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RMSE - Root mean square Error

Asked by Joe
on 27 Mar 2011
Latest activity Commented on by arun kumar on 26 Jul 2017

[EDIT: 20110610 00:17 CDT - reformat - WDR]

So i was looking online how to check the RMSE of a line. found many option, but I am stumble about something,

there is the formula to create the RMSE:

Dates - a Vector

Scores - a Vector

is this formula is the same as RMSE=sqrt(sum(Dates-Scores).^2)./Dates

or did I messed up with something?


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4 Answers

Answer by John D'Errico
on 10 Jun 2011
 Accepted Answer

Yes, it is different. The Root Mean Squared Error is exactly what it says.

(y - yhat)    % Errors
(y - yhat).^2   % Squared Error
mean((y - yhat).^2)   % Mean Squared Error
RMSE = sqrt(mean((y - yhat).^2));  % Root Mean Squared Error

What you have written is different, in that you have divided by dates, effectively normalizing the result. Also, there is no mean, only a sum. The difference is that a mean divides by the number of elements. It is an average.


Thus, you have written what could be described as a "normalized sum of the squared errors", but it is NOT an RMSE. Perhaps a Normalized SSE.


Dear John, your answer has helped many of us! I'm also struggling with RMSE and I want to calculate the minimum and maximum RMSE for each row of data. based on this example from Joe, would it make sense to use these functions for the calculation of the minimum and maximum value to have an idea about the rmse range?



To compute the range of an array (of any dimension), simply do this:

RMSE_min = min(RMSE(:));
RMSE_max = max(RMSE(:));
RMSE_range = RMSE_max - RMSE_min;

Dear image analyst, Thank you very much for your reply and help! You really helped me a lot!

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Answer by Image Analyst
on 9 Jan 2016

If you have the Image Processing Toolbox, you can use immse():

rmse = sqrt(immse(scores, dates));


Dear Analyst, could you please re-write this command for the matrix? I need to calculate the RMSE between every point. thank you

It will work with matrixed, no problem. Just pass in your two matrices:

err = immse(X,Y) calculates the mean-squared error (MSE) between the arrays X and Y. X and Y can be arrays of any dimension, but must be of the same size and class.

Thank you. Even i was having same doubt

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Answer by Yella on 10 Jun 2011

Root mean square error is difference of squares of output an input. Let say x is a 1xN input and y is a 1xN output. square error is like (y(i) - x(i))^2. Mean square error is 1/N(square error). and its obvious RMSE=sqrt(MSE).

ur code is right. But how r dates and scores related?

  1 Comment

RMSE= sqrt(MSE) = sqrt( 1/length(y)* sum( (y-yhat).^2  )) = sqrt( mean(y-yhat).^2 )

However, he divided after the square root.

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Answer by ziad zaid on 4 Jun 2017

How to apply RMSE formula to measure differences between filters to remove noisy pictures such a median , mean and weiner fiters ? how can i get the result or how to apply it . Rgards .

  1 Comment

Just do it like my code says. Compare each of your results with the original noisy image. Whichever had the higher RMSE had the most noise smoothing because it's most different from the noisy original..

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