Loading...

Multivariate Mutual Information via Secret-key Agreement

Mostafa Zadflah Chobari, Mohammad | 2020

448 Viewed
  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 53611 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Ebrahimi, Javad
  7. Abstract:
  8. Shannon (1948) for the first time defined the "mutual information'' parameter for two random variables, but still there is no common definition for multivariate mutual information has been agreed upon, despite the multitude of research on the subject and various proposed definitions. In 2015, a study suggested that the maximum rate of secret-key, in the secret-key agreement problem, is a suitable candidate for defining multivariate mutual information. Csiszár and Narayan's research on the secret-key agreement problem provides an accessible bound for the maximum rate of secret-key rate, which in the bivariate case is the shannon's mutual information. The proposed definition has all expected properties compared to other similar defined quantities. This definition also offers a new perspective on the problem of tree packing; This means that calculation of the strength of graph and calculation of the multivariate mutual information have the same answer. In addition, the most refined partition that represents the optimal answer to this definition provides a clustering of data in which the data in each cluster are most semantically related and each cluster is least semantically related to the other clusters. In this thesis, the mentioned researches are studied and a comprehensive conclusion on the matter is presented
  9. Keywords:
  10. Information Theory ; Secret Key Agreement ; Submodular Optimization ; Dilworth Truncation ; Fundamental Partition ; Multivariate Mutual Information ; Shannon’s Mutual Information ; Partitions Lattices

 Digital Object List