How do I standardize a matrix?

Question

Basically, take a matrix and change it so that its mean is equal to 0 and variance is 1. I\'m using numpy\'s arrays so if it can already do it it\'s better, but I can implem

Answer 1

from sklearn.preprocessing import StandardScaler

standardized_data = StandardScaler().fit_transform(your_data)

Example:

>>> import numpy as np
>>> from sklearn.preprocessing import StandardScaler

>>> data = np.random.randint(25, size=(4, 4))
>>> data
array([[17, 12,  4, 17],
       [ 1, 16, 19,  1],
       [ 7,  8, 10,  4],
       [22,  4,  2,  8]])

>>> standardized_data = StandardScaler().fit_transform(data)
>>> standardized_data
array([[ 0.63812398,  0.4472136 , -0.718646  ,  1.57786412],
       [-1.30663482,  1.34164079,  1.55076242, -1.07959124],
       [-0.57735027, -0.4472136 ,  0.18911737, -0.58131836],
       [ 1.24586111, -1.34164079, -1.02123379,  0.08304548]])

Works well on large datasets.

Answer 2

import scipy.stats as ss

A = np.array(ss.zscore(A))

Answer 3

Use sklearn.preprocessing.scale.

http://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.scale.html

Here is an example.

>>> from sklearn import preprocessing
>>> import numpy as np
>>> X_train = np.array([[ 1., -1.,  2.],
...                     [ 2.,  0.,  0.],
...                     [ 0.,  1., -1.]])
>>> X_scaled = preprocessing.scale(X_train)
>>> X_scaled
array([[ 0.  ..., -1.22...,  1.33...],
       [ 1.22...,  0.  ..., -0.26...],
       [-1.22...,  1.22..., -1.06...]])

http://scikit-learn.org/stable/modules/preprocessing.html#standardization-or-mean-removal-and-variance-scaling

Answer 4

import numpy as np

A = np.array([[1,2,6], [3000,1000,2000]]).T  

A_means = np.mean(A, axis=0)
A_centr = A - A_means
A_norms = np.linalg.norm(A_centr, axis=0)

A_std = A_centr / A_norms

Answer 5

The following subtracts the mean of A from each element (the new mean is 0), then normalizes the result by the standard deviation.

import numpy as np
A = (A - np.mean(A)) / np.std(A)

The above is for standardizing the entire matrix as a whole, If A has many dimensions and you want to standardize each column individually, specify the axis:

import numpy as np
A = (A - np.mean(A, axis=0)) / np.std(A, axis=0)

Always verify by hand what these one-liners are doing before integrating them into your code. A simple change in orientation or dimension can drastically change (silently) what operations numpy performs on them.