基于核函数的SVM机与三层前向神经网络的关系

针对尚未完全解决的SVM理论中求核函数的问题，首先证明了Vapnik的基于核函数的SVM机与三层前向神经网络的等价性；其次以作者提出的神经网络的覆盖算法为工具，证明了如下的定理（核函数存在性定理）；对任给的样本集（规模有限），必存在一函数（或相应的核函数），样本集在此函数映射下，映成某高维空间中的一子集（样本集的像集），在此高维空间中，像集是线性可分的；最后给出求解此函数的算法，算法的计算复杂性是多项式的，且算法求到的解在高维空间上是最大间隔解。

The Relationship Between Kernel Functions Based SVM and Three-Layer Feedforward Neural Networks

In this paper, the equivalent between kernel functions based SVM (Vapnik) and the three layer feedforward neural network is demonstrated. From the covering algorithms of neural networks that author proposed, a kernel function existence theorem is proved. The theory shows that given a set of training samples, there must exist a corresponding function such that the image of the training samples is linear separated in a high dimensional space under the mapping of the function. An algorithm of seeking the kernel functions is given. The computational complexity of the algorithm is polynomial growing with the sample size and the solution is the maximal margin one in the high dimensional space.