Preprocessing Data with Scale and then Binarize in Python

I am working on some proof of concepts for ML and want to try an unusual scaling method. I would like to group my data and then "scale" it and apply a binarize to that data. Basically I want all data above the mean to be 1 and below to be 0.

I can get the scale to work but the binarize needs a reshape and I want to do them all in groupby step.

    import pandas as pd
    from sklearn import preprocessing


    df = pd.DataFrame({'group': ['A', 'A', 'A', 'B','B', 'B'],
                        'column_to_scale': [4, 2, 6, 4, 9, 6]})
    print(df)
    df['column_to_scale'] = df.groupby("group")['column_to_scale'].transform(lambda x: preprocessing.scale(x))
    print(df)

I expect the output to look like:

# inital
  group  column_to_scale
0     A                4
1     A                2
2     A                6
3     B                4
4     B                9
5     B                6

# preprocessing.scale()
  group  column_to_scale
0     A         0.000000
1     A        -1.224745
2     A         1.224745
3     B        -1.135550
4     B         1.297771
5     B        -0.162221

# preprocessing.binarize()
  group  column_to_scale
0     A         0
1     A         0
2     A         1
3     B         0
4     B         1
5     B         0