模型中采用的正则化技术导致更小的泛化误差。在回归和分类任务中的实验表明了该方法的有效性。
A ridgelet kernel regression method is presented in this paper to approximate multi-dimensional functions, especially those with certain kinds of spatial inhomogeneities. This method is based on ridgelet theory, kernel and regularization techniques from which we can deduce a regularized kernel regression form. By representing this form with quadratic programming and taking the obtained solution to define a fitness function, we use particle swarm optimization to optimize the directions of ridgelets. The properties of ridgelet can guarantee the stability of this method in approximating multi-dimensional functions, as well as its superiority for functions with linear singularities. Additionally, the regularized technique employed in this model leads to smaller generalization error. Experiments in the tasks of regression and classification show its effectiveness.