Skip to main content

Features Spaces with Reduced Variables Based on Nearest Neighbor Relations and Their Inheritances

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12861))

Abstract

Generation of useful variables in the features spaces is an important issue throughout the neural networks, the machine learning and artificial intelligence for their efficient and discriminative computations. In this paper, the nearest neighbor relations are proposed for the minimal generation and the reduced variables for the feature spaces. First, the nearest neighbor relations are shown to be minimal independent and inherited for the construction of the feature space. For the analysis, convex cones are made of the nearest neighbor relations, which are independent vectors for the generation of the reduced variables. Then, edges of convex cones are compared for the discrimination of variables. Finally, feature spaces with the reduced variables based on the nearest neighbor relations are shown to be useful for the real documents classification.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Bansal, N., Chen, X., Wang, Z.: Can We gain more from orthogonality regularizations in training deep networks? In: Bengio, S., Wallach, H.M., Larochelle, H., Grauman, K., Cesa-Bianchi, N., Garnett, R. (eds.) Advances in Neural Information Processing Systems 31: Annual Conference on Neural Information Processing Systems 2018, NeurIPS 2018, 3–8 December 2018, Montréal, Canada, pp. 4266–4276 (2018). https://proceedings.neurips.cc/paper/2018/hash/bf424cb7b0dea050a42b9739eb261a3a-Abstract.html

  2. Bishop, C.M.: Pattern Recognition and Machine Learning (Information Science and Statistics). Springer, Heidelberg (2006). https://www.springer.com/jp/book/9780387310732

  3. Cover, T., Hart, P.: Nearest neighbor pattern classification. IEEE Trans. Inf. Theory 13(1), 21–27 (1967)

    Article  Google Scholar 

  4. Hu, S.T.: Threshold Logic. University of California Press, Berkeley (1965)

    Google Scholar 

  5. Ishii, N., Torii, I., Iwata, K., Odagiri, K., Nakashima, T.: Generation of reducts and threshold functions using discernibility and indiscerniblity matrices. In: 2017 IEEE 15th International Conference on Software Engineering Research, Management and Applications (SERA), pp. 55–61 (2017). https://ieeexplore.ieee.org/document/7965707

  6. Kuhn, H.W., Tucker, A.W.: On systems of linear inequalities. In: Linear Inequalities and Related Systems (AM-38), vol. 38, pp. 99–156. Princeton University Press (1966)

    Google Scholar 

  7. Porter, M.F.: An algorithm for suffix stripping. Program Electron. Libr. Inf. Syst. 40(3), 130–137 (1980). https://www.emerald.com/insight/content/doi/10.1108/eb046814/full/html

  8. Reuters-21578 Text Categorization Collection. https://kdd.ics.uci.edu/databases/reuters21578/reuters21578.html

  9. Shi, W., Gong, Y., Cheng, D., Tao, X., Zheng, N.: Entropy and orthogonality based deep discriminative feature learning for object recognition. Pattern Recogn. 81, 71–80 (2018). https://www.sciencedirect.com/science/article/pii/S0031320318301262

  10. Skowron, A., Polkowski, L.: Decision algorithms: a survey of rough set - theoretic methods. Fundam. Informaticae 30, 345–358 (1997)

    Article  Google Scholar 

  11. Wang, J., Chen, Y., Chakraborty, R., Yu, S.X.: Orthogonal convolutional neural networks. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), June 2020

    Google Scholar 

  12. Zhang, S., Jiang, H., Dai, L.: Hybrid orthogonal projection and estimation (HOPE): a new framework to learn neural networks. J. Mach. Learn. Res. 17(37), 1–33 (2016). http://jmlr.org/papers/v17/15-335.html

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Naohiro Ishii .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Ishii, N., Iwata, K., Mukai, N., Odagiri, K., Matsuo, T. (2021). Features Spaces with Reduced Variables Based on Nearest Neighbor Relations and Their Inheritances. In: Rojas, I., Joya, G., Català, A. (eds) Advances in Computational Intelligence. IWANN 2021. Lecture Notes in Computer Science(), vol 12861. Springer, Cham. https://doi.org/10.1007/978-3-030-85030-2_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-85030-2_7

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-85029-6

  • Online ISBN: 978-3-030-85030-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics