Normalizing a complex dataset

Question

I am currently working with a dataset which has complex values. I need to normalize it such that I can use $\tanh$ as activation function, which is within $-1$ to $1$. But how can we normalize complex values?.. The normalizing should not remove the complex part, but also be normalized.

Answer 1

To clarify: The problem is that the output layer he wants to use has tanh as activation function and the complex numbers are the labels are complex numbers.

The solution is simple: Split the real and the imaginary part and use the neural network for regression on $\mathbb{R}^2$ instead of $\mathbb{C}$.

The normalization is simple:

1. Subtract the mean value
2. Divide by the range of the values
3. Multiply with 2

However, if your range is not limited you should think about removing the tanh activation function.

You might also be interested in this answer to regression with neural networks.