Preprocess multi-sample time series data: encode each sample separately or in aggregate?

Question

Let's say I have 3 dense sequences of uniform length. Should I fit a scaler on them separately or together?

import numpy as np
from sklearn.preprocessing import StandardScaler

arr = np.array([
    [
        [1.1],[2.2],[3.3]
    ],
    [
        [1.2],[2.3],[3.4]
    ],
    [
        [4.0],[5.0],[6.0]
    ]
])

SS = StandardScaler()

Separately:

SS.fit_transform(arr[0])
SS.fit_transform(arr[1])
SS.fit_transform(arr[2])

Or together?

tall_2d = np.concatenate((arr[0],arr[1],arr[2]))
SS.fit(tall_2d)

SS.transform(arr[0])
SS.transform(arr[1])
SS.transform(arr[2])

I suppose I would be performing interpolation on each sequence separately, so should I encode and detect outliers separately too?

Answer 1

After getting hands on with the data, it feels ridiculous not to fit on all samples in the split/fold.

• In 2D data 'sample==row'. You don't fit on a single sample.
• In 3D data 'sample==sequence' so you encode on all of the sequences.

This also means less encoders to keep track of for the sake of inverse transform and inference encoding.