multiple training data for cascade-forward backpropagation network

Question

I am training my neural network with data from 3 consecutive days and testing it with data from a 4th day. The values in this example are randomly chosen and have no relation with reality. I want the neural network to learn the current, depending on the temperature and the solar radiation.

%% initialize data for training
Temperature_Day1 = [25 26 27 26 25];
Temperature_Day2 = [25 24 24 23 24];
Temperature_Day3 = [21 20 22 21 20];
SolarRadiation_Day1 = [990 944 970 999 962];
SolarRadiation_Day2 = [993 947 973 996 967];
SolarRadiation_Day3 = [993 948 973 998 965];
Current_Day1 = [0.11 0.44 0.44 0.45 0.56];
Current_Day2 = [0.41 0.34 0.43 0.55 0.75];
Current_Day3 = [0.34 0.98 0.34 0.76 0.71];
Day1 = [Temperature_Day1; SolarRadiation_Day1]; % 2-by-5
Day2 = [Temperature_Day2; SolarRadiation_Day2]; % 2-by-5
Day3 = [Temperature_Day3; SolarRadiation_Day3]; % 2-by-5

%% training input and training target
Training_Input = [Day1; Day2; Day3]; % 6-by-5
Training_Target = [Current_Day1; Current_Day2; Current_Day3]; % 3-by-5

%% training the network
hiddenLayers= 2;
net = newcf(Training_Input, Training_Target, hiddenLayers);
y = sim(net, Training_Input);
net.trainParam.epochs = 100;
net = train(net, Training_Input, Training_Target);

%% initialize data for prediction
Temperature_Day4 = [45 23 22 11 24];
SolarRadiation_Day4 = [960 984 980 993 967];
Current_Day4 = [0.14 0.48 0.37 0.46 0.77];
Day4 = [Temperature_Day4; SolarRadiation_Day4]; % 2-by-5
Test_Input = [Day4; Day4; Day4]; % same dimension as Training_Input; subject to question

%% prediction
Predicted_Target = sim(net, Test_Input); % yields 3-by-5

My question is: How do I train it with the data of 3 days and then predict the target of the 4th day? Since training and testing inputs must have the same dimension, how do I test it for only one day? Here it is solved by just concatenating three identical data sets of the test input. However, this also yields 3 different data sets for the predicted target.

What is here the right way to do it?

BTW: I have seen this type of question many times, but the answers are never satisfying because they always suggest to change the dimensions of the test input without considering the nature of the problem (which is that only one data set is available for testing). So please don't mark this as a duplicate.

Answer 1

The features that you have for your network are Temperature and SolarRadiation, each taken at specific times during the day. The day on which these readings are taken are irrelevant (otherwise you wouldn't be able to predict the outputs for day 4 given data for days 1-3).

This means that we can simply pass each observation separately by concatenating the days horizontally (and similarly for the target data):

Training_Input = [Day1, Day2, Day3]; % 2-by-15
Training_Target = [Current_Day1, Current_Day2, Current_Day3]; % 1-by-15

The resulting network will give you one output (Current) per observation in the test set, so you don't need to duplicate:

Day4 = [Temperature_Day4; SolarRadiation_Day4]; % 2-by-5
Test_Input = [Day4]; % 2-by-5

PredictedTarget will now be 1-by-5 showing the predicted Current for each of the test observations.

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You might consider adding a third feature as input to your net representing the time at which each observations was taken. Assuming that you have t timeslots each day at which observations are taken (thus, length(Temperature) == length(SolarRadiation) == t for all days) and observation s is taken at the same time every day, you can add a feature called TimeSlot:

TimeSlot_Day1 = 1:numel(Temperature_Day1);
TimeSlot_Day2 = 1:numel(Temperature_Day2);
TimeSlot_Day3 = 1:numel(Temperature_Day3)];
Day1 = [Temperature_Day1; SolarRadiation_Day1; TimeSlot_Day1]; % 3-by-5
Day2 = [Temperature_Day2; SolarRadiation_Day2; TimeSlot_Day2]; % 3-by-5
Day3 = [Temperature_Day3; SolarRadiation_Day3; TimeSlot_Day3]; % 3-by-5