How to standard scale a 3D matrix?

An elegant way of doing this is using class Inheritance as follows:

from sklearn.preprocessing import MinMaxScaler
import numpy as np

class MinMaxScaler3D(MinMaxScaler):

    def fit_transform(self, X, y=None):
        x = np.reshape(X, newshape=(X.shape[0]*X.shape[1], X.shape[2]))
        return np.reshape(super().fit_transform(x, y=y), newshape=X.shape)

Usage:

scaler = MinMaxScaler3D()
X = scaler.fit_transform(X)

With only 3 line of code...

scaler = StandardScaler()
X_train = scaler.fit_transform(X_train.reshape(-1, X_train.shape[-1])).reshape(X_train.shape)
X_test = scaler.transform(X_test.reshape(-1, X_test.shape[-1])).reshape(X_test.shape)

If you want to scale each feature differently, like StandardScaler does, you can use this:

import numpy as np
from sklearn.base import TransformerMixin
from sklearn.preprocessing import StandardScaler


class NDStandardScaler(TransformerMixin):
    def __init__(self, **kwargs):
        self._scaler = StandardScaler(copy=True, **kwargs)
        self._orig_shape = None

    def fit(self, X, **kwargs):
        X = np.array(X)
        # Save the original shape to reshape the flattened X later
        # back to its original shape
        if len(X.shape) > 1:
            self._orig_shape = X.shape[1:]
        X = self._flatten(X)
        self._scaler.fit(X, **kwargs)
        return self

    def transform(self, X, **kwargs):
        X = np.array(X)
        X = self._flatten(X)
        X = self._scaler.transform(X, **kwargs)
        X = self._reshape(X)
        return X

    def _flatten(self, X):
        # Reshape X to <= 2 dimensions
        if len(X.shape) > 2:
            n_dims = np.prod(self._orig_shape)
            X = X.reshape(-1, n_dims)
        return X

    def _reshape(self, X):
        # Reshape X back to it's original shape
        if len(X.shape) >= 2:
            X = X.reshape(-1, *self._orig_shape)
        return X

It simply flattens the features of the input before giving it to sklearn's StandardScaler. Then, it reshapes them back. The usage is the same as for the StandardScaler:

data = [[[0, 1], [2, 3]], [[1, 5], [2, 9]]]
scaler = NDStandardScaler()
print(scaler.fit_transform(data))

prints

[[[-1. -1.]
  [ 0. -1.]]

 [[ 1.  1.]
  [ 0.  1.]]]

The arguments with_mean and with_std are directly passed to StandardScaler and thus work as expected. copy=False won't work, since the reshaping does not happen inplace. For 2-D inputs, the NDStandardScaler works like the StandardScaler:

data = [[0, 0], [0, 0], [1, 1], [1, 1]]
scaler = NDStandardScaler()
scaler.fit(data)
print(scaler.transform(data))
print(scaler.transform([[2, 2]]))

prints

[[-1. -1.]
 [-1. -1.]
 [ 1.  1.]
 [ 1.  1.]]
[[3. 3.]]

just like in the sklearn example for StandardScaler.

You'll have to fit and store a scaler for each channel

from sklearn.preprocessing import StandardScaler

scalers = {}
for i in range(X_train.shape[1]):
    scalers[i] = StandardScaler()
    X_train[:, i, :] = scalers[i].fit_transform(X_train[:, i, :]) 

for i in range(X_test.shape[1]):
    X_test[:, i, :] = scalers[i].transform(X_test[:, i, :])