基于广义判别分析的光谱分类

提出了基于广义判别分析(generalized discriminant analysis, GDA)方法对恒星(Star)、星系(Galaxy)和类星体(Quasars)的光谱进行分类。广义判别分析将核技巧与Fisher判别分析结合起来，通过非线性映射将样本集映射到高维特征空间F，在F空间中进行线性判别分析。实验对比了LDA, GDA, PCA, KPCA算法对于恒星、星系和类星体的光谱分类性能。结果表明基于GDA的算法对于这3种类型光谱的分类正确率最高，LDA次之;尽管KPCA也是一种基于核的方法，但是选择主成分个数较少时效果较差，甚至低于LDA;基于PCA的分类效果最差。

Spectra Classification Based on Generalized Discriminant Analysis

A kernel based generalized discriminant analysis(GDA) technique is proposed for the classification of stars,galaxies,and quasars.GDA combines the LDA algorithm with kernel trick,and samples are projected by nonlinear mapping onto the feature space F with high dimensions,and then LDA is conducted in F.Also,it could be inferred that GDA which combines the extension of Fisher's criterion with kernel trick is complementary to kernel Fisher discriminant framework.LDA,GDA,PCA and KPCA were experimentally compared with these three different kinds of spectra.Among these four techniques,GDA obtains the best result,followed by LDA,and PCA is the worst.Although KPCA is also a kernel based technique,its performance is not satisfactory if the selected number of the principal components is small,and in some cases,it appears even worse than LDA,a non-kernel based technique.