Scale Operator

This IKATS operator implements a scaling (also called normalization).

Input and parameters

This operator only takes one input of the functional type ts_list.

It also takes an optional parameter from the user:

• scaler: The scaler used to normalize the data

  • Z-Norm: Center and scale data: result = (X - mean) / correct_std, where correct_std = sqrt(1/(N-1) sum(x - mean)^2)
  • MinMax: Scale values between 0 and 1: result = (X - min) / (max - min). If min = max (constant TS), result = max / 2
  • MaxAbs: Scale TS by its maximum absolute value: result = X / max( abs(X.max), abs(X.min) )

Outputs

The operator has one output:

• TS list: The resulting list of time series

Warnings

• In case of Z-Norm usage, the correct_std used corresponds to the corrected sample standard deviation, which is computed as the square root of the unbiased sample variance (where the denominator is number of observations - 1). More precisely, it's an un-biased estimation of the standard deviation. It differs than the "classic" population standard deviation. These two standard deviations are the same for large dataset.

Implementation remarks: Z-Norm

The Spark implementation of Z-Norm differs from sklearn. Spark behaviour: Use the corrected sample standard deviation. See this doc for more details about implementation. Sklearn behaviour: Use the "classic" population standard deviation. See this doc for more details about implementation) Operator implementation: Use the Spark's behaviour: (X - mean) / correct_std, where correct_std = sqrt(1/(N**-1**) * sum(X-mean)^2). A coefficient (sqrt(N-1/N)) is applied to correct the calculation, in case of sklearn usage.