Data/Feature normalization

Question

I've a set of features within the interval (-1,1). I'm looking for a bijective function or a procedure to normalize the data to a certain range with a mean close to 0 and a variance close to 1.

It's very import that the function is bijective since I need the features normalized as input for a neutral network with tanh activation function. My process would be to in-memory transform the data, feed them to the net and to transform the network result back to the initial scale.

Community · Accepted Answer · 2017-05-23 10:29:18Z

2

This normalization task is quite usual in neural network aplications. The most common approach is to simply compute the mean and the standard deviation of your data and store that values in your training program. So the pipeline for your data is then:

Compute mean and sd of your input data and store it in memory.
Apply normalizing transformation : normed_data = (data - mean) / sd.
Train / evaluate / use the network.
Denormalize data using : original_data = (normed_data * sd) + mean.

I wrote a longer post on data normalization. You may read it here.

edited May 23, 2017 at 10:29

CommunityBot

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answered Jul 27, 2016 at 9:11

Marcin Możejko

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2 Comments

Bastian Over a year ago

Thank you for your answer. I just realized transformation function Phi can be applied in this case as well. Before, I just knew that it is used to transform, standardize normal distributed data to use the normal distribution tables.

Bastian Over a year ago

You said in your post that it is necessary to calculate the mean and std. deviation for the Ys, the outputs, as well. Could you please explain the reason? Let's consider following example: A sample is a set S of random numbers of a specific interval (x0,x1). The input xi and also the target yj is always a subset of S. The inputs are chosen by a sequence from n to m-1 and the target is m. Does the separate calculation of the mean and std. deviation apply in this chase as well?

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