Stellar Spectral Subclasses Classification Based on Fisher Criterion and Manifold Learning

Linear Discriminant Analysis (LDA) and Locality Preserving Projections (LPP) are two widely used feature extraction methods. The advantage of LDA is that it takes the global structure of the data into consideration by maximizing the ratio of the between-class scatter to the within-class scatter. LPP tries to preserve the local structure of the data. The global and local structure of the data are very important in dealing with feature extraction problems but it is regretful that the above two methods cannot fully utilize all the information. In view of this, Modified Discriminant Analysis based on Fisher Criterion and Manifold Learning (MDA) is proposed in this paper. Two important concepts are introduced: Manifold based Within-Class Scatter (MWCS) and Manifold based Between-Class Scatter (MBCS). MDA aims to find an optimal projection matrix by maximizing the ratio of MBCS to MWCS based on Fisher criterion. In this paper, we will investigate the performance of MDA in the stellar spectral subclasses classification. We first reduce the dimension of spectra data by PCA (Principal Component Analysis), LDA, LPP, and MDA, respectively. Then we apply support vector machine (SVM) to classify the four subclasses of K-type spectra, three subclasses of F-type spectra, and three subclasses of G-type spectra from Sloan Digital Sky Survey (SDSS). The comparative experiment results verify MDA can preserve both the local and global structure of the data when embed the original data into much lower dimensional space.