Classification of stellar spectra with SVM based on within-class scatter and between-class scatter

  • Zhong-bao LiuEmail author
  • Fang-xiao Zhou
  • Zhen-tao Qin
  • Xue-gang Luo
  • Jing Zhang
Original Article


Support Vector Machine (SVM) is a popular data mining technique, and it has been widely applied in astronomical tasks, especially in stellar spectra classification. Since SVM doesn’t take the data distribution into consideration, and therefore, its classification efficiencies can’t be greatly improved. Meanwhile, SVM ignores the internal information of the training dataset, such as the within-class structure and between-class structure. In view of this, we propose a new classification algorithm-SVM based on Within-Class Scatter and Between-Class Scatter (WBS-SVM) in this paper. WBS-SVM tries to find an optimal hyperplane to separate two classes. The difference is that it incorporates minimum within-class scatter and maximum between-class scatter in Linear Discriminant Analysis (LDA) into SVM. These two scatters represent the distributions of the training dataset, and the optimization of WBS-SVM ensures the samples in the same class are as close as possible and the samples in different classes are as far as possible. Experiments on the K-, F-, G-type stellar spectra from Sloan Digital Sky Survey (SDSS), Data Release 8 show that our proposed WBS-SVM can greatly improve the classification accuracies.


Support Vector Machine (SVM) Linear Discriminant Analysis (LDA) Within-class scatter Between-class scatter 



This work was supported by the National Nature Science Foundation of China (61202311, U1731128), the Natural Science Foundation of Shanxi (201601D011042), the Program for Outstanding Innovative Team of High Learning Institutions of Shanxi and the Outstanding Youth Funds of North University of China.


  1. Bailer-Jones, C.A.L., Irwin, M., Hippel, T.V.: Mon. Not. R. Astron. Soc. 298(2), 361 (1998) ADSCrossRefGoogle Scholar
  2. Bazarghan, M.: Astrophys. Space Sci. 337(1), 93 (2012) ADSCrossRefGoogle Scholar
  3. Bazarghan, M., Gupta, R.: Astrophys. Space Sci. 315, 201 (2008) ADSCrossRefGoogle Scholar
  4. Bolton, A.S., Schlegel, D.J., Aubourg, E., et al.: Astron. J. 144(5), 507 (2012) CrossRefGoogle Scholar
  5. Bora, A., Gupta, R., Harinder, P.S., et al.: Mon. Not. R. Astron. Soc. 384(2), 827 (2008) ADSCrossRefGoogle Scholar
  6. Bu, Y.D., Pan, J.C., Jiang, B., et al.: Publ. Astron. Soc. Jpn. 65(4), 173 (2013) Google Scholar
  7. Bu, Y.D., Chen, F.Q., Pan, J.C.: New Astron. 28, 35 (2014) ADSCrossRefGoogle Scholar
  8. Gray, R.O., Corbally, C.J.: Astron. J. 147(4), 80 (2014) ADSCrossRefGoogle Scholar
  9. Gulati, R., Gupta, R.A., Gothoskar, P., et al.: Astrophys. J. 426, 340 (1994) ADSCrossRefGoogle Scholar
  10. Gupta, R., Harinder, P.S., Volk, K., et al.: Astrophys. J. Suppl. 152(2), 201 (2004) ADSCrossRefGoogle Scholar
  11. Harinder, P.S., Gulati, R.K., Gupta, R.: Mon. Not. R. Astron. Soc. 295(2), 312 (2018) Google Scholar
  12. Hernandez, R.D., Barreto, H.P., Robles, L.A., et al.: Exp. Astron. 38(1), 193 (2014) ADSCrossRefGoogle Scholar
  13. Jiang, B., Li, Z.X., Qu, M.X., et al.: Spectrosc. Spectr. Anal. 36(7), 2275 (2016) Google Scholar
  14. Liu, Z.B.: J. Astrophys. Astron. 37(2), 9 (2016) ADSCrossRefGoogle Scholar
  15. Liu, Z.B., Song, L.P., Zhao, W.J.: Mon. Not. R. Astron. Soc. 455(4), 4289 (2016) ADSCrossRefGoogle Scholar
  16. Qin, D.M., Hu, Z.Y., Zhao, Y.H.: Spectrosc. Spectr. Anal. 24(4), 507 (2004) Google Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  • Zhong-bao Liu
    • 1
    • 2
    Email author
  • Fang-xiao Zhou
    • 1
  • Zhen-tao Qin
    • 1
  • Xue-gang Luo
    • 1
  • Jing Zhang
    • 1
  1. 1.School of Mathematics and Computer SciencePanzhihua UniversityPanzhihuaChina
  2. 2.School of SoftwareNorth University of ChinaTaiyuanChina

Personalised recommendations