Facilitating the application of Support Vector Regression by using a universal Pearson VII function based kernel
Facilitating the application of Support Vector Regression by using a universal Pearson VII function based kernel
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DOI：
10.1016/j.chemolab.2005.09.003
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发表时间：
2006-03-15
影响因子：
3.9
通讯作者：
Buydens, LMC
中科院分区：
文献类型：
--
作者：
Üstün, B;Melssen, WJ;Buydens, LMC
在过去的几年里，支持向量机（svm）在解决分类和回归问题上的应用越来越多，特别是由于它具有高泛化性能和建模非线性关系的能力。后者只有在应用合适的核函数时才能实现。该核函数将非线性输入空间转换为高维特征空间，在高维特征空间中，问题的解可以表示为一个直接的线性分类或回归问题。然而，有很多可能的内核函数可以用来创建这样的高维特征空间。最常用的核函数是线性和多项式内积函数以及径向基函数（RBF）。由于数据的性质通常是未知的，因此很难事先从上述内核中做出适当的选择。因此，在模型构建过程中，通常会使用多个核来选择预测性能最好的核。不幸的是，这将导致一个非常耗时的优化过程。为了克服这一缺点，本文引入了一种基于Pearson VII函数的通用核函数。这个函数在光谱学领域是众所周知的。通过将其应用于模拟和现实世界的数据集，研究了该替代内核与常用内核相比的适用性、适用性、性能和鲁棒性。从这些检验的结果可以得出结论，PUK核是鲁棒的，并且与标准核函数相比具有相同甚至更强的映射能力，从而使svm具有相同或更好的泛化性能。一般来说，PUK可以用作通用核函数，能够作为通用线性、多项式和RBF核函数的通用替代方案。(c) 2005 Elsevier B.V.版权所有
In the last few years, application of Support Vector Machines (SVMs) for solving classification and regression problems has increased, in particular, due to its high generalization performance and its ability to model non-linear relationships. The latter can only be realised if a suitable kernel function is applied. This kernel function transforms the non-linear input space into a high dimensional feature space in which the solution of the problem can be represented as being a straight linear classification or regression problem. However, there are a lot of possible kernel functions that can be used to create such high dimensional feature space. The most commonly used kernel functions are the linear and polynomial inner-product functions and the Radial Basis Function (RBF). Since the nature of the data is usually unknown, it is very difficult to make, on beforehand, a proper choice out of the mentioned kernels. For this reason, during the model building process, usually more than one kernel is applied to select the one which gives the best prediction performance. Unfortunately, this will lead to a very time-consuming optimization procedure. To circumvent this disadvantage, a universal kernel function based on the Pearson VII function (PUK) is introduced in this paper. This function is well-known in the field of spectroscopy. The applicability, suitability, performance and robustness of this alternative kernel in comparison to the commonly applied kernels is investigated by applying this to simulated as well as real-world data sets. From the outcome of these examinations, it was concluded that the PUK kernel is robust and has an equal or even stronger mapping power as compared to the standard kernel functions leading to an equal or better generalization performance of SVMs. In general, PUK can be used as a universal kernel that is capable to serve as a generic alternative to the common linear, polynomial and RBF kernel functions. (c) 2005 Elsevier B.V. All rights reserved.