I have a covariance matrix and a set of another covariance matrices. I need some similarity measure which chooses the most similar cov. matrix to the current one.
If you have any suggestions, please write me.
Thanks!
This is a good question with many different paths to follow in looking for answers.
A test statistic in the complex Wishart distribution is used to test the equality of covariance matrices in
J. Schou, H. Skriver, A.A. Nielson, K. Conradsen, CFAR edge detector for polarimetric SAR images, IEEE Trans. on Geoscience and Remote Sensing 41(1), 2003:
file:///Users/jfpeters/Downloads/imm1224.pdf
Other papers by J. Schou, Technical University of Denmark are available on RG.
More to the point, in comparing covariance matrices, the Riemannian metric corresponding to the manifold inhabited by covariance matrices as well as the Jensen-Bregman logdet divergence similarity measure, are considered in
A. Cherian, S. Sra, A. Banerjee, N. Papanikolopoulos, Efficient similarity search for covariance matrices via the Jensen-Bregman logdet divergence:
http://suvrit.de/work/iccv11.pdf
The Jensen-Bregman logdet divergence similarity measure is introduced in Section 2 (see equation (3), also Theorem 1 (bounds)).
This is a good question with many different paths to follow in looking for answers.
A test statistic in the complex Wishart distribution is used to test the equality of covariance matrices in
J. Schou, H. Skriver, A.A. Nielson, K. Conradsen, CFAR edge detector for polarimetric SAR images, IEEE Trans. on Geoscience and Remote Sensing 41(1), 2003:
file:///Users/jfpeters/Downloads/imm1224.pdf
Other papers by J. Schou, Technical University of Denmark are available on RG.
More to the point, in comparing covariance matrices, the Riemannian metric corresponding to the manifold inhabited by covariance matrices as well as the Jensen-Bregman logdet divergence similarity measure, are considered in
A. Cherian, S. Sra, A. Banerjee, N. Papanikolopoulos, Efficient similarity search for covariance matrices via the Jensen-Bregman logdet divergence:
http://suvrit.de/work/iccv11.pdf
The Jensen-Bregman logdet divergence similarity measure is introduced in Section 2 (see equation (3), also Theorem 1 (bounds)).
there is a most complete discussion of this subject in the book
Skelton, Iwasaki, Grigoriadis "A Unified Algebraic Approach to Control Design"
Taylor and Francis, 1998
This book describes all covariance matrices that can be assigned to a dynamic system bu a feedback control law, but the discussions are not only about control.
You may consider looking at articles that determine the closest positive definite matrix to a positive semi definite matrix. There are various metrics that are required to accomplish this.
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