[ENH] Add global scalers for time series pre-treatment

[melpiro]

Reference Issues/PRs

#3792

What does this implement/fix? Explain your changes.

Implement global versions of Centerer, MinMaxScaler, and Normalizer :

• GlobalCenterer: Transform a collection of time series so that the mean of the collection is equal to zero
• GlobalMinMaxScaler : Transform a collection of time series so that the minimal value and the maximal value of the collection are respectively zero and one.
• GlobalNormalizer: Transform a collection of time series so that the mean and the standard deviation of the collection are respectively zero and one.

Does your contribution introduce a new dependency? If yes, which one?

No

Any other comments?

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[TonyBagnall]

Thanks for this, I agree its a useful thing to add in. I have one issue with the unequal-length normalisation: this calculates the standard deviation of the individual series' standard deviations, rather than the pooled standard deviation of all observations.

For example, if X = [np.array([[0, 2]]), np.array([[10, 12]])], both series have std 1, so the current calculation returns zero, whereas the pooled std is approximately 5.099.

Im not sure how this should work, but I think, given its global, a pooled mean and variance per channel would be right? Happy to discuss

[melpiro]

Hello, thank you for taking the time to review my code.
Yes, you are right; the previous implementation for unequal-length time series was wrong and has now been fixed.

I took the opportunity to improve the generalisation of global scalers by adding an axis parameter, allowing to use the scaler on any numpy.array like :

• [sample, channel, time] axis = 2 | default with 3D
• [sample, time, channel] axis = 1
• list[(channels, time)] unequal lenght collection
• [sample, time] default case with 2D (univariate collection)
• [channels, time] axis = 1 (multivariate serie) useful for forecasting
• [time, channels] axis = 0 (multivariate serie) useful for forecasting

To go further, the code is in reality, able to run on any NumPy array dimensionality. Even if it makes poor sense for time series, I found interesting to test my scalers with 1D numpy array and 4D NumPy array to check that they are able to generalise correctly. In theory, it could even be used with any higher dimensionality.

From there, very weird scenarios with the following input shape could be imagined :

• 1D array of shape [time] (univariate serie)
• Collections of videos: [sample, x, y, time] axis=3 | default with 4D
• Even with two time axes?? [sample, channels, time1, time2] axis=(2, 3)

In short, it turns out to be useless but shows robustness and was fun to see that it works on unusual inputs.