Eigengap

In linear algebra, the eigengap of a linear operator is the difference between two successive eigenvalues, where eigenvalues are sorted in ascending order.

The Davis–Kahan theorem, named after Chandler Davis and William Kahan, uses the eigengap to show how eigenspaces of an operator change under perturbation.[1] Essentially, a larger eigengap indicates that the corresponding eigenvectors are more robust and less sensitive to small changes or noise in the data.

In spectral clustering, the eigengap is often referred to as the spectral gap; although the spectral gap may often be defined in a broader sense than that of the eigengap. In this context, a significant jump or gap between successive eigenvalues often suggests a natural division in the underlying data structure, helping to determine the ideal number of clusters.

See also

References

  1. ^ Davis, C.; W. M. Kahan (March 1970). "The rotation of eigenvectors by a perturbation. III". SIAM J. Numer. Anal. 7 (1): 1–46. Bibcode:1970SJNA....7....1D. doi:10.1137/0707001.
Stub icon

This linear algebra-related article is a stub. You can help Wikipedia by adding missing information.

Content Disclaimer

Informasi ini disarikan dari Wikipedia dan disajikan kembali untuk tujuan edukasi. Konten tersedia di bawah lisensi CC BY-SA 3.0. Kami tidak bertanggung jawab atas ketidakakuratan data yang bersumber dari kontribusi publik tersebut.

  1. The information displayed on this website is sourced in part or in whole from Wikipedia and has been adapted for the purpose of restating it. We strive to provide accurate and relevant information, however:
  2. There is no guarantee of absolute accuracy. Wikipedia is an open, collaborative project that can be edited by anyone, so information is subject to change.
  3. It is not intended to constitute professional advice. The content displayed is for informational and educational purposes only. For important decisions (e.g., medical, legal, or financial), please consult a professional.
  4. Content copyright. Wikipedia is licensed under the Creative Commons Attribution-ShareAlike License (CC BY-SA). This means that content may be reused with appropriate attribution and shared under a similar license.
  5. Responsible use. Any risk arising from the use of information from this website is entirely the responsibility of the user.