Baudat G, Anouar F
Mars Electronics International, Geneva, Switzerland.
Neural Comput. 2000 Oct;12(10):2385-404. doi: 10.1162/089976600300014980.
We present a new method that we call generalized discriminant analysis (GDA) to deal with nonlinear discriminant analysis using kernel function operator. The underlying theory is close to the support vector machines (SVM) insofar as the GDA method provides a mapping of the input vectors into high-dimensional feature space. In the transformed space, linear properties make it easy to extend and generalize the classical linear discriminant analysis (LDA) to nonlinear discriminant analysis. The formulation is expressed as an eigenvalue problem resolution. Using a different kernel, one can cover a wide class of nonlinearities. For both simulated data and alternate kernels, we give classification results, as well as the shape of the decision function. The results are confirmed using real data to perform seed classification.
我们提出了一种新方法，我们称之为广义判别分析（GDA），用于使用核函数算子处理非线性判别分析。其基础理论与支持向量机（SVM）相近，因为GDA方法将输入向量映射到高维特征空间。在变换后的空间中，线性特性使得将经典线性判别分析（LDA）扩展并推广到非线性判别分析变得容易。该公式表示为一个特征值问题的求解。使用不同的核，可以涵盖广泛的非线性情况。对于模拟数据和替代核，我们给出了分类结果以及决策函数的形状。使用真实数据进行种子分类证实了这些结果。
