In [1]:

    

import numpy as np
import scipy.stats
from sklearn import preprocessing


    

In [2]:

    

a = np.array([0, 1, 2, 3, 4])
print(a)


    

    




[0 1 2 3 4]

In [3]:

    

print((a - a.min()) / (a.max() - a.min()))


    

    




[0.   0.25 0.5  0.75 1.  ]

In [4]:

    

print((a - a.mean()) / a.std())


    

    




[-1.41421356 -0.70710678  0.          0.70710678  1.41421356]

In [5]:

    

print((a - a.mean()) / a.std(ddof=1))


    

    




[-1.26491106 -0.63245553  0.          0.63245553  1.26491106]

In [6]:

    

a_2d = np.array([[0, 1, 2], [3, 4, 5], [6, 7, 8]])
print(a_2d)


    

    




[[0 1 2]
 [3 4 5]
 [6 7 8]]

In [7]:

    

def min_max(x, axis=None):
    x_min = x.min(axis=axis, keepdims=True)
    x_max = x.max(axis=axis, keepdims=True)
    return (x - x_min) / (x_max - x_min)


    

In [8]:

    

print(min_max(a_2d))


    

    




[[0.    0.125 0.25 ]
 [0.375 0.5   0.625]
 [0.75  0.875 1.   ]]

In [9]:

    

print(min_max(a_2d, axis=0))


    

    




[[0.  0.  0. ]
 [0.5 0.5 0.5]
 [1.  1.  1. ]]

In [10]:

    

print(min_max(a_2d, axis=1))


    

    




[[0.  0.5 1. ]
 [0.  0.5 1. ]
 [0.  0.5 1. ]]

In [11]:

    

print(min_max(a))


    

    




[0.   0.25 0.5  0.75 1.  ]

In [12]:

    

def standardization(x, axis=None, ddof=0):
    x_mean = x.mean(axis=axis, keepdims=True)
    x_std = x.std(axis=axis, keepdims=True, ddof=ddof)
    return (x - x_mean) / x_std


    

In [13]:

    

print(standardization(a_2d))


    

    




[[-1.54919334 -1.161895   -0.77459667]
 [-0.38729833  0.          0.38729833]
 [ 0.77459667  1.161895    1.54919334]]

In [14]:

    

print(standardization(a_2d, ddof=1))


    

    




[[-1.46059349 -1.09544512 -0.73029674]
 [-0.36514837  0.          0.36514837]
 [ 0.73029674  1.09544512  1.46059349]]

In [15]:

    

print(standardization(a_2d, axis=0))


    

    




[[-1.22474487 -1.22474487 -1.22474487]
 [ 0.          0.          0.        ]
 [ 1.22474487  1.22474487  1.22474487]]

In [16]:

    

print(standardization(a_2d, axis=0, ddof=1))


    

    




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

In [17]:

    

print(standardization(a_2d, axis=1))


    

    




[[-1.22474487  0.          1.22474487]
 [-1.22474487  0.          1.22474487]
 [-1.22474487  0.          1.22474487]]

In [18]:

    

print(standardization(a_2d, axis=1, ddof=1))


    

    




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

In [19]:

    

print(standardization(a))


    

    




[-1.41421356 -0.70710678  0.          0.70710678  1.41421356]

In [20]:

    

print(standardization(a, ddof=1))


    

    




[-1.26491106 -0.63245553  0.          0.63245553  1.26491106]

In [21]:

    

print(scipy.stats.zscore(a))


    

    




[-1.41421356 -0.70710678  0.          0.70710678  1.41421356]

In [22]:

    

print(scipy.stats.zscore(a_2d))


    

    




[[-1.22474487 -1.22474487 -1.22474487]
 [ 0.          0.          0.        ]
 [ 1.22474487  1.22474487  1.22474487]]

In [23]:

    

print(scipy.stats.zscore(a_2d, axis=None, ddof=1))


    

    




[[-1.46059349 -1.09544512 -0.73029674]
 [-0.36514837  0.          0.36514837]
 [ 0.73029674  1.09544512  1.46059349]]

In [24]:

    

mm = preprocessing.MinMaxScaler()


    

In [25]:

    

print(mm.fit_transform(a_2d.astype(float)))


    

    




[[0.  0.  0. ]
 [0.5 0.5 0.5]
 [1.  1.  1. ]]

In [26]:

    

print(preprocessing.minmax_scale(a.astype(float)))


    

    




[0.   0.25 0.5  0.75 1.  ]

In [27]:

    

print(preprocessing.minmax_scale(a_2d.astype(float), axis=1))


    

    




[[0.  0.5 1. ]
 [0.  0.5 1. ]
 [0.  0.5 1. ]]

In [28]:

    

ss = preprocessing.StandardScaler()


    

In [29]:

    

print(ss.fit_transform(a_2d.astype(float)))


    

    




[[-1.22474487 -1.22474487 -1.22474487]
 [ 0.          0.          0.        ]
 [ 1.22474487  1.22474487  1.22474487]]

In [30]:

    

print(preprocessing.scale(a.astype(float)))


    

    




[-1.41421356 -0.70710678  0.          0.70710678  1.41421356]

In [31]:

    

print(preprocessing.scale(a_2d.astype(float), axis=1))


    

    




[[-1.22474487  0.          1.22474487]
 [-1.22474487  0.          1.22474487]
 [-1.22474487  0.          1.22474487]]