Sign in to follow this  
asad_82

Formula for computing RMSE percentage

Recommended Posts

I want to find the percentage error from Root Mean Square Error (RMSE). What should be the correct formula for RMSE normalization so that I get correct percentage value.

Should I normalize RMSE with L2 norm of original data or the mean value of original data ?
[font="Calibri, sans-serif"] [/font]

Share this post


Link to post
Share on other sites
Dear Alvaro
Thanks for your reply.

I have one more question regarding the formula for RMS error when there are more than one entities involved.
Like I have 20 images and each image has 1000 pixels and three color channels so in this setting when computing the RMS error between the original and estimated points should I compute it as option A or option B in the formulas attached with this post.

The issue is whether I should compute the mean of all 20 images only or should I compute the mean of each image pixels first and then compute the final mean.

I later want to divide it by L2 norm of 20 images to get percentage error.
Which formula among these is correct ?

Share this post


Link to post
Share on other sites
[quote name='Asad' timestamp='1318411619' post='4871779']
The issue is whether I should compute the mean of all 20 images only or should I compute the mean of each image pixels first and then compute the final mean.

I later want to divide it by L2 norm of 20 images to get percentage error.
Which formula among these is correct ?
[/quote]

Those formulas are the same up to a constant, and that constant will cancel out when you divide by the L2 norm of the original data, as long as you use an analogous formula to compute the L2 norm.

Share this post


Link to post
Share on other sites
Dear Alvaro
Thanks for your reply.

Now I have attached the complete formula that I intend to use for finding the ratio with this post.
RMS as well as the L2 norm formula.

Which of the two options is practically correct options A or option B formula ?

Share this post


Link to post
Share on other sites
Neither. As I said, you need to use an analogous formula for the L2 norm. That means using the same constants, but it doesn't matter which. I personally don't use any of those constants, and simply compute the square root of the sum of the squares.

The way I think about this type of situation is that you are dealing with a Euclidean vector space of dimension (M*N*C). Your given data rho_org is a vector in that space and so is rho_estimated. You are computing the distance between them, and dividing by the length of rho_org.

Share this post


Link to post
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now

Sign in to follow this