流形判别分析和支持向量机的恒星光谱数据自动分类方法

尽管经典的分类方法支持向量机SVM在天文学领域广泛应用，但其只考虑类间的绝对间隔而忽略类内的分布性状，因而分类性能有待于进一步提升。鉴于此，提出一种新颖的基于流形判别分析和支持向量机的恒星光谱数据自动分类方法。该方法引入流形判别分析的两个重要概念：基于流形的类内离散度M_W和基于流形的类间离散度M_B。所提方法找到的分类面同时保证M_W最小且M_B最大。可建立相应最优化问题，然后将原最优化问题转化为QP对偶形式求得支持向量和判别函数，最后利用判别函数判断测试样本的类属。该方法的最大优势在于进行分类决策时，不仅考虑样本的类间信息和分布特征，而且还保持了各类的局部流形结构。SDSS恒星光谱数据上的比较实验表明该方法的有效性。

Automatic Classification Method of Star Spectra Data Based on Manifold-Based Discriminant Anaysis and Support Vector Machine

Although Support Vector Machine (SVM) is widely used in astronomy, it only takes the margin between classes into consideration while neglects the data distribution in each class, which seriously limits the classification efficiency. In view of this, a novel automatic classification method of star spectra data based on manifold-based discriminant analysis (MDA) and SVM is proposed in this paper. Two important concepts in MDA, manifold-based within-class scatter (MWCS) and manifold-based between-class scatter (MBCS), are introduced in the proposed method, the separating hyperplane found by which ensures MWCS is minimized and MBCS is maximized. Based on the above analysis, the corresponding optimal problem can be established, and then MDA transforms the original optimization problem to the QP dual form and we can obtain the support vectors and decision function. The classes of test samples are decided by the decision function. The advantage of the proposed method is that it not only focuses on the information between classes and distribution characteristics, but also preserves the manifold structure of each class. Experiments on SDSS star spectra datasets verify the effectiveness of the proposed method.