MHB What does the notation $||A-B||_{2,a}$ represent in terms of matrix norms?

[OhMyMarkov]

Hello everyone!

I came across, in a reading, an unfamiliar norm notation: $||A-B||_{2,a}$ where $a$ is the standard deviation of a Gaussian kernel. Now I know that the index 2 represents the $\ell _2$ norm, but what about the $a$?

Moreover, is the matrix norm defnied in a similar way to the vector norm?Any help is apptreciated!

 

[Sudharaka]

Hello everyone!

I came across, in a reading, an unfamiliar norm notation: $||A-B||_{2,a}$ where $a$ is the standard deviation of a Gaussian kernel. Now I know that the index 2 represents the $\ell _2$ norm, but what about the $a$?

Moreover, is the matrix norm defnied in a similar way to the vector norm?Any help is apptreciated!

Hi OhMyMarkov, :)

The definition of the matrix norm and the notation you are taking about are explained here.

Kind Regards,
Sudharaka.

 

[OhMyMarkov]

Thank you, Sudharaka,

I may need to point this out in case someone else comes across it in the future: this notation means the Element-wise (or Frobenius I guess) norm of the 2D-convolution of A with a Gaussian kernel of standard deviation a.