Interpreting the output of a neural network I've implemented a neural network for prediction, and for the input data, I've used the following formula to normalize data: 
Data_normalized_i= [Data_i - Min_data]/[Max_Data- Min_data]

I've some questions:


*

*How do I interpret the output of my network according to my inputs?

*Must I use the real data input to compare it with my outputs?

*If I have to do some transformation of my outputs, how should I go about doing it?  For the test error in this case, will be it calculated from the output or from the transformed outputs?

 A: What the output of your neurons can be depends on the objective function you use and the activation function for the output neurons. For example, if you use sum of squared errors (regression), then one can prove that the output of the network is conditional average of the target data conditioned on the input. With equations,
$$y_{k}\left(\mathbf{x},\mathbf{w}\right) = \int t_{k} p(t_{k}|\mathbf{x})dt_{k}$$
where $k$ is the indicator for the neuron, $x$ is the input vector, $t$ is the target vector and $y(x,w)$ is the mapping carried out by the network.
If you use the cross entropy error function with sigmoidal output units (classification), then the output of each neuron is the probability that the sample corresponds to the class encoded by the neuron. A brief discussion and derivation of this result can be found here.
Try to get a copy of the book for a detailed description. It's a great book and you will learn a lot.
That said, how you transform your outputs (if it makes sense) depends on what you are doing and how those outputs are to be understood. You don't explain that in your question
A: If you are doing binary classification, then after applying sigmoid activation function, you receive probabilities of belonging to the classes.
If you are doing multi-class classification, you'd better use softmax.
But if you are building a regression model, you shouldn't apply activation functions to the output layer.
A: You haven't specified 'what' your output or target variable is. A neural network is a supervised learner and requires input and output data to train.
So, in order of questions:
1) The output will be the response or target based upon the output it is trained on.    
2) It would probably make sense to undue any transformations after the NN returns results, in order to make them more understandable.   
3) It depends on what the outputs are. The error will be a result corresponding to the method you use to pre-process and transform data and the loss function you use (which is usually something like rmse between prediction and actual).
