In case of multiple output in ANN ,what does R value represent?

I have 4 inputs and 3 outputs , I am getting only one regression (R-value) , how this is calculated out of 3 outputs?

Answer 1

[Aiswarya]

Hi Sunita,

I understand that you want to know how R is calculated for a multiple output ANN(Artificial Neural Network). The formula for calculating the R value is provided in the following documentation:

https://www.mathworks.com/help/stats/coefficient-of-determination-r-squared.html

The R value for multiple outputs can be calculated as follows (where y_predicted and y_actual will be matrices):

% Sum of squared errors
SSE = sum((y_predicted - y_actual).^2,"all")
% Total sum of squares
SST = sum((y_actual - mean(y_actual)).^2,"all");
% Normalized Mean Square Error
NMSE = SSE/SST
% R squared
Rsquared = 1 - NMSE

You may also refer to this MATLAB answer for MSE calculation for multiple output neural network :

https://www.mathworks.com/matlabcentral/answers/405606-how-to-calculate-the-mse-for-multi-output-neural-network?s_tid=answers_rc1-2_p2_MLT

[Sunita]

Thank you for your response. I'm curious about the R-value displayed when there are three predicted outputs (columns 1, 2, and 3). does the R-value shown correspond to column 1, 2, or 3?

[Aiswarya]

It basically represents the cumulative of all three predicted outputs, as mentioned in the sum (SSE and SST), the 'all' term refers to summing up across all dimensions (considering the 3 outputs as different dimensions). So, as answer to your question it represents all the output columns.